disturbance estimator based output feedback exponential stabilization for euler bernoulli beam equation with boundary control in this paper we are concerned with the output feedback exponential stabilization problem for a system plant described by a one dimensional euler bernoulli beam equation the measurements are only the displacement and the angular velocity at the right end an infinite dimensional estimator is designed to estimate the disturbance with the estimated disturbance we propose a state observer that is exponentially convergent to the original system then design two different kinds of stabilizing controllers one is based on the velocity feedback the other is based on the angular velocity feedback in both cases by adopting the riesz basis approach the exponential stability of the closed loop systems is built with guaranteeing that all internal systems are uniformly bounded the numerical experiments are carried out to illustrate the theoretical results

transversal waves in beams via the network simulation method abstract in this paper the network simulation method nsm is proposed as a tool for solving the transverse motion of thin beams resulting from a bending action the reliability and robustness of the proposed technique is demonstrated with two examples in which a pinned pinned beam and a clamped mass load beam are respectively submitted to different flexural forces the nsm is a numerical technique for the solution of linear and non linear problems which are defined by a mathematical model assuming that the electrical variables of voltage and current are equivalent respectively to the displacement and the spatial variation of the displacement a network model for each volume element is designed such that electrical equations are formally equivalent to the spatial discretised equations of the mechanical model the whole network model including the devices associated with the boundary conditions is solved by the numerical computer code pspice the numerical results have been compared with those obtained by the mode superposition method the agreement between them is impressive the temporal behaviour of each quantity involved in the problem is obtained without transform complications since the whole study has been conducted in the time domain with the possibility of obtaining the corresponding spectral content at the end of calculation the main contribution of the present paper therefore is to employ the nsm numerical method in order to arrive at solutions in the time domain of dynamic mechanical problems one must also emphasize that nsm has not previously been used by other authors to solve physical problems like the ones presented here

optimal harvesting of diffusive models in a nonhomogeneous environment abstract we study the optimal harvesting strategy for populations whose dynamics is described by reaction diffusion equations the production function can be of logistic gilpin ayala or gompertz type the diffusion structure is discussed we suggest to consider u k where k is the carrying capacity of the environment rather than u and study optimal harvesting for models with this diffusion type maximum yield is investigated for both continuous and impulsive models for continuous harvesting the optimal policy is obtained for the impulsive equation some limit cases are considered the paper also outlines a variety of open problems

dynamics of timoshenko beam on linear and nonlinear foundation phase relations significance of the second spectrum stability abstract some controversial and unclear issues in the timoshenko beam tb theory are analyzed with emphasis on features of two branches of frequencies taking into account the elastic foundation creates additional opportunities for comparative analysis of both the branches relationship between the second branch modes and so called thickness shear mode is discussed phase relations between the deformation and force factors in beam for both the branches are established which generalize the previously established relations it is shown that the elastic foundation can change these relations for the first branch based on this analysis the significance of the second spectrum is assessed and peculiarities of dispersion relations for frequency phase and group velocities are explained free transverse waves in infinitely long beam on nonlinear cubic foundation are studied using the multiple scales method the obtained nonlinear schrodinger equation enables us to check stability of the harmonic waves in infinite beam and to determine diapasons of their modulational instability

exponential stability for a class of boundary conditions on a euler bernoulli beam subject to disturbances via boundary control abstract this paper outlines the procedure for applying a sliding mode backstepping boundary control technique to a euler bernoulli beam subject to unknown bounded disturbances on the boundary for four different types of boundary conditions referred to in this paper as a class of boundary conditions these boundary conditions include all combinations of pinned and sliding types with control and disturbances on one boundary i e pinned pinned pinned sliding sliding pinned and sliding sliding with input on the second boundary the technique was developed for the specific case of a pinned pinned beam in the literature and in this paper the technique is generalized to the degree that it is possible to cover all four of the aforementioned cases furthermore a proof of the fully arbitrary exponential stability of the closed loop system is provided in this paper to this point only asymptotic stability was shown for the closed loop system for one case the technique outlined in this paper provides for a class of boundary conditions a controller that exponentially stabilizes the vibrations in a beam in the presence of bounded unknown disturbances the beam displacement returns to the origin and its decay is bounded by a known exponential decay function after a known finite time reaching phase

theoretical analysis of transient waves in a simply supported timoshenko beam by ray and normal mode methods abstract the dynamic transient responses of a simply supported timoshenko beam subjected to an impact force are investigated by two theoretical approaches ray and normal mode methods the mathematical methodology proposed in this study for the ray method enable us to construct the solution for the interior source problem and to extend to solve the complicated problem for the multi span of the timoshenko beam numerical results based on these two approaches are compared the comparison in this study indicates that the normal mode method is more computationally efficient than the ray method except for very short time after the impact the long time transient responses are easily calculated using the normal mode method it is shown that the average long time transient response converges to the corresponding static value the timoshenko beam theory is more accurate than the bernoulli euler beam theory because it includes shear and rotary inertia this study also provides the slender ratio for which the bernoulli euler beam can be used for the transient response analysis of the displacement moreover the resonant frequencies obtained from finite element calculation based on the three dimensional model are compared with the results calculated using the timoshenko beam and bernoulli euler beam theories it is noted in this study that the resonant frequency can be accurately determined by the timoshenko beam theory if the slender ratio is larger than 100 and by the bernoulli euler beam theory if the slender ratio is larger than 400

identification of unknown temporal and spatial load distributions in a vibrating euler bernoulli beam from dirichlet boundary measured data source identification problems in a system governed by euler bernoulli beam equation x u t t r x u x x x x f x h t x t 0 l 0 t from available boundary observation measured data namely from measured slope t u x 0 t at x 0 are considered we propose a new approach to identifying the unknown temporal h t and spatial f x loads this novel approach is based on weak solution theory for pdes and quasi solution method for inverse problems combined with the adjoint method it allows to construct not only a mathematical theory of inverse source problems for euler bernoulli beam but also an effective numerical algorithm for reconstruction of unknown loads introducing the input output operators h t u x 0 t h and f t u x 0 t f t 0 t we show that both operators are compact based on this result and general regularization theory we prove an existence of unique solutions of the regularized normal equations i h and i f then we develop the adjoint problem approach to prove frechet differentiability of the corresponding cost functionals and lipschitz continuity of the frechet gradients derived explicit gradient formulas via the adjoint problem solution and known load allow use of gradient type convergent iterative algorithms results of numerical simulations for benchmark problems illustrate robustness and high accuracy of the algorithm based on the proposed approach

modelling of floating slab tracks with continuous slabs under oscillating moving loads this paper discusses modelling of floating slab tracks on rigid foundations the model consists of an upper euler bernoulli beam to account for both the rails and a lower euler bernoulli beam to account for the slab there are two continuous resilient layers in the model one to account for railpads between the rails and the slab and one to account for slab bearings underneath the slab the fourier transformation method is used to calculate displacements of such a track under an oscillating moving load these results are used to calculate the cut on frequencies and critical velocity of the track the work in this paper also demonstrates some basic concepts in the context of vibration of infinite systems including dispersion curves critical velocities load velocity lines and coupling of systems in the wavenumber frequency domain the paper offers a complete treatment of the issues important to the analysis of a double beam system not elsewhere available in the published literature

recent developments in nonparametric density estimation advances in computation and the fast and cheap computational facilities now available to statisticians have had a significant impact upon statistical research and especially the development of nonparametric data analysis procedures in particular theoretical and applied research on nonparametric density estimation has had a noticeable influence on related topics such as nonparametric regression nonparametric discrimination and nonparametric pattern recognition this article reviews recent developments in nonparametric density estimation and includes topics that have been omitted from review articles and books on the subject the early density estimation methods such as the histogram kernel estimators and orthogonal series estimators are still very popular and recent research on them is described different types of restricted maximum likelihood density estimators including order restricted estimators maximum penalized likelihood estimators and sieve estimators are discussed where restrictions are imposed upon the class of densities or on the form of the likelihood function nonparametric density estimators that are data adaptive and lead to locally smoothed estimators are also discussed these include variable partition histograms estimators based on statistically equivalent blocks nearest neighbor estimators variable kernel estimators and adaptive kernel estimators for the multivariate case extensions of methods of univariate density estimation are usually straightforward but can be computationally expensive a method of multivariate density estimation that did not spring from a univariate generalization is described namely projection pursuit density estimation in which both dimensionality reduction and density estimation can be pursued at the same time finally some areas of related research are mentioned such as nonparametric estimation of functionals of a density robust parametric estimation semiparametric models and density estimation for censored and incomplete data directional and spherical data and density estimation for dependent sequences of observations

invariant boundary value problems for a fourth order dynamic euler bernoulli beam equation we obtain the complete lie symmetry group classification of the dynamic fourth order euler bernoulli partial differential equation where the elastic modulus the area moment of inertia are constants and the applied load is a nonlinear function in the lie analysis the principal lie algebra which is two dimensional extends in three cases viz the linear the exponential and the general power law for each of the nontrivial cases we determine symmetry reductions to ordinary differential equations which are of order four in only one case related to the power law we are able to have a compatible initial boundary value problem for a clamped end and a free beam for these cases we deduce the corresponding fourth order ordinary differential equations with appropriate boundary conditions we provide an asymptotic solution for the reduced fourth order ordinary differential equation corresponding to a clamped or free beam

consistency of orthogonal series density estimators based on grouped observations in this correspondence we show that nonparametric orthogonal series estimators of probability densities retain the mean integrated square error mise consistency when observations are grouped to the points of a uniform grid prebinned this kind of grouping is typical for computer rounding errors and may also be useful in data compression before calculating estimates e g using the fft the main result shows that mise consistency holds for all square integrable densities under mild conditions on the grid step size

mathematical models of flageolet harmonics on stringed instruments flageolet is a common technique to elicit harmonics on stringed instruments like guitars pianos and the violin family the bowed or plucked string is subdivided by a slight touch of the finger the paper discusses appropriate linear wave equations which model the flageolet phenomenon the standard second order wave equation fails because the resulting dirichlet boundary condition at the finger uncouples the two parts of the string and produces tones different from the flageolet we include and discuss fourth order corrections due to string stiffness as a possible source for the flageolet phenomenon

lyapunov approach to output feedback stabilization for the euler bernoulli beam equation with boundary input disturbance we propose a boundary output feedback control law for a one dimensional euler bernoulli beam equation with general external disturbance entering the control end a galerkin approximation scheme is constructed to show the existence of solution to the closed loop system the exponential stability of the closed loop system is obtained by the lyapunov functional method numerical simulations are presented for illustration

transient wave analysis of a cantilever timoshenko beam subjected to impact loading by laplace transform and normal mode methods abstract this study applies two analytical approaches laplace transform and normal mode methods to investigate the dynamic transient response of a cantilever timoshenko beam subjected to impact forces explicit solutions for the normal mode method and the laplace transform method are presented the durbin method is used to perform the laplace inverse transformation and numerical results based on these two approaches are compared the comparison indicates that the normal mode method is more efficient than the laplace transform method in the transient response analysis of a cantilever timoshenko beam whereas the laplace transform method is more appropriate than the normal mode method when analyzing the complicated multi span timoshenko beam furthermore a three dimensional finite element cantilever beam model is implemented the results are compared with the transient responses for displacement normal stress shear stress and the resonant frequencies of a timoshenko beam and bernoulli euler beam theories the transient displacement response for a cantilever beam can be appropriately evaluated using the timoshenko beam theory if the slender ratio is greater than 10 or using the bernoulli euler beam theory if the slender ratio is greater than 100 moreover the resonant frequency of a cantilever beam can be accurately determined by the timoshenko beam theory if the slender ratio is greater than 100 or by the bernoulli euler beam theory if the slender ratio is greater than 400

non linear coupled transverse and axial vibration of a compliant structure part 1 formulation and free vibration a compliant tower in the ocean environment is modelled as a beam undergoing coupled transverse and axial motion the equations of motion are non linear and coupled and are derived here the beam is assumed to be supported by a linear elastic torsional spring at one end and with a point mass at the other end such a model is representative of numerous applications the equations of motion and boundary conditions are obtained using hamilton s variational principle it is assumed that strains are small but the rotation is moderate compared to the strain so that the equations of motion for the axial and transverse motion are non linearly coupled the free response in vacua and the free response in water are considered in particular the fluid forces the added mass and drag forces are modelled using a semi empirical morison equation the resulting non linear coupled partial differential equations are solved numerically using the finite difference approach in part 2 of this work various forced responses are studied

variational derivation of governing differential equations for truncated version of bresse timoshenko beams abstract in this paper we provide a variational derivation of modified bresse timoshenko equations this process leads to the additional term to so called truncated set of bresse timoshenko equations this new term is associated with the modified slope inertia the two sets of truncated versions of the bresse timoshenko equations are contrasted with each other as well as with the original bresse timoshenko equations on the example of the a beam that is simply supported at its both ends and b the cantilever beam with end mass it is concluded that application of either truncated sets of equations is advantageous over the original bresse timoshenko equations as far as two truncated sets of equations are concerned the variationally derived set appears to be preferable

vibration confinement in a general beam structure during harmonic excitations abstract in the present paper the green s function is utilized to provide a simple exact and direct analytical method for analysis of a beam structure of generic boundary conditions with attached springs and or finite masses the aim is to confine the vibration in a certain part of the structure the beam equation is based on the timoshenko beam theory with corrections for shear deformation and rotary inertia effects in the analysis the beam is driven by a harmonic external excitation the attached springs are modeled as simple reactions that provide transverse forces to the beam while each added mass provides a transverse force in addition to a moment at its location these forces moments act as secondary forces moments that reduce the response caused by the external force numerical simulations are conducted to find the optimal masses and or springs that confine the vibration in a certain chosen region the results were compared to that obtained from euler bernoulli beam theory beams that are excited by a bi harmonic force as well as dual excitation forces are analyzed in addition the case when the beams are excited near resonances is discussed also a method is proposed to impose a node at any desired location along the structure

quasicontinuum based multiscale approaches for plate like beam lattices experiencing in plane and out of plane deformation the quasicontinuum qc method is a multiscale approach that aims to reduce the computational cost of discrete lattice computations the method incorporates smallscale local lattice phenomena e g a single lattice defect in macroscale simulations since the method works directly and only on the beam lattice qc frameworks do not require the construction and calibration of an accompanying continuum model e g a cosserat micropolar description furthermore no coupling procedures are required between the regions of interest in which the beam lattice is fully resolved and coarse domains in which the lattice is effectively homogenized hence the method is relatively straightforward to implement and calibrate in this contribution four variants of the qc method are investigated for their use for planar beam lattices which can also experience out of plane deformation the different frameworks are compared to the direct lattice computations for three truly multiscale test cases in which a single lattice defect is present in an otherwise perfectly regular beam lattice

density estimation using exponentials of orthogonal series abstract if a density is represented as an exponential of a series of orthogonal polynomials it has a simple likelihood with a complete set of sufficient statistics to ensure that the maximum likelihood equations are well conditioned the polynomials should be orthogonal with respect to the estimated density the optimal number of terms in the series can be determined by minimizing an estimate of a loss function the penalized likelihood equations can be solved with little extra effort computer simulations show that the resulting density estimator has a smaller mean integrated squared error than the linear orthogonal series estimator

data based optimal smoothing of orthogonal series density estimates let f be a density possessing some smoothness properties and let x 1 cdots x n be independent observations from f some desirable properties of orthogonal series density estimates f n m lambda of f of the form f n m lambda t sum n nu 1 frac hat f nu 1 lambda nu 2m phi nu t where phi nu is an orthonormal sequence and hat f nu 1 n sum n j 1 phi nu x j is an estimate of f nu int phi nu t f t dt are discussed the parameter lambda plays the role of a bandwidth or smoothing parameter and m controls a shape factor the major novel result of this note is a simple method for estimating lambda and m from the data in an objective manner to minimize integrated mean square error the results extend to multivariate estimates

material point method enhanced by modified gradient of shape function a numerical scheme of computing quantities involving gradients of shape functions is introduced for the material point method mpm so that the quantities are continuous as material points move across cell boundaries the noise and instability caused by cell crossing of the material points are then eliminated in this scheme the formulas used to compute these quantities can be expressed in the same forms as in the original material point method but with the gradient of the shape function modified for one dimensional cases the gradient of the shape function used in the generalized interpolation material point gimp method is a special case of the modified gradient if the characteristic function of a material point is introduced the characteristic function of a material point is not otherwise needed in this scheme therefore difficulties in tracking its evolution are avoided although the support of the modified gradient of a shape function is enlarged from the cell containing the material point to also include the immediate neighbor cells all the non local effects of a material point can be accounted for by two consecutive local operations therefore this scheme can be used in calculations with unstructured grids this scheme is proved to satisfy mass and momentum conservations exactly the error in energy conservation is shown to be second order on both spatial and temporal discretizations although the error in energy conservation is the same order as that in the original material point method numerical examples show that this scheme has significantly better energy conservation properties than those of the original material point method

vibration of composite beams with deformable shear connection mathematical modelling and numerical solution using general purpose software for two point boundary value problems abstract in this paper we develop from first principles a linear one dimensional mathematical model for the dynamic response of planar composite beams with deformable shear connection in which the inertias associated with the axial motion of the components and with the bending rotations of their cross sections are consistently taken into account to the best of our knowledge the paper by auclair et al j sound vib 366 2016 230 247 is the only work which heretofore considered these two effects however we point out and correct a flaw in the derivations of these authors to solve the eigenproblem defining the natural vibration frequencies of the composite beam and the corresponding vibration modes we advocate an untried approach the eigenproblem is converted into a standard inhomogeneous boundary value problem which can be solved using freely available state of the art mathematical software for benchmarking purposes the formulation of a conventional displacement based conforming finite element is also briefly addressed the effect of rotational and axial inertias on the natural vibration frequencies is found to be marginal and considerably less pronounced than the predictions of auclair and coworkers in disagreement with the findings of these authors it appears legitimate to ignore the above mentioned effect in a full dynamic analysis of composite beams at least within the practical range of span to depth ratios

multiwavelet density estimation accurate density estimation methodologies play an integral role in a variety of scientific disciplines with applications including simulation models decision support tools and exploratory data analysis in the past histograms and kernel density estimators have been the predominant tools of choice primarily due to their ease of use and mathematical simplicity more recently the use of wavelets for density estimation has gained in popularity due to their ability to approximate a large class of functions including those with localized abrupt variations however a well known attribute of wavelet bases is that they cannot be simultaneously symmetric orthogonal and compactly supported multiwavelets more general vector valued constructions of wavelets overcome this disadvantage making them natural choices for estimating density functions many of which exhibit local symmetries around features such as a mode we extend the methodology of wavelet density estimation to use multiwavelet bases and illustrate several empirical examples of multiwavelet density estimation

uniform consistency of automatic and location adaptive delta sequence estimators the class of delta sequence estimators for a probability density includes the kernel histogram and orthogonal series types because each can be characterized as a collection of averages of some function that is indexed by a smoothing parameter there are two important extensions of this class the first allows a random smoothing parameter for example that specified by a cross validation method the second allows the smoothing parameter to be a function of location for example an estimator based on nearest neighbor distance in this paper a general method is presented which establishes uniform consistency for all of these estimators

on the valid frequency range of timoshenko beam theory abstract the frequency equation of timoshenko beam theory factorises for hinged hinged end conditions leading to a first and second spectrum of natural frequencies the latter is largely inaccurate and can be isolated and disregarded for the majority of other end conditions when the frequency equation does not factorise one may think in terms of pseudo second spectrum contributions arising when evanescent waves become propagating above the cut off frequency co ag i and it is conjectured that these may have a corrupting effect on the frequency predictions comparisons with measured and simulated frequencies lead to the conclusion that timoshenko predictions above the cut off frequency should be disregarded for those end conditions for which the frequency equation does not factorise

approximating the ideal free distribution via reaction diffusion advection equations abstract we consider reaction diffusion advection models for spatially distributed populations that have a tendency to disperse up the gradient of fitness where fitness is defined as a logistic local population growth rate we show that in temporally constant but spatially varying environments such populations have equilibrium distributions that can approximate those that would be predicted by a version of the ideal free distribution incorporating population dynamics the modeling approach shows that a dispersal mechanism based on local information about the environment and population density can approximate the ideal free distribution the analysis suggests that such a dispersal mechanism may sometimes be advantageous because it allows populations to approximately track resource availability the models are quasilinear parabolic equations with nonlinear boundary conditions

modes for the coupled timoshenko model with a restrained end abstract the modes of the second order timoshenko system for the displacement and rotation of a fixed beam with a restrained end at the left are formulated in terms of a fundamental spatial response this is done without decoupling the system into fourth order scalar equations the restrained end leads to time space boundary conditions which introduce the frequency as a parameter into the system of equations for determining the modes these equations involve first order derivatives and consequently the modes are determined by solving a non conservative differential system this modal differential equation is discussed in terms of a fundamental matrix response it is determined by applying a closed formula that was obtained by the first author and involves the characteristic polynomial of the modal differential equation

a new rectangular beam theory abstract a new theory for beams of rectangular cross section which includes warping of the cross sections is presented in the present work by satisfying the shear free conditions on the lateral surfaces of the beam a pair of coupled equations of motion are obtained such that no arbitrary shear coefficient is required it is shown that the uncoupled equation for the transverse displacement is the same as the corresponding equation in timoshenko beam theory provided that for the timoshenko equation the shear coefficient is taken to be 5 6 this value lies within the range of values 0 822 0 870 appearing in the literature for the beam of rectangular cross section results for two typical static examples are given for both the new theory and timoshenko beam theory these results are compared with the solutions of the comparable problems in the linear theory of elasticity for the end loaded cantilever beam the new theory predicts the same result for the neutral surface deflection as does the linear theory of elasticity while timoshenko beam theory underestimates the shear correction term by 20 for the uniformly loaded and simply supported case both beam theories provide the same overestimate of the central deflection when compared with the theory of elasticity solution

the second spectrum of timoshenko beam theory further assessment a review of contributions and views on the second spectrum of timoshenko beam theory tbt over the past two decades together with some new results are presented it is shown that the timoshenko frequency equation factorises not solely for hinged hinged end conditions as is often claimed but also for guided guided and guided hinged these new cases may be regarded as portions of a multi span hinged hinged beam a higher derivative lagrangian that leads directly to the well known fourth order timoshenko beam equation is reviewed a simple relationship between the so called ostrogradski energy and the mechanical energy is derived for hinged hinged end conditions it is shown that the ostrogradski energy is positive for the first spectrum but negative for the second within some branches of physics this would be sufficient to conclude that the second spectrum is unphysical a numerical example presented by levinson and cooke is re examined using both tbt and exact plane stress elastodynamic theory agreement is excellent for the first spectrum however the second spectrum predictions are not in consistent agreement with any single mode of vibration for long wavelength it is very close to the second asymmetric mode but as wavelength shortens it becomes closer to the second symmetric then the third asymmetric modes the conclusion remains unchanged the second spectrum predictions of tbt should be disregarded

review papers recent developments in nonparametric density estimation abstract advances in computation and the fast and cheap computational facilities now available to statisticians have had a significant impact upon statistical research and especially the development of nonparametric data analysis procedures in particular theoretical and applied research on nonparametric density estimation has had a noticeable influence on related topics such as nonparametric regression nonparametric discrimination and nonparametric pattern recognition this article reviews recent developments in nonparametric density estimation and includes topics that have been omitted from review articles and books on the subject the early density estimation methods such as the histogram kernel estimators and orthogonal series estimators are still very popular and recent research on them is described different types of restricted maximum likelihood density estimators including order restricted estimators maximum penalized likelihood estimators and sieve estimators are discussed where re

the equivalence problem for the euler bernoulli beam equation via cartan s method we completely solve the local point equivalence problem for the euler bernoulli beam equation using cartan s method of equivalence we obtain five equivalence classes for each equivalence class we establish the necessary and sufficient conditions for similarity and derive a basis of differential invariants as well as operators of invariant differentiation

flexural waves on narrow plates flexural wave speeds on beams or plates depend upon the bending stiffnesses which differ by a well known factor depending on the poisson s ratio a quantitative analysis of a plate of finite lateral width displays the plate to beam transition and permits asymptotic analysis that shows the dependence on the width orthotropic plates are analyzed using both the kirchhoff and kirchhoff rayleigh theories and isotropic plates are considered for mindlin s theory with and without rotational inertia a frequency dependent young s modulus for beams or strips of finite width is suggested although the form of the correction to the modulus is not unique and depends on the theory used the sign of the correction for the kirchhoff theory is opposite to that for the mindlin theory these results indicate that the different plate and beam theories can produce quite distinct behavior this divergence in predictions is further illustrated by comparison of the speeds for antisymmetric flexural modes on narrow plates th

persistence and extinction in spatial models with a carrying capacity driven diffusion and harvesting abstract for the reaction diffusion equation u t x t d u t x k t x r t x u t x g k t x u t x e t x u t x with the general type of growth diffusion stipulated by the carrying capacity k and harvesting existence positivity persistence extinction and stability of solutions are investigated in numerical simulations the results are compared to the model with a regular diffusion

stability of a flexible structure with destabilizing boundary conditions the euler bernoulli beam model with non dissipative boundary conditions of feedback control type is investigated components of the two dimensional input vector are shear and moment at the right end and components of the observation vector are time derivatives of displacement and slope at the right end the codiagonal matrix depending on two control parameters relates input and observation the paper contains five results first asymptotic approximation for eigenmodes is derived second the main identity is established it provides a relation between mode shapes of two systems one with non zero control parameters and the other one with zero control parameters third when one control parameter is positive and the other one is zero the main identity yields stability of all eigenmodes though the system is non dissipative fourth the stability of eigenmodes is extended to the case when one control parameter is positive and the other one is sufficiently small finally existence and properties of deadbeat modes are investigated

the second frequency spectrum of timoshenko beams abstract a second spectrum of frequencies was reported in early analytical work on the vibrations of timoshenko beams however in subsequent finite element modelling this phenomenon was either ignored or not definitively classified and recorded in fact from a recent finite element analysis with a high precision element it was even concluded that there is no separate second spectrum of frequencies except for the special case of hinged hinged beams and it was asserted that previous investigators had misinterpreted some frequencies thus introducing the notion of second frequencies in this paper a simple linear beam element with independent displacement fields and reduced integration to eliminate shear locking is used and enables one to detect the second spectrum accurately guidelines are provided which help to identify and classify the frequencies into two separate spectra

lie and noether symmetries for a class of fourth order emden fowler equations a group classification of a fourth order ordinary differential equation is carried out the noether symmetries are considered and some first integrals are established solutions for special lane emden systems are also obtained from the invariant solutions of the investigated equation

orthogonal bases approach for comparing nonnormal continuous distributions summary we present an orthonormal bases approach for detecting general differences among continuous distributions an unknown density function is represented by a finite vector of its estimated fourier coefficients with respect to a suitable orthonormal basis for a wide class of orthonormal bases we establish asymptotic normality of the vector of estimated fourier coefficients and propose an unbiased and consistent estimator of its asymptotic covariance matrix fourier coefficients are modelled as functions of fixed and possibly random effects this approach allows simultaneous detection of distributional differences attributable to various factors in clustered and correlated data with sufficiently large numbers of observations per each cluster with the same fixed and random effects realisations this work was motivated by multi level clustered non gaussian datasets from genetic studies

the effects of diffusion and spatial variation in lotka volterra competition diffusion system i heterogeneity vs homogeneity abstract it is well known that the interactions between diffusion and spatial heterogeneity could create very interesting phenomena in this series of two papers using the classical lotka volterra competition system we will illustrate the combined effects of dispersal and spatial variations on the outcome of the competition in part i with the total resources being fixed at exactly the same level we first show that a heterogeneous distribution of resources is usually superior to its homogeneous counterpart in the presence of diffusion then we study the more general case when both species have heterogeneous carrying capacities but still with the same total resources limiting behaviors of co existence steady states as the dispersal rates tend to 0 or are also obtained in part ii we continue our investigation but under much broader situations including different strengths and distributions of the resources and with different competition abilities

a method to solve the nonlinear eigenvalue problem of timoshenko plane frames with rigid offsets and end releases abstract the study reported here makes use of the dynamic stiffness matrix dsm for timoshenko beams hence considering rotatory inertia and shear deflection to obtain the exact solution of the associated free vibration problem the natural frequencies and vibration modes in the presence of end releases and rigid offsets are all exactly obtained for different combinations of boundary conditions and in plane arrangements of members this is possible by solving the resulted nonlinear and transcendental eigenvalue problem using two general methods one based on the wittrick williams algorithm adapted to handle end release and rigid offset and the other on the power deflation secant method the latter offered here as a novelty is proven to be an efficient technique judging from the examples given using both algorithms and the finite element method it is concluded that the power deflation method is a powerful tool to solve the nonlinear eigenvalue problem leading to exact solutions of the free vibration of complex skeleton like structures

dynamics of transversely vibrating beams using four engineering theories abstract in this paper the full development and analysis of four models for the transversely vibrating uniform beam are presented the four theories are the euler bernoulli rayleigh shear and timoshenko first a brief history of the development of each beam model is presented second the equation of motion for each model and the expressions for boundary conditions are obtained using hamilton s variational principle third the frequency equations are obtained for four sets of end conditions free free clamped clamped hinged hinged and clamped free the roots of the frequency equations are presented in terms of normalized wave numbers the normalized wave numbers for the other six sets of end conditions are obtained using the analysis of symmetric and antisymmetric modes fourth the orthogonality conditions of the eigenfunctions or mode shape and the procedure to obtain the forced response using the method of eigenfunction expansion is presented finally a numerical example is shown for a non slender beam to signify the differences among the four beam models

classical jacobi polynomials closed form solutions for transverse vibrations this paper deals with transverse vibrations of nonuniform homogeneous beams and plates classes of beams and axisymmetrical circular plates whose boundary value problems of free transverse vibrations and free transverse axisymmetrical vibrations respectively can be reduced to an eigenvalue singular problem singularities occur at both ends of orthogonal polynomials are reported exact natural frequencies and jacobi polynomials as exact mode shapes which result directly from eigenvalues and eigenfunctions of eigenvalue singular problems of classical orthogonal polynomials are reported for these classes the above classes of beams and plates hereafter called jacobi classes are given by geometry and boundary conditions the geometry consists of parabolic thickness variation with respect to the axial coordinate for beams and with respect to the radius for plates beams belonging to this class have either one or two sharp ends singularities along with certain boundary conditions plates have zero thickness at zero and outer radii the boundary value problems associated with plates and beams of two sharp ends are free boundary problems two other boundary value problems hinged free and sliding free are reported for beams with one sharp end also exact natural frequencies and mode shapes for uniformly rotating beams with hinged free boundary are reported

positive solutions of a lotka volterra competition model with cross diffusion abstract this paper concerns a lotka volterra competition reaction diffusion system with nonlinear diffusion effects we first briefly discuss the stability of trivial solutions by spectrum analysis based on the boundedness of the solutions the existence of the positive steady state solution is also investigated by the monotone iteration method

vibration analysis of periodic cellular solids based on an effective couple stress continuum model abstract cellular solids are usually treated as homogeneous continuums with effective properties nevertheless these mechanical properties depend strongly on the ratio of the specimen size to the cell size these size effects may be accounted for according to preliminary static analysis of effective continuums based on couple stress theory in this paper an effective dynamic continuum model based on couple stress theory is proposed to analyze the behavior of free vibrations of periodic cellular solids in this continuum model the effective mechanical constants of the effective continuum are deduced by an equivalent energy method the cellular solid structure is then replaced with the equivalent couple stress continuum with same overall dimension and shape moreover the finite element formulation of the couple stress continuum for the generalized eigenvalue analysis is developed to implement the free vibration analysis the eigenfrequencies of the effective continuum are then obtained via the shear beam theory or the finite element method a conventional finite element analysis by discretizing each cell of the cellular solids is also carried out to serve as an exact solution several structural cases are calculated to demonstrate the accuracy and effectiveness of the proposed continuum model good agreement on structural eigenfrequencies between the effective continuum solutions and the exact solutions shows that the proposed continuum model can accurately simulate the dynamic behavior of the cellular solids

a simple mathematical model of microtubules surrounded by an elastic matrix by nonlocal finite element method a size dependent finite element model is developed nonlocal elasticity theory is used finite element solution is presented for buckling of microtubules the effect of elastic matrix surrounded by microtubules is modeled a simple nonlocal beam model is proposed to study buckling response of protein microtubules the size effect for buckling model of microtubules is considered by using the nonlocal continuum theory finite element procedure is used for solution of nonlocal differential equation of microtubules for elastic stability the influence of the small length scale on the buckling value is examined for different geometric parameters the effect of elastic matrix surrounded of microtubules is also examined and some benchmark results are presented

the active disturbance rejection and sliding mode control approach to the stabilization of the euler bernoulli beam equation with boundary input disturbance in this paper we are concerned with the boundary feedback stabilization of a one dimensional euler bernoulli beam equation with the external disturbance flowing to the control end the active disturbance rejection control adrc and sliding mode control smc are adopted in investigation by the adrc approach the disturbance is estimated through an extended state observer and canceled online by the approximated one in the closed loop it is shown that the external disturbance can be attenuated in the sense that the resulting closed loop system under the extended state feedback tends to any arbitrary given vicinity of zero as the time goes to infinity in the second part we use the smc to reject the disturbance by removing the condition in adrc that the derivative of the disturbance is supposed to be bounded the existence and uniqueness of the solution for the closed loop via smc are proved and the monotonicity of the reaching condition is presented without the differentiation of the sliding mode function for which it may not always exist for the weak solution of the closed loop system the numerical simulations validate the effectiveness of both methods

active disturbance rejection control for rejecting boundary disturbance from multidimensional kirchhoff plate via boundary control in this paper an algorithm is developed to reject time and spatially varying boundary disturbances from a multidimensional kirchhoff plate via boundary control the disturbance and control input are assumed to be matched the active disturbance rejection control approach is adopted for developing the algorithm a state feedback scheme is designed to estimate the disturbance based on an infinite number of ordinary differential equations obtained from the original multidimensional system using infinitely many time dependent test functions the proposed control law cancels the disturbance using its estimated value all subsystems in the closed loop are shown to be asymptotically stable simulation results are presented to validate the theoretical conclusions and to exhibit the reduction in the peaking phenomenon due to the use of time varying gains instead of constant high gains

a series expansion approach to interpreting the spectra of the timoshenko beam abstract the timoshenko beam model results in two fourth order partial differential equations in time and space consequently solving the boundary value problem yields two independent sequences of natural frequencies and two corresponding sequences of mode shapes a particular natural frequency and its corresponding mode shape describe one particular solution to the boundary value problem of the timoshenko beam from an eigenfunction expansion sense all these possible solutions have to be considered in the complete series expansion of the solution however the question of whether these two independent sequences of natural frequencies implies the existence of two distinct spectra of frequencies has been a long standing topic of debate and hitherto has not been resolved completely the object of this paper is to provide answers to some of the issues raised by this debate in this context the complete solution in a series form to the timoshenko beam is investigated and it is shown for the first time that a particular mode shape of the solution is naturally expressed by an ordered pair of characteristic values rather than a single characteristic value this representation facilitates the progressive ordering of all the natural frequencies of the system and their respective mode shapes in a single set and eliminates the remaining argument for the two spectra interpretation

parametric resonance voltage response of electrostatically actuated micro electro mechanical systems cantilever resonators abstract this paper investigates the parametric resonance voltage response of nonlinear parametrically actuated micro electro mechanical systems mems cantilever resonators a soft ac voltage of frequency near natural frequency is applied between the resonator and a parallel ground plate this produces an electrostatic force that leads the structure into parametric resonance the model consists of an euler bernoulli thin cantilever under the actuation of electrostatic force to include fringe effect and damping force two methods of investigation are used namely the method of multiple scales mms and reduced order model rom method rom convergence of the voltage response and the limitation of mms to small to moderate amplitudes with respect to the gap gap amplitudes are reported mms predicts accurately both hopf supercritical and supercritical bifurcation voltages however mms overestimates the large gap amplitudes of the resonator and misses completely or overestimates the saddle node bifurcation occurring at large gap amplitudes rom produces valid results for small and or large gap amplitudes for a sufficient number of terms vibration modes as the voltage is swept up at constant frequency the resonator maintains zero amplitude until reaches the subcritical hopf bifurcation voltage where it loses stability and jumps up to large gap amplitudes next the gap amplitude decreases until it reaches the supercritical hopf bifurcation point and after that the gap amplitude remains zero for the voltage range considered in this work as the voltage is swept down at constant frequency the zero gap amplitude of the resonator starts increasing continuously after reaching the supercritical hopf bifurcation voltage until it reaches the saddle node bifurcation voltage when a sudden jump to zero gap amplitude occurs effects of frequency damping and fringe parameters on the voltage response show that 1 the supercritical hopf bifurcation is shifted to lower voltage values with the increase of any of the mentioned parameters 2 the subcritical hopf bifurcation is shifted to larger voltage values with the increase of damping shifted to lower voltage values with the increase of the fringe parameter and not significantly altered by the change in frequency 3 the saddle node bifurcation voltage decreases with the increase of frequency and damping and decrease of fringe parameter and 4 the saddle node bifurcation gap amplitude decreases with the increase of frequency and damping and it is not significantly altered by the change of the fringe parameter

matching experimental and three dimensional numerical models for structural vibration problems with uncertainties abstract the simulation model which examines the dynamic behavior of real structures needs to address the impact of uncertainty in both geometry and material parameters this article investigates three dimensional finite element models for structural dynamics problems with respect to both model and parameter uncertainties the parameter uncertainties are determined via laboratory measurements on several beam like samples the parameters are then considered as random variables to the finite element model for exploring the uncertainty effects on the quality of the model outputs i e natural frequencies the accuracy of the output predictions from the model is compared with the experimental results to this end the non contact experimental modal analysis is conducted to identify the natural frequency of the samples the results show a good agreement compared with experimental data furthermore it is demonstrated that geometrical uncertainties have more influence on the natural frequencies compared to material parameters and material uncertainties are about two times higher than geometrical uncertainties this gives valuable insights for improving the finite element model due to various parameter ranges required in a modeling process involving uncertainty

using energy methods to compare linear vibration models abstract in this paper it is proved that the series representation of the solutions of the general linear vibration model with modal damping is valid with respect to the energy norm the partial sums of the series representation of solutions may therefore be used to compare different models parseval type relationships are obtained for the eigenfunction expansions of functions these relationships are used to derive expressions for the relative error in energy for partial sum approximations of functions an example is included where a string model wave equation model and a modified euler bernoulli beam model for the transverse vibration of a steel wire are compared

non ambiguous recovery of biot poroelastic parameters of cellular panels using ultrasonicwaves abstract the inverse problem of the recovery of the poroelastic parameters of open cell soft plastic foam panels is solved by employing transmitted ultrasonic waves usw and the biot johnson koplik champoux allard bjkca model it is shown by constructing the objective functional given by the total square of the difference between predictions from the bjkca interaction model and experimental data obtained with transmitted usw that the inverse problem is ill posed since the functional exhibits several local minima and maxima in order to solve this problem which is beyond the capability of most off the shelf iterative nonlinear least squares optimization algorithms such as the levenberg marquadt or nelder mead simplex methods simple strategies are developed the recovered acoustic parameters are compared with those obtained using simpler interaction models and a method employing asymptotic phase velocity of the transmitted usw the retrieved elastic moduli are validated by solving an inverse vibration spectroscopy problem with data obtained from beam like specimens cut from the panels using an equivalent solid elastodynamic model as estimator the phase velocities are reconstructed using computed measured resonance frequencies and a time frequency decomposition of transient waves induced in the beam specimen these confirm that the elastic parameters recovered using vibration are valid over the frequency range ofstudy

estimation of an asymmetrical density from several small samples summary a method for estimation of the measurement error probability density from three or more measurements on each of several dissimilar items is presented differences between measurements on the same item provide estimates of the densities of the first and second differences between error realizations the relations between these densities and the error density expressed in terms of characteristic functions and hermite function expansions are the basis for a nonlinear least squares algorithm estimated percentiles of the error density are investigated by monte carlo experiments the method is applied to measurements by several laboratories on an inhomogeneous reference material with asymmetric variability

on the rate of convergence of orthogonal series density estimators on montre que si l optimalite est evaluee en termes de comportement des coefficients de fourier alors plusieurs estimateurs de series orthogonales tres simples sont asymptotiquement optimaux

a gradient elasticity theory for second grade materials and higher order inertia abstract second grade elastic materials featured by a free energy depending on the strain and the strain gradient and a kinetic energy depending on the velocity and the velocity gradient are addressed an inertial energy balance principle and a virtual work principle for inertial actions are envisioned to enrich the set of traditional theoretical tools of thermodynamics and continuum mechanics the state variables include the body momentum and the surface momentum related to the velocity in a nonstandard way as well as the concomitant mass accelerations and inertial forces which do intervene into the motion equations and into the force boundary conditions the boundary traction is the sum of two parts i e the cauchy traction and the gurtin murdoch traction whereas the traction boundary condition exhibits the typical format of the equilibrium equation of a material surface as known from the principles of surface mechanics whereby the gurtin murdoch traction incorporating the inertial surface force plays the role of applied surfacial force density the body s boundary surface constitutes a thin boundary layer which is in global equilibrium under all the external forces applied on it a feature that makes it possible to exploit the traction cauchy theorem within second grade materials this means that a second grade material is formed up by two sub systems that is the bulk material operating as a classical cauchy continuum and the thin boundary layer operating as a gurtin murdoch material surface the classical linear and angular momentum theorems are suitably extended for higher order inertia from which the local motion equations and the moment equilibrium equations stress symmetry can be derived for an isotropic material featured by four constants i e the lame constants and two length scale parameters aifantis model the dynamic evolution problem is characterized by a hamilton type variational principle and a solution uniqueness theorem closed form solutions of the wave dispersion analysis problem for beam models are presented and compared with known results from the literature the paper indicates a correct thermodynamically consistent way to take into account higher order inertia effects within continuum mechanics

on the two frequency spectra of timoshenko beams abstract this paper is concerned with the question of whether there are indeed two distinct spectra of frequencies for the transverse vibrations of timoshenko beams as has been claimed by a number of prior authors for the case of the simply supported beam and more recently for beams supported in an arbitrary manner elementary analysis leads to the conclusion that there is only a single frequency spectrum in the particular case of the simply supported beam the two frequency spectra viewpoint may be expedient as a device to compute frequencies but does not serve otherwise to explain the complex dynamical behavior of timoshenko beams

competitive cooperative models with various diffusion strategies the paper is concerned with different types of dispersal chosen by competing species we introduce a model with the diffusion type term a u p which includes some previously studied systems as special cases where a positive space dependent function p can be interpreted as a chosen dispersal strategy the well known result that if the first species chooses p proportional to the carrying capacity while the second does not then the first species will bring the second one to extinction is also valid for this type of dispersal however we focus on the case when the ideal free distribution is attained as a combination of the two strategies adopted by the two species then there is a globally stable coexistence equilibrium its uniqueness is justified if both species choose the same dispersal strategy non proportional to the carrying capacity then the influence of higher diffusion rates is negative while of higher intrinsic growth rates is positive for survival in a competition this extends the result of dockery et al 1998 for the regular diffusion to a more general type of dispersal