poincare friedrichs type constants for operators involving grad curl and div theory and numerical experiments abstract we give some theoretical as well as computational results on laplace and maxwell constants i e on the smallest constants c n 0 arising in estimates of the form u l 2 c 0 grad u l 2 e l 2 c 1 curl e l 2 h l 2 c 2 div h l 2 besides the classical de rham complex we investigate the complex of elasticity and the complex related to the biharmonic equation and general relativity as well using the general functional analytical concept of hilbert complexes we consider mixed boundary conditions and bounded lipschitz domains of arbitrary topology our numerical aspects are presented by examples for the de rham complex in 2d and 3d which not only confirm our theoretical findings but also indicate some interesting conjectures

free vibration analysis of a uniform multi span beam carrying multiple spring mass systems abstract the literature regarding the free vibration analysis of single span beams carrying a number of spring mass systems is plenty but that of multi span beams carrying multiple spring mass systems is fewer thus this paper aims at determining the exact solutions for the natural frequencies and mode shapes of a uniform multi span beam carrying multiple spring mass systems firstly the coefficient matrices for an intermediate pinned support an intermediate spring mass system left end support and right end support of a uniform beam are derived next the numerical assembly technique for the conventional finite element method is used to establish the overall coefficient matrix for the whole vibrating system finally equating the last overall coefficient matrix to zero one determines the natural frequencies of the vibrating system and substituting the corresponding values of integration constants into the related eigenfunctions one determines the associated mode shapes in this paper the natural frequencies and associated mode shapes of the vibrating system are obtained directly from the differential equation of motion of the continuous beam and no other assumptions are made thus the last solutions are the exact ones the effects of attached spring mass systems on the free vibration characteristics of the 1 4 span beams are studied

absolute conductivity reconstruction in magnetic induction tomography using a nonlinear method magnetic induction tomography mit attempts to image the electrical and magnetic characteristics of a target using impedance measurement data from pairs of excitation and detection coils this inverse eddy current problem is nonlinear and also severely ill posed so regularization is required for a stable solution a regularized gauss newton algorithm has been implemented as a nonlinear iterative inverse solver in this algorithm one needs to solve the forward problem and recalculate the jacobian matrix for each iteration the forward problem has been solved using an edge based finite element method for magnetic vector potential a and electrical scalar potential v a so called a a v formulation a theoretical study of the general inverse eddy current problem and a derivation paying special attention to the boundary conditions of an adjoint field formula for the jacobian is given this efficient formula calculates the change in measured induced voltage due to a small perturbation of the conductivity in a region this has the advantage that it involves only the inner product of the electric fields when two different coils are excited and these are convenient computationally this paper also shows that the sensitivity maps change significantly when the conductivity distribution changes demonstrating the necessity for a nonlinear reconstruction algorithm the performance of the inverse solver has been examined and results presented from simulated data with added noise

an electromagnetic inverse problem in chiral media we consider the inverse boundary value problem for maxwell s equations that takes into account the chirality of a body in r3 more precisely we show that knowledge of a boundary map for the electromagnetic fields determines the electromagnetic parameters namely the conductivity electric permittivity magnetic permeability and chirality in the interior we rewrite maxwell s equations as a first order perturbation of the laplacian and construct exponentially growing solutions and obtain the result in the spirit of complex geometrical optics

an elementary proof for a compact imbedding result in generalized electromagnetic theory propriete de plongement compact et certaines de ses consequences on etudie la validite du plongement suivant r 9 g e q 1 d q g l 2 q loc g

vibration analysis of a continuous system subject to generic forms of actuation forces and sensing devices this work provides a general formulation to solve vibration problems for continuous systems with damping effects including modal transient harmonic and spectrum response analyses in modal analysis the system eigenvalues and corresponding eigenfunctions can be determined the orthogonal relations of eigenfunctions are shown for transient harmonic and spectrum analyses the generic force actuator functions and response sensing operators are introduced respectively and used to derive the system response the time domain response is obtained for transient analysis the frequency response function is derived for harmonic analysis and statistical quantities of response variables due to random excitation are determined in spectrum analysis the solution for each type of analysis can be formulated and expressed in a concise format in terms of generic force actuator and response sensor mode shape functions in particular one dimensional beam and two dimensional plate vibration analyses are illustrated by following the developed generic formulation this work provides the complete analytical solutions of four types of vibration analyses for continuous systems and can be applied to other engineering structures as well

a linearized inverse boundary value problem for maxwell s equations abstract in this paper we consider the problem of determining the electromagnetic state of a body from measurements made on the surface of the body we study the full set of maxwell s equations that govern time harmonic electric and magnetic fields we seek to reconstruct the magnetic permeability the electric permitivity and the electric conductivity in the interior of the body from measurements made on the surface we exhibit appropriate boundary measurements in the form of a boundary mapping specifically the mapping from the tangential components of the electric field to the tangential components of the magnetic field this data can be used to reconstruct and approximately provided they deviate only slightly from known constants we also estimate the reconstruction errors

computation of propagative waves in free rail using a finite element technique abstract a method is presented for the numerical computation of the wavenumbers and associated modes of the cross section of solid waveguides the method based on the finite element technique is well suited to the computation of both the propagative and the evanescent waves in a straight waveguide with an arbitrary cross section the solution is obtained by factorization with the cross section of the waveguide being modelled by numerical discretization the dispersion curves of propagative waves in a free rail are computed by using triangular and quadrilateral finite elements of the cross section the evolution of cross section modes as the frequency increases is evaluated and discussed

guided waves in layered cubic media convergence study of a polynomial expansion approach a new numerical method to compute propagation constants and mode functions of a planar layered acoustic waveguide is described the basic feature is the expansion of velocity and stress fields in each layer on different legendre polynomial bases which ensures an exponential convergence rate of the method no transcendental equation has to be solved and also modes that have very close propagation constants e g coupled rayleigh waves are computed with great accuracy convergence of the method is studied and a way to estimate and control the error on the solutions is discussed

on the maxwell and friedrichs poincare constants in nd we prove that for bounded and convex domains in arbitrary dimensions the maxwell constants are bounded from below and above by friedrichs and poincare s constants respectively especially the second positive maxwell eigenvalues in nd are bounded from below by the square root of the second neumann laplace eigenvalue

finite element implementation of maxwell s equations for image reconstruction in electrical impedance tomography traditionally image reconstruction in electrical impedance tomography eit has been based on laplace s equation however at high frequencies the coupling between electric and magnetic fields requires solution of the full maxwell equations in this paper a formulation is presented in terms of the maxwell equations expressed in scalar and vector potentials the approach leads to boundary conditions that naturally align with the quantities measured by eit instrumentation a two dimensional implementation for image reconstruction from eit data is realized the effect of frequency on the field distribution is illustrated using the high frequency model and is compared with laplace solutions numerical simulations and experimental results are also presented to illustrate image reconstruction over a range of frequencies using the new implementation the results show that scalar vector potential reconstruction produces images which are essentially indistinguishable from a laplace algorithm for frequencies below 1 mhz but superior at frequencies reaching 10 mhz

the pseudospectral method comparisons with finite differences for the elastic wave equation the pseudospectral or fourier method has been used recently by several investigators for forward seismic modeling the method is introduced here in two different ways as a limit of finite differences of increasing orders and by trigonometric interpolation an argument based on spectral analysis of a model equation shows that the pseudospectral method for the accuracies and integration times typical of forward elastic seismic modeling may require in each space dimension as little as a quarter the number of grid points compared to a fourth order finite difference scheme and one sixteenth the number of points as a second order finite difference scheme for the total number of points in two dimensions these factors become 1 16 and 1 256 respectively in three dimensions they become 1 64 and 1 4 096 respectively in a series of test calculations on the two dimensional elastic wave equation only minor degradations are found in cases with variable coefficients and discontinuous interfaces

dynamic response of a viscously damped cantilever with a viscous end condition this paper deals with the dynamical analysis of a cantilevered bernoulli euler beam subjected to distributed external viscous damping in span and with a viscous end condition by a single damper in order to evaluate the vibration characteristics of the system a procedure is presented where overdamped and underdamped modes are investigated simultaneously via the dynamic stiffness matrix of the system further the orthogonality conditions which allow the decoupling of the equations of motion in terms of principal coordinates are derived then the complex frequency response function is obtained through a formula which was established for the receptance matrix previously finally the dynamic impulse response function of the system is evaluated in the time domain comparison with the numerical results obtained via a boundary value formulation justifies the approaches used here

forced vibration of euler bernoulli beams by means of dynamic green functions abstract a method for determining the dynamic response of prismatic damped euler bernoulli beams subjected to distributed and concentrated loads is presented the method yields exact solutions in closed form and may be used for single and multi span beams single and multi loaded beams and statically determinate and indeterminate beams also green functions for various beams with different homogenous and elastic boundary conditions are given in order to demonstrate the use of the green functions method several examples are given some of the obtained results are compared with those given in the references

a sextic formalism for three dimensional elastodynamics of cylindrically anisotropic radially inhomogeneous materials elasticity of arbitrary cylindrically anisotropic radially inhomogeneous media is considered the system of six first order ordinary differential equations describing time harmonic cylindrical waves propagating along the cylinder axis is obtained the matrix of the system coefficients has a specific algebraic symmetry underlying the structure of the formalism the matricant solution in the form of the peano expansion is discussed the wentzel kramers brillouin approximation is derived algebraic features of the solution are analysed and their physical content is elucidated the dispersion equation for waves in a hollow cylinder with free or clamped lateral surfaces is formulated in terms of the impedance admittance matrices their analytical properties are established which are useful for analysis of the resulting frequency spectrum the theory is extended to anisotropic radially inhomogeneous piezoelectric cylinders for which the octet generalization of the formalism is developed and studied

spectral method algorithm for modeling dispersion of acoustic modes in elastic cylindrical structures a new spectral method algorithm can be used to study wave propagation in cylindrically layered fluid and elastic structures the cylindrical structure is discretized with chebyshev points in the radial direction whereas differentiation matrices are used to approximate the differential operators we express the problem of determining modal dispersions as a generalized eigenvalue problem that can be solved readily for all eigenvalues corresponding to various axial wavenumbers modal dispersions of guided modes can then be expressed in terms of axial wavenumbers as a function of frequency the associated eigenvectors are related to the displacement potentials that can be used to calcu late radial distributions of modal amplitudes as well as stress components at a given frequency the workflow includes input parameters and the construction of differentiation matrices and boundary conditions that yield the generalized eigenvalue problem results from this algorithm for a fluid filled borehole surrounded by an

on the low frequency asymptotics in electromagnetic theory on considere les equations de maxwell harmoniques par rapport au temps avec des conditions aux limites on etudie le comportement asymptotique a basse frequence

free vibration analysis of a uniform cantilever beam with point masses by an analytical and numerical combined method abstract the natural frequencies and mode shapes of a uniform cantilever beam carrying any number of concentrated masses were determined by using an analytical and numerical combined method anc method the eigenvalue equation was first derived analytically by using the expansion theorem and then the eigenvalues and eigenvectors were calculated numerically in comparison with the general finite element method fem the anc method has the advantage that there is no necessity to derive the property matrices of each beam element and then to develop the overall ones of the entire beam in comparison with the transfer matrix method tmm the anc method requires no tedious matrix multiplication so that some computer time may be saved the anc method is also better than the pure analytical closed form method since instead of a few special cases a uniform beam carrying any number of point masses of various magnitudes or distributions along the beam length can be easily solved besides by using the anc method there is no difficulty in taking more modes in the mode superposition equation and hence more higher mode natural frequencies of better accuracy may be obtained

a fourier series solution for the transverse vibration response of a beam with a viscous boundary abstract this paper presents the generalized fourier series solution for the transverse vibration of a beam subjected to a viscous boundary the model of the system produces a non self adjoint eigenvalue like problem which does not yield orthogonal eigenfunctions therefore such functions cannot be used to calculate the coefficients of expansion in the fourier series furthermore the eigenfunctions and eigenvalues are complex valued nevertheless the eigenfunctions can be utilized if the space of the operator is extended and a suitable inner product is defined the methodology presented in this paper utilizes hilbert space methods and is applicable in general to other problems of this type as an adjunct to the theoretical discussion the results from numerical simulations are presented

multidimensional inverse problems and completeness of the products of solutions to pde a method is given for proving uniqueness theorems for some inverse problems the method is based on a result on completeness of the products of solutions to pde as an example the following uniqueness theorems are proved 1 the scattering amplitude a k known for all s2 and a fixed k 0 determines the compactly supported q x l2 d uniquely 2 the surface data u x y k known for all x y p x x3 0 and a fixed k 0 determine the compactly supported x l2 d d r 3 x x3 0 is arbitrarily small determine aj x j 1 2 uniquely here 2u k2u k2a1x a2 x u x y in r3 a1 l2 d a2 h2 d the same conclusion holds if the surface data are known at two distinct frequencies 4 the surface data u x y k known for all x y p and all k 0 determine v x and h k uniquely here 2 k2 k2 x u x y h k x l2 d h k is fourier transform of a wavelet of compact support 5 the conductivity x w2 2 d x c 0 is uniquely determined by the measurements of u and un on d here n is the outward normal to d d r3 is a bounded domain with a smooth boundary d x u 0 in d 6 necessary and sufficient conditions are given for a function a k s2 k 0 is fixed to be the scattering amplitude corresponding to a local potential from a certain class

inverse problems for the anisotropic maxwell equations we prove that the electromagnetic material parameters are uniquely determined by boundary measurements for the time harmonic maxwell equations in certain anisotropic settings we give a uniqueness result in the inverse problem for maxwell equations on an admissible riemannian manifold and a uniqueness result for maxwell equations in euclidean space with admissible matrix coefficients the proofs are based on a new fourier analytic construction of complex geometrical optics solutions on admissible manifolds and involve a proper notion of uniqueness for such solutions

calculating the spectrum of anisotropic waveguides using a spectral method the computation of the spectrum of a waveguide with arbitrary anisotropy with spatial dependence is a challenging task due to the coupling between axial and azimuthal harmonics this problem is tackled in cylindrical coordinates by extending a spectral method for the general case by considering the matrix representation of the operator on the right hand side of the governing equations the latter are exactly reformulated as an infinite set of integro differential equations essential part of this study is taking into account the coupling of different harmonics which becomes evident from the kernels of these equations provided a waveguide is translationally invariant in the axial direction the coupling of axial harmonics vanishes a practical approximation and truncation procedure yields a generalized eigenvalue problem which can be solved numerically to obtain the entire spectrum of the operator and to construct the dispersion curves for the eigenmodes the spectral method is tested against the results from the measurements of dispersion curves for the monopole dipole and quadrupole normal modes of scaled boreholes in tilted transverse isotropy anisotropic rock sample besides the comparison of dispersion curves calculated by the spectral method and those computed from the synthetic data is discussed

dynamic analysis of a multi span uniform beam carrying a number of various concentrated elements abstract this paper employs the numerical assembly method nam to determine the exact frequency response amplitudes of a multiple span beam carrying a number of various concentrated elements and subjected to a harmonic force and the exact natural frequencies and mode shapes of the beam for the case of zero harmonic force first the coefficient matrices for the intermediate concentrated elements pinned support applied force left end support and right end support of a beam are derived next the overall coefficient matrix for the whole vibrating system is obtained using the numerical assembly technique of the conventional finite element method fem finally the exact dynamic response amplitude of the forced vibrating system corresponding to each specified exciting frequency of the harmonic force is determined by solving the simultaneous equations associated with the last overall coefficient matrix the graph of dynamic response amplitudes versus various exciting frequencies gives the frequency response curve for any point of a multiple span beam carrying a number of various concentrated elements for the case of zero harmonic force the above mentioned simultaneous equations reduce to an eigenvalue problem so that natural frequencies and mode shapes of the beam can also be obtained

determining conductivity by boundary measurements a p calderon pose la question est il possible de determiner la conductivite thermique d un objet a partir de mesures statiques de la temperature et du flux de chaleur a la limite on demontre que ces mesures determinent de facon unique la conductivite thermique et toutes ses derivees a la limite

on a first order hyperbolic system including bean s model for superconductors with displacement current abstract this paper deals with a class of first order systems with generally multivalued damping terms including bean s model for superconductors with displacement current the main goal is to prove the convergence of solutions to stationary states as t

derivation of structural design sensitivities from vibration test data abstract structural sensitivities are often required in dynamic analyses of engineering structures such as system identification and control structural modification and optimization many different methods have been developed in the last three decades for the efficient computation of such sensitivities though these existing methods have proven to be very useful tools to structural analysts they are restricted to those cases where accurate analytical or finite element models are available in many practical applications where sensitivities are needed in the solution of troubleshooting problems only limited measured data are available existing methods being inapplicable in this paper a new and effective method has been developed to derive structural design sensitivities both frequency response function sensitivities and eigenvalue and eigenvector sensitivities from limited vibration test data design sensitivities calculated directly from measured data are more accurate than those calculated from analytical or finite element models since structural modelling errors are inevitable due to the complexity of almost all engineering structures the relationship between frequency response function sensitivities and eigenvalue and eigenvector sensitivities has been established this relationship provides the theoretical basis for the experimental determination of eigenvalue and eigenvector sensitivities the effect of residue contribution of out of range modes upon analysis accuracy has been examined detailed numerical assessment based on a turbine bladed disk model as well as experimental investigation of a beam structure have been conducted and the results have demonstrated the practicality of the proposed method

modeling of wave dispersion along cylindrical structures using the spectral method algorithm and code are presented that solve dispersion equations for cylindrically layered media consisting of an arbitrary number of elastic and fluid layers the algorithm is based on the spectral method which discretizes the underlying wave equations with the help of spectral differentiation matrices and solves the corresponding equations as a generalized eigenvalue problem for a given frequency the eigenvalues correspond to the wave numbers of different modes the advantage of this technique is that it is easy to implement especially for cases where traditional root finding methods are strongly limited or hard to realize i e for attenuative anisotropic and poroelastic media the application of the new approach is illustrated using models of an elastic cylinder and a fluid filled tube the dispersion curves so produced are in good agreement with analytical results which confirms the accuracy of the method particle displacement profiles of the fundamental mode in a free solid cylinder are computed for a range of frequencies

an inverse source problem for maxwell s equations in magnetoencephalography consider an inverse source problem for maxwell s equations which arises in determining locations of epileptic foci in the living human brain the human brain is modeled as a heterogeneous medium where the electric permittivity magnetic permeability and conductivity may all be functions a current dipole is used to model the epilepsy the inverse source problem in this context is to determine the current dipole from boundary measurements of the fields in this paper a new computational method is introduced for solving the inverse problem the method is based on a low frequency asymptotic analysis of maxwell s equations our method is constructive and has good convergence properties a crucial step of the method is to construct special test functions uniqueness and stability results for the inverse problem are also established the method and results are expected to find applications particularly in magnetoencephalography

a closed form solution of a longitudinal bar with a viscous boundary condition abstract a closed form solution of a longitudinal bar with a viscous boundary condition subjected to point loading is developed in this paper a new series solution is formulated that allows the time and space modes of the beam to decouple this expansion yields explicit eigenvalues and eigenvectors a frequency domain example is presented and the results are compared with finite element solutions of the same problem it is shown that the closed form solution is computationally more efficient than a finite element solution additionally the truncation error at lower frequencies is shown to be extremely small the method is easily implemented and can provide time and frequency domain solutions to this class of problems

solution of the equations of dynamic elasticity by a chebychev spectral method we present a spectral method for solving the two dimensional equations of dynamic elasticity based on a chebychev expansion in the vertical direction and a fourier expansion for the horizontal direction the technique can handle the free surface boundary condition more rigorously than the ordinary fourier method the algorithm is tested against problems with known analytic solutions including lamb s problem of wave propagation in a uniform elastic half space reflection from a solid solid interface and surface wave propagation in a haft space containing a low velocity layer agreement between the solutions is very good a fourth example of wave propagation in a laterally heterogeneous structure is also presented results indicate that the method is very accurate and only about a factor of two slower than the fourier method

an exact generalised function approach to frequency response analysis of beams and plane frames with the inclusion of viscoelastic damping abstract this paper concerns the frequency response analysis of beams and plane frames with an arbitrary number of kelvin voigt viscoelastic dampers typical external and internal dampers are considered as grounded translational tuned mass rotational and axial dampers for bending and axial vibrations respectively using the theory of generalised functions within a 1d formulation of equations of motion exact closed form expressions are derived for beam dynamic green s functions and frequency response functions under arbitrary polynomial load for any number of dampers for a plane frame exact global frequency response matrix and load vector are built with size depending only on the number of beam to column nodes for any number of dampers and point polynomial loads along the frame members from the nodal displacement solution the exact frequency response in all frame members is also obtained in closed analytical form numerical applications show many of the advantages of the proposed method

complex modal analysis of a flexural vibrating beam with viscous end conditions abstract the complex mode superposition method for the dynamical analysis of a simply supported beam with two rotational dampers attached at its end is presented first a numerical procedure for the evaluation of complex frequencies and modes of vibration has been worked out second the appropriate orthogonality conditions have been established in order to decouple the equation of motion the complex mode superposition method has then been used for the dynamic analysis in the time and frequency domains finally some numerical applications under impulsive and harmonic transverse accelerations of both ends have been reported in order to illustrate the effects of the dampers on the response amplitude

dynamic analysis of a uniform cantilever beam carrying a number of elastically mounted point masses with dampers abstract the free and forced vibration analyses of a uniform cantilever beam carrying a number of spring damper mass systems with arbitrary magnitudes and locations were made by means of the analytical and numerical combined method ancm first of all a method was presented to replace each spring damper mass system by a massless equivalent spring damper system with effective spring constant keffand effective damping coefficient ceffso that the ancm is available for the title problem next the equation of motion for the constrained beam with spring damper mass systems attached was derived by using the natural frequencies and normal mode shapes of the unconstrained beam without carrying any attachments incorporating the expansion theorem finally the eigenvalues and the forced vibration responses of the constrained beam were determined by conventional numerical methods to confirm the reliability of the presented theory all the numerical results obtained from the ancm were compared with the corresponding ones obtained from the conventional finite element method fem and good agreement was achieved the influence of the damping magnitude of each spring damper mass system on the eigenvalues and the forced vibration responses of the constrained beam was studied because the order of the overall property matrices for the equation of motion of the constrained beam derived from the ancm is much lower than that from the conventional fem the storing memory and the cpu time required by the ancm are much less than those required by the fem

on multiple frequency power density measurements ii the full maxwell s equations abstract we shall give conditions on the illuminations i such that the solutions to maxwell s equations curl e i i h i in curl h i i e i e i in e i i on satisfy certain non zero qualitative properties inside the domain provided that a finite number of frequencies are chosen in a fixed range the illuminations are explicitly constructed this theory finds applications in several hybrid imaging problems where unknown parameters have to be imaged from internal measurements some of these examples are discussed this paper naturally extends a previous work of the author 2013 7 where the helmholtz equation was studied

perturbational and nonperturbational inversion of rayleigh wave velocities the inversion of rayleigh wave dispersion curves is a classic geophysical inverse problem we have developed a set of matlab codes that performs forward modeling and inversion of rayleigh wave phase or group velocity measurements we describe two different methods of inversion a perturbational method based on finite elements and a nonperturbational method based on the recently developed dix type relation for rayleigh waves in practice the nonperturbational method can be used to provide a good starting model that can be iteratively improved with the perturbational method although the perturbational method is well known we solve the forward problem using an eigenvalue eigenvector solver instead of the conventional approach of root finding features of the codes include the ability to handle any mix of phase or group velocity measurements combinations of modes of any order the presence of a surface water layer computation of partial derivatives due to changes in material properties and layer boundaries and the implementation of an automatic grid of layers that is optimally suited for the depth sensitivity of rayleigh waves

identification of small amplitude perturbations in the electromagnetic parameters from partial dynamic boundary measurements we consider the inverse problem of reconstructing small amplitude perturbations in the conductivity for the wave equation from partial on part of the boundary dynamic boundary measurements through construction of appropriate test functions by a geometrical control method we provide a rigorous derivation of the inverse fourier transform of the perturbations in the conductivity as the leading order of an appropriate averaging of the partial dynamic boundary perturbations this asymptotic formula is generalized to the full time dependent maxwell s equations our formulae may be expected to lead to very effective computational identification algorithms aimed at determining electromagnetic parameters of an object based on partial dynamic boundary measurements

sharp hodge decompositions maxwell s equations and vector poisson problems on nonsmooth three dimensional riemannian manifolds we solve three basic potential theoretic problems hodge decompositions for vector fields poisson problems for the hodge laplacian and inhomogeneous maxwell equations in arbitrary lipschitz subdomains of a smooth compact three dimensional riemannian manifold in each case we derive sharp estimates on sobolev besov scales and establish integral representation formulas for the solution the proofs rely on tools from harmonic analysis and algebraic topology such as calderon zygmund theory and de rham theory

modeling of axisymmetric wave modes in a poroelastic cylinder using spectral method algorithm and code are presented which solve the dispersion equation for cylindrical poroelastic structures the algorithm is based on the spectral method which discretizes the underlying wave equations with the help of spectral differentiation matrices and solves the corresponding equations as a generalized eigenvalue problem the results are illustrated for the case of a fluid saturated free cylinder with open and closed pore boundary conditions on its surface the computed dispersion curves are in good agreement with analytical results which confirms the accuracy of the method

numerical simulation of borehole acoustic logging in the frequency and time domains with hp adaptive finite elements accurate numerical simulation of borehole acoustic measurements is of great relevance to improving the efficacy of acoustic logging techniques and to computationally estimating elastic formation properties such simulations require sound physical modeling combined with accurate and efficient numerical discretization and solution techniques the objective of this paper is to concomitantly model acoustic wave propagation in a fluid filled borehole coupled with elastic wave propagation both in the probed rock formation and in the elastic logging tool to ensure the accuracy and efficiency of our simulations we use a self adaptive finite element discretization method enhanced with perfectly matched layer spatial domain truncation this work constitutes the first application of automatic hp adaptivity to a coupled multi physics problem which requires the non trivial capability of propagating refinements between acoustics and elasticity subdomains through their common interface computations are carried out in the frequency domain subsequently using an inverse fourier transform frequency domain solutions are transformed into the time domain to obtain waveforms at the receiver positions numerical results are presented for monopole and dipole sources with and without the presence of the logging tool and for a layered formation to validate our method we compare our results to published reference data and to results obtained using an in house finite difference code convergence to a user specified tolerance for the discretization error confirms the accuracy delivered by our method in the presence of complex geometrical and physical conditions and indicates its potential for the simulation of borehole acoustic measurements

back propagating modes in elastic logging while drilling collars and their effect on pml stability the perfectly matched layer pml approach is widely used to implement the absorbing boundary conditions for coupled multi physics wave propagation problems however it has been recognized that the solution in the pml absorbing layer can become unstable in the presence of back propagating modes this paper analyzes the spectral location of those modes excited by monopole acoustic sources in logging while drilling cylindrical tools to recover the stability of the solution for such a class of problems involving the modeling of elastic cylindrical waveguides we propose the implementation of artificial attenuation in the waveguide to dampen undesirable modes thereby making their amplitude negligible in the pml absorbing layer due to the limited numerical accuracy and round off errors

modelling wave propagation in two dimensional structures using finite element analysis a method is described by which the dispersion relations for a two dimensional structural component can be predicted from a finite element fe model the structure is homogeneous in two dimensions but the properties might vary through the thickness this wave finite element wfe method involves post processing the mass and stiffness matrices found using conventional fe methods of a segment of the structure this is typically a 4 noded rectangular segment although other elements can be used periodicity conditions are applied to relate the nodal degrees of freedom and forces the wavenumbers real imaginary or complex and the frequencies then follow from various resulting eigenproblems the form of the eigenproblem depends on the nature of the solution sought and may be a linear quadratic polynomial or transcendental eigenproblem numerical issues are discussed examples of a thin plate an asymmetric laminated plate and a laminated foam cored sandwich panel are presented for the last two examples developing an analytical model is a formidable task at best the method is seen to give accurate predictions at very little computational cost furthermore since the element matrices are typically found using a commercial fe package the meshing capabilities and the wealth of existing element libraries can be exploited

state vector formalism and the legendre polynomial solution for modelling guided waves in anisotropic plates abstract we presented a numerical method to solve phase dispersion curve in general anisotropic plates this approach involves an exact solution to the problem in the form of the legendre polynomial of multiple integrals which we substituted into the state vector formalism in order to improve the efficiency of the proposed method we made a special effort to demonstrate the analytical methodology furthermore we analyzed the algebraic symmetries of the matrices in the state vector formalism for anisotropic plates the basic feature of the proposed method was the expansion of field quantities by legendre polynomials the legendre polynomial method avoid to solve the transcendental dispersion equation which can only be solved numerically this state vector formalism combined with legendre polynomial expansion distinguished the adjacent dispersion mode clearly even when the modes were very close we then illustrated the theoretical solutions of the dispersion curves by this method for isotropic and anisotropic plates finally we compared the proposed method with the global matrix method gmm which shows excellent agreement

on electric and magnetic problems for vector fields in anisotropic nonhomogeneous media r 3 2 initiated by saranen 131 in the above n is the outward drawn unit normal to the boundary and a denotes the exterior product according to the simple models for static magnetic fields resp electric fields which are governed by 0 1 resp 0 2 we call 0 1 the magnetic type problem and 0 2 the electric type problem considering bounded smooth domains a c r3 we discussed in 131 by means of an appropriate hilbert space method the solvability and the representation of the solutions for both problems 0 1 and 0 2 such a new approach was necessary to cover the general nonhomogeneous cases where v and e are matrix valued functions here our aim is twofold first we will now include exterior domains in our consideration this will be achieved by using certain weighted spaces which slightly restrict the behavior of the fields at infinity to find the scalar potentials we have to solve the dirichlet and neumann problems in exterior domains consequently in order to define the vector potentials we solve appropriate auxiliary second order boundary problems for vector fields the other aspect of this paper is to point out that the dimension of the space of solutions for 0 1 or 0 2 with homogeneous right side is 254 0022 247x 83 010254 22 03 00 0

on the frequency response function of a damped cantilever simply supported in span and carrying a tip mass abstract this paper deals with the determination of the frequency response function of a cantilevered bernoulli euler beam which is viscously damped by a single damper the beam is simply supported in span and carries a tip mass the frequency response function is obtained through a formula that was established for the receptance matrix of discrete linear systems subjected to linear constraint equations by considering the simple support as a linear constraint imposed on generalized co ordinates the comparison of the numerical results obtained via a boundary value problem formulation justifies the approach used here

finite element computation of dispersion properties of thin walled waveguides abstract a method is presented for the numerical computation of the wavenumbers and associated modes of the cross section of thin walled waveguides the method is based on finite element techniques a thin shell type finite element of the cross section is developed by using the virtual work formulation for one dimensional propagation the case of a waveguide the set of equations of motion evaluated by finite element discretization is then transformed into a simple eigenvalue problem involving a general real matrix two examples are analyzed by the finite element method developed the circular cylindrical shell straight thin walled pipe and the thin walled beam of i shaped cross section the so called i profile results obtained by the finite element method by donnell s shell theory and by using simple euler bernoulli beam theory are compared

regularity and stability for the scattering map of a linearized inverse medium problem the main goal of this paper is to study the linearization of an inverse medium problem regularity and stability results are established for the near field scattering map or scattering matrix which maps the scatterer to the scattered field properties on continuity and frechet differentiability of the scattering map are examined a lower bound of the linearized scattering map is obtained which in particular characterizes the stability properties these results are useful in the analysis of the nonlinear inverse scattering problem

spectral differencing with a twist spectral collocation methods have become very useful in providing highly accurate solutions to differential equations a straightforward implementation of these methods involves the use of spectral differentiation matrices to obtain optimal accuracy these matrices must be computed carefully we demonstrate that naive algorithms for computing these matrices suffer from severe loss of accuracy due to roundoff errors several improvements are analyzed and compared a number of numerical examples are provided demonstrating significant differences between the sensitivity of the forward problem and the inverse problem

a new approach for determining the natural frequencies and mode shapes of a uniform beam carrying any number of sprung masses abstract in theory one may obtain five equations from each attaching point of a spring mass system and two boundary equations from each end of the uniform beam hence for a uniform beam carrying n spring mass systems simultaneous equations of the form b c 0 will be obtained the solutions of b 0 where represents a determinant give the natural frequencies of the constrained beam and the substitution of each corresponding values of c j j 1 4 into the eigenfunction will define the associated mode shapes while the foregoing theory is simple the lengthy explicit mathematical expressions become impractical if the total number of spring mass systems is larger than two for this reason it was applied to do the free vibration analysis of a uniform beam carrying one spring mass system only in the existing literature the purpose of this paper is to present a numerical technique to apply the foregoing theory to obtain the exact solutions for the lowest several natural frequencies and mode shapes of a uniform beam carrying any number of spring mass systems with various boundary conditions to this end each integration constant c vi and each mode displacement z v v 1 n i 1 4 at the attaching point and the two ends of the beam are considered as nodal displacements of a finite beam element and are assigned an appropriate degree of freedom dof hence each associated coefficient matrix will be equivalent to the stiffness matrix of a beam element and the conventional numerical assembly technique for the finite element method fem may be used to determine the overall coefficient matrix b therefore the eigenvalue equation b c 0 is easily obtained

the essential spectrum of the nonself adjoint maxwell operator in a bounded domain 1 introductionin this work we study the spectrum of the maxwell operator in theself adjoint case it is well known that the spectrum consists of oneeigenvalue with infinite multiplicity in zero and other eigenvalues havingfinite multiplicities however the spectrum of the nonself adjoint operatorwas not studied much though the nonself adjoint perturbation rises from avery common phenomena namely from the conductivity in this work weshow that the maxwell system with conductivity in a bounded domain hasquite a large essential spectrum the essential spectrum contains aninterval or another nondiscrete set let v be a

on the natural frequencies and mode shapes of a multispan timoshenko beam carrying a number of various concentrated elements abstract the purpose of this paper is to utilize the numerical assembly method nam to determine the exact natural frequencies and mode shapes of the multispan timoshenko beam carrying a number of various concentrated elements including point masses rotary inertias linear springs rotational springs and spring mass systems first the coefficient matrices for an intermediate pinned support an intermediate concentrated element left and right end support of a timoshenko beam are derived next the overall coefficient matrix for the whole structural system is obtained using the numerical assembly technique of the finite element method finally the exact natural frequencies and the associated mode shapes of the vibrating system are determined by equating the determinant of the last overall coefficient matrix to zero and substituting the corresponding values of integration constants into the associated eigenfunctions respectively the effects of distribution of in span pinned supports and various concentrated elements on the dynamic characteristics of the timoshenko beam are also studied

legendre and laguerre polynomial approach for modeling of wave propagation in layered magneto electro elastic media a numerical method to compute propagation constants and mode shapes of elastic waves in layered piezoelectric piezomagnetic composites potentially deposited on a substrate is described the basic feature of the method is the expansion of particle displacement stress fields electric and magnetic potentials in each layer on different polynomial bases legendre for a layer of finite thickness and laguerre for the semi infinite substrate the exponential convergence rate of the method for propagation of love waves is numerically verified the main advantage of the method is to directly determine complex wave numbers for a given frequency via a matricial eigenvalue problem in a way that no transcendental equation has to be solved results are presented and the method is discussed

determination of small amplitude perturbations for the electric permittivity from partial dynamic boundary measurements the paper deals with reconstruction of small perturbation of the uniform isotropic complex electric permittivity from dynamic measurements of the tangential component of the magnetic field on the boundary or a part of the boundary of a domain the method is based on derived asymptotic inverse fourier transform of the perturbation in the complex permittivity through construction of appropriate test functions by a geometrical control method we provide a rigorous derivation of the inverse fourier transform of the perturbations in the electric permittivity as the leading order of an appropriate averaging of the partial dynamic boundary perturbations

free and forced vibrations of a restrained uniform beam carrying an intermediate lumped mass and a rotary inertia abstract the free and forced vibrations of a uniform beam elastically restrained against rotation at one end and against translation at the other end and carrying a lumped mass with rotary inertia and external loading at an arbitrary intermediate point are analyzed the analysis involves solving the exact eigenvalue problem for the base beam to obtain the exact mode shape functions which account for the effects of the elastic restraints at the beam ends these mode shape functions are then used in conjunction with galerkin s method with the lumped mass and rotary inertia treated as applied loads to obtain the approximate eigenvalue parameters and resonance response of the beam mass system parametric studies are carried out to investigate the effects of the stiffness of elastic restraints and location and magnitude of the lumped mass and rotary inertia on the eigenfrequency parameters and resonance response of the beam mass system partial computational results are compared with existing data the agreement is generally good for convenience the results are presented in dimensionless form

relative sensitivity analysis of responses using transmissibility abstract to identify the most effective position for solving vibrational problems it is necessary to analyze the system sensitivities in this study new sensitivity indices based on the concept of transmissibility are proposed for analyzing the relative sensitivities of the responses with respect to the design variables that are used to indicate the sensitive positions where small design modifications can be applied and analyze the effect of these modifications on the responses the transmissibility concept is applied after differentiating the equation of motion to consider the crosstalk effects more important information regarding the relative sensitivity characteristics of a system with easily measured response data to reduce unintended responses can be acquired by using the proposed indices further the proposed indices are applicable to the variables of mass stiffness and damping the indices are validated analytically and numerically and the results demonstrate the effectiveness of the proposed indices