model based data assessment for terrestrial carbon processes implications for sampling strategy in face experiments the value of different types of data in the estimation of different carbon transfer parameters is investigated a carbon accounting model is used with different observation operators to generate data the effectiveness of the inversion is assessed by observing relative errors of estimators and likelihood ratios it is demonstrated that for an observation operator that relative errors vary widely with the sample test problems an effective strategy to test types of data is to test the effectiveness of corresponding observation operators on an ensemble of sample problems for which parameters are selected from the space of admissible parameters the selection is carried out under the assumption that the test parameters themselves are random variables uniformly distributed over the space of admissible parameters

on the definiteness of gauss kronrod integration rules the nondefiniteness of the kronrod extension of the gauss gegenbauer integration rule with weight function w x 1 x2 1 2 0 0 f d 1 5 0 and rnf 0 then the open rule qn of precision d received february 11 1985 1980 mathematics subject classification primary 65d30

orthogonal polynomials associated polynomials and functions of the second kind abstract a survey is given of the interaction between orthogonal polynomials associated polynomials and functions of the second kind with an emphasis on asymptotic results various formulas are presented in a unified way in terms of wronskians of solutions of linear recurrence relations some of these formulas are classical and go back to the previous century but usually they are hard to locate in the literature some new formulas are also given in particular a formula expressing the derivative of an orthogonal polynomial in terms of the orthogonal polynomials and the associated polynomials

estimation of parameters in carbon sequestration models from net ecosystem exchange data the use of net ecosystem exchange nee data to estimate carbon transfer coefficients is investigated in the context of a deterministic compartmental carbon sequestration system sensitivity and approximation properties are investigated for the underlying model initial value problems joint probability distributions are obtained by including nee data along with corresponding synthetic nee values generated from the model and are compared with a priori distributions these distributions are used to estimate individual transfer parameters and to predict future carbon states results are compared with those obtained using only a priori information without the benefit of data shannon information content is introduced to measure the dependence of results on the lengths of observational intervals and provide an additional indicator of the value added by the inclusion of nee data

subgrid modeling in a galerkin method for the helmholtz equation abstract we improve the accuracy of finite element acoustic wave solutions without introducing additional degrees of freedom with physically inspired subgrid models the models explored here will not adversely impact system matrix storage or bandwidth can be used for structured or unstructured meshes do not require the solution of any auxiliary value problems and have minimal marginal overall computational cost one interpretation of the new models is as momentum transferred to and from modes at length scales below the local mesh dimension we show a method to approximate the effects of all subgrid modes on the grid scale solution and the significant improvements in local accuracy that the new models provide the new subgrid models also improve global or pollution accuracy through a reduction in the element dispersion error in addition we draw comparisons between this proposed method and much of the alternative and related work in this area

free vibration of stiffened rectangular plates using green s functions and integral equations a new method for the free vibration analysis of stiffened rectangular plates based on the use of green s functions and the solution of a system of fredholm integral equations of the second kind is demonstrated the lateral forces and twisting moments of constraint between the plate and beam stiffeners are accounted for for plates with simply supported edges perpendicular to the stiffeners the integral equations are solved exactly to yield the characteristic equations for the natural frequencies the characteristic equations are then solved to yield the exact natural frequencies within the context of the mathematical model chosen the pertinent parameters of the problem all appear explicitly in the characteristic equation which then has implications for its use as a mathematical design tool the exact natural modes can be calculated and the orthogonality relation for the natural modes is given which implies that the forced response of the stiffened plate including the effects of damping can be determined by modal analysis as an example a table and figures show the natural frequencies for a stiffened simply supported rectangular plate with a single stiffener

transverse vibrations of rectangular plates with edges elastically restrained against translation and rotation abstract the fundamental frequency coefficient for a rectangular plate with edges elastically restrained against both translation and rotation is calculated by using polynomial coordinate functions and the rayleigh ritz method the approach is simple and straightforward and allows the solution of a rather difficult elastodynamics problem complicating factors orthotropic properties in plane forces concentrated masses etc can also be taken into account without formal difficulties

an approximation for the point mobility at the intersection of two perpendicular plates abstract the problem of point excitation at a t intersection of two perpendicular plates is studied in order to establish expressions for the point mobility it is found that the theory for point excitation of the free surface of a semi infinite elastic solid is applicable in the frequency range associated with structure borne sound transmission from this theory the mobility for an infinite system is derived based on this model and on an experimental investigation an estimation procedure for the point mobility in the finite dimension case is developed the agreement with measurements performed in situ is quite acceptable both the theoretical and the experimental investigations reveal that the real part of this mobility is small although it is larger in the experimental results this indicates that other components of excitation are difficult to eliminate and may contribute to the power input in practice because of the small real part of the mobility it is advantageous with respect to the reduction of structure borne sound power transmission to locate the contact points between a source and the receiver at such intersections corrections are deduced for the measured magnitude of the mobility for the case when separate force and motion transducers are used

stieltjes polynomials and functions of the second kind abstract in this paper we discuss known and new facts on the asymptotic behaviour of the stieltjes polynomials and the close relation to the asymptotic behaviour of the boundary values of the functions of the second kind on 1 1 most of the results are derived by new methods of proof where mainly the theory of real orthogonal polynomials is used

the effects of large vibration amplitudes on the mode shapes and natural frequencies of thin elastic shells part i coupled transverse circumferential mode shapes of isotropic circular cylindrical shells of infinite length the effects of large vibration amplitudes on the first and second coupled radial circumferential mode shapes of isotropic circular cylindrical shells of infinite length are examined a theoretical model based on hamilton s principle and spectral analysis developed previously for clamped clamped beams and fully clamped rectangular plates is extended to shell type structures reducing the large amplitude free vibration problem to the solution of a set of non linear algebraic equations the transverse and circumferential displacements are assumed to be harmonic and expanded in the form of a finite series of functions the donnel mushtarie shell theory taking into account the coupling between extensional and flexural deformations is used then the non linear deformation energy is expressed by taking into account the non linear term due to the considerable stretching of the middle surface of the shell induced by large deflections tables of numerical results are given for the first and second non linear modes for a wide range of the vibration amplitude which may be used for engineering purposes for each value of the vibration amplitude considered the corresponding contributions of the basic functions defining the non linear transverse and circumferential displacement shapes are given with the corresponding non linear frequencies selected plots of mode shapes and bending stress distributions are presented with an extensive discussion of the effects of non linearity on the dynamic behaviour of shells

free vibration analysis of a cylindrical shell circular plate system with general coupling and various boundary conditions abstract the free vibration of a structure consisting of a finite circular cylindrical shell closed at one end by a circular plate is analyzed in this paper emphasis is given to the characterization of structural coupling and boundary conditions these are incorporated into the model by means of continuous distributions of springs along the shell and the plate interface a general formulation based on a variational principle is used this formulation allows a wide spectrum of boundary conditions and coupling conditions between the shell and the plate an issue the importance of which is clearly shown by a literature review very good accuracy of the method is demonstrated by solving test problems for lower order modes of the plate and of the shell for which some results are available in the literature comparisons are also made using finite element analysis on a plate ended shell showing that the proposed approach is a convenient effecient and accurate one for determining the modal behavior of such a complex structural system other numerical results are then presented for a shell rigidly attached to a plate to illustrate the coupling phenomena between the shell and the plate it is shown that there exist three different types of modes for this combined structure they are termed plate controlled modes shell controlled modes and strongly coupled modes respectively it is also shown that each type is closely related to the modal character of each of uncoupled elements

stopping functionals for gaussian quadrature formulas abstract gaussian formulas are among the most often used quadrature formulas in practice in this survey an overview is given on stopping functionals for gaussian formulas which are of the same type as quadrature formulas i e linear combinations of function evaluations in particular methods based on extended formulas like the important gauss kronrod and patterson schemes and methods which are based on gaussian nodes are presented and compared

modeling and inversion of net ecological exchange data using an ito stochastic differential equation approach a system of stochastic differential equations is studied describing a compartmental carbon transfer model that includes uncertainties arising in the model from environmental and photosynthetic effects as well as initial conditions justification is given for the modeling of observed times series as weiner processes the solution of the resulting system is obtained as a stochastic process a formulation is given appropriate for obtaining continuity and differentiability with respect to model transfer coefficients and numerical approximation results are given estimation results of coefficients from nee data are obtained using quasi monte carlo techniques the error resulting in nee stochastic models is observed to be approximately gaussian this result is used to construct a joint probability density defined on a sample space of transfer coefficients finally the joint probability density function is used with quasi monte carlo to obtain information on transfer coefficients and predicted carbon pools this information is compared with a priori results obtained without the benefit of nee data

gauss kronrod integration rules for cauchy principal value integrals kronrod extensions to two classes of gauss and lobatto integration rules for the evaluation of cauchy principal value integrals are derived since in one frequently occurring case the kronrod extension involves evaluating the derivative of the integrand a new extension is introduced using n 2 points which requires only values of the integrand however this new rule does not exist for all n and when it does several significant figures are lost in its use 1 introduction in this paper we shall consider kronrod extensions ke to integration rules based on gauss and lobatto points for the evaluation of cauchy principal value cpv integrals of the form fix vyx 1 since the existence theory of ke s for regular integrals insures such extensions for only certain classes of weight functions w x we shall restrict our attention here to the most important class namely w x 1 x2y x 2 where 0 p 2 in the gauss case and p 1 in the lobatto case 9 the only other relevant weight functions are the jacobi weight functions w x 1 x a l x with a i s or s y a f and w x x2 i rx2 oo r 1 5 for our case w x 1 x2 m 1 2 the corresponding orthogonal polynomials are the gegenbauer polynomials c x usually written c x which have the following normalization 11 p 174 2 w x c x cmil x dx 8 mhnil where 3 hn i ft n 2p r p n u n r p r 2p

stieltjes polynomials and related quadrature rules in this paper we present a survey of theoretical results some of them new and numerical evidence of others concerning stieltjes polynomials kronrod schemes and their generalizations applied to integrals with a classical nonnegative weight function the use of these schemes in automatic integration routines is briefly outlined

gauss kronrod quadrature formulae for weight functions of bernstein szego type ii we study the kronrod extensions of gaussian quadrature rules whose weight functions on 1 l consist of any one of the four chebyshev weights divided by an arbitrary quadratic polynomial that remains positive on 1 11 we show that in almost all cases these extended gauss kronrod quadrature rules have all the desirable properties kronrod nodes interlacing with gauss nodes all nodes contained in 1 11 and all weights positive and representable by semiexplicit formulas exceptions to these properties occur only for small values of n the number of gauss nodes namely n 3 and are carefully identified the precise degree of exactness of each of these gauss kronrod formulae is determined and shown to grow like 4n rather than 3n as is normally the case our findings are the result of a detailed analysis of the underlying orthogonal polynomials and stieltjes polynomials the paper concludes with a study of the limit case of a linear divisor polynomial in the weight function

use of lagrange multipliers with polynomial series for dynamic analysis of constrained plates part i polynomial series abstract a theory for prediction of the dynamic response of a constrained plate is presented here the boundaries of the plate may be partially fixed its dynamic loading is due to elastically mounted vibrating machines and its constraints include beam like stiffeners the theory yields the eigenvalues and modal shapes of the plate and stiffeners which comprise the system the solution given in part i is based on galerkin s method combined with use of special polynomial series presented by kantorovich and krylov these eigenvalues are used in part ii 1 for response analysis of the complete system and the eigenvalues of the complete system will be obtained by the application of lagrange equations and multipliers the various coefficients used in the process are presented in the appendices to the work comparisons with published results show good agreement

on the efficacy of the wavelet decomposition for high frequency vibration analyses abstract this paper reports the extraordinary ability of the wavelet decomposition for vibration analyses under the framework of rayleigh ritz method using a beam as an example daubechies wavelet scale functions are used as admissible functions for decomposing the flexural displacement of the structure along with the artificial springs at the boundary to predict vibration of an euler bernoulli beam in an extremely large frequency range it is shown that the use of wavelet basis allows reaching very high frequencies typically covering more than 1000 modes using conventional computational facility within the available numerical dynamics of the computers with no particular care needed for round off errors as a side benefit the use of spring boundary also allows handling any elastic boundary conditions through a dynamic contribution in the hamiltonian of the beam the wavelet decomposed approach combines the flexibility of the global methods and the accuracy of local methods by inheriting the versatility of the rayleigh ritz approach and the superior fitting ability of the wavelets numerical results on both free and forced vibrations are given in excellent agreement with predictions of classical methods

the exterior matrix method for sequentially coupled fourth order equations abstract this paper introduces the exterior matrix method as a means to compute asymptotically the eigenfrequencies for the vibrations of serially connected elements which are each governed by fourth order equations the timoshenko beams and a tapered euler bernoulli beams are just two examples that are solved by this method the technique involves not just lifting the transfer matrices into the higher dimensional exterior algebra space but also lifting the original fourth order equation to generally produce a sixth order exterior equation but occasionally the exterior equation is only fifth order the original fourth order equation does not have to be solvable for this technique to work since only the approximate solutions for the exterior equation are needed to compute the eigenfrequencies asymptotically

response of force excited elastic solids with internal fluid loading a general approach to solving for the velocity response and associated pressure field of elastic solids loaded internally by a fluid is formulated an in vacuo eigenvector expansion is used to describe the time dependent velocity field of the fluid loaded solid resulting from an arbitrary force excitation the pressure field in the fluid is expressed using a green s function and fluid loading on the structure is included via the use of the impulse responses of the modal acoustic radiation impedances the time dependent modal velocity responses are obtained from the solution to a set of coupled convolution integral equations a fourier transform approach is used to develop the associated equations of motion for the harmonic response the special case of a fluid filled axisymmetric elastic cylindrical shell with a base plate is considered transient and harmonic velocity and pressure responses due to a bandlimited axisymmetric point force excitation applied to the base plate are discussed and compared with

asymptotic modelling theorems for the static analysis of linear elastic structures the work presented here justifies the use of restraints with large positive and negative stiffness values to asymptotically model geometric constraints of a structure in linear structural analysis replacing constraints by very stiff restraints improves the versatility of variational methods such as the rayleigh ritz method as the limitation on the choice of functions is removed based on recently published theorems on the existence of natural frequencies of systems with artificial restraints of positive and negative stiffness and their convergence towards the frequencies of the corresponding constrained systems a proof is given to show that the displacement of a constrained structure caused by any action along its direction is approached and bracketed by the displacement of systems with artificial restraints of positive and negative stiffness positive and negative penalty functions as the magnitude of stiffness is increased a procedure for the practical use of positive and negative penalty functions in static analysis of linear structures is also proposed

existence of natural frequencies of systems with artificial restraints and their convergence in asymptotic modelling a major limitation of the rayleigh ritz method for determining the natural frequencies of a system is the need to choose admissible functions that do not violate the geometric constraints of that system courant 1943 bulletin of the american mathematical society49 1 23 several researchers have attempted to overcome this problem by asymptotically modelling the rigid constraints with artificial imaginary restraints of very large stiffness courant 1943bulletin of the american mathematical society49 1 23 warburton and edney 1984 journal of sound and vibration95 537 552 gorman 1989 journal of applied mechanics56 893 899 kim et al 1990 journal of sound and vibration143 379 394 yuan and dickinson 1992 journal of sound and vibration153 203 216 yuan and dickinson 1992 journal of sound and vibration159 39 55 cheng and nicolas 1992 journal of sound and vibration155 231 247 yuan and dickinson 1994computers and structures53 327 334 lee and ng 1994 applied acoustics42 151 163 amabili and garziera 1999 journal of sound and vibration224 519 539 amabili and garziera 2000 journal of fluids and structures14 669 690 while the numerical results thus obtained for the systems considered in the literature were in close agreement with exact values for the natural frequencies corresponding to the first few modes sample calculations show that the error introduced by the asymptotic modelling increases with mode number and therefore to obtain accurate results for higher modes the magnitude of stiffness should also be increased in any event the error due to the asymptotic modelling would remain uncertain except when the correct frequency values are known however the use of artificial restraints with negative stiffness a new concept which was introduced in a recent publication ilanko and dickinson 1999 journal of sound and vibration219 370 378 paves the way for estimating the error due to asymptotic modelling this is possible since in this work the rayleigh ritz frequencies of the constrained system were found to be bracketed by the frequencies of the asymptotic models with positive and negative restraints however the use of artificial restraints with negative stiffness has raised some important questions would a system with a large negative restraint become unstable and if so what is the guarantee that the frequencies of the asymptotic model would converge to that of the constrained system this paper is the result of the author s attempt to answer these questions and gives a proof of existence of natural frequencies for systems with artificial restraints springs having positive or negative stiffness coefficients and their convergence towards constrained systems based on rayleigh s theorem of separation it has been shown that a vibratory system obtained by the addition of h restraints to an n degree of freedom d o f system where h n will have at least n h natural frequencies and modes and that as the magnitude of the stiffness of the added restraints becomes very large these n h natural frequencies will converge to the n h natural frequencies of a constrained system in which the displacements restrained by the springs are effectively constrained

a general formulation for the sound radiation from rectangular baffled plates with arbitrary boundary conditions the radiation of sound from a baffled rectangular plate with edges elastically restrained against deflection and rotation is analyzed the elastic constants along the contour can be varied to reproduce simply supported clamped free or guided edges as limiting cases the formulation is based on a variational method for the vibration of the plate and assumes no fluid loading of the structure the elastic boundary conditions appear in the hamiltonian of the plate through a dynamic contribution which is expressed in terms of nondimensional edge parameters the extremalization of the hamiltonian is achieved using a rayleigh ritz method and both the free vibrations and the forced vibrations of the plate are presented the radiation of sound from the plate is analyzed in the far field and is calculated from one dimensional fourier transforms numerical results are presented for the radiation efficiency of modes of simply supported clamped free and guided plates the values found agree well with predic

vibration analysis of line coupled structures using a coupling load decomposition technique a new substructuring technique is proposed to perform vibration analysis of line coupled structures in dividing the whole structure into a master structure and several auxiliary structures a variational formulation is used to model the master structure enabling one to introduce the effects of all auxiliary structures by using their compliance characteristics at several observation points along the junction continuous functions of the compliance are obtained via a regression analysis given the problem of using the compliance inverse to attain a straightforward formulation a coupling load decomposition technique is proposed since a direct formulation using the compliance inverse is not feasible by decomposing the interactive load between substructures relations with displacement decomposition of the master structure can be found this new formulation permits the direct use of the compliance of the junction which may be obtained analytically numerically or experimentally numerical examples using both calculated and experimentally measured compliance data are given simulation results are also compared to those obtained experimentally showing good agreement in low and medium frequency ranges

asymptotic behaviour of stieltjes polynomials for ultraspherical weight functions abstract for the ultraspherical weight functions w x 1 x 2 1 2 an asymptotic representation of the stieltjes polynomials is proved for 1 n n the main result is applied to prove positivity results for kronrod extensions of gauss and lobatto quadrature formulae

a thin plate model for the moment mobility at the intersection of two perpendicular plates the global response of a t intersection configuration due to a moment excitation has been analyzed the moment is applied at the intersection and the moment vector is parallel with the intersection line a thin plate model has been used to derive the moment mobility for arbitrary combinations of plate elements the imaginary part of the mobility is found to be dependent on both size and rigidity of the indenter whereas the real part is essentially independent numerical results are presented for the practically important case of three identical plate elements constituting the t intersection configuration these results clearly confirm the necessity of taking into account a potential moment excitation for the determination of structure borne sound and vibration transmission at an intersection point

on the analysis of laterally vibrating slender beams subject to various complicating effects the rayleigh ritz method with orthogonally generated polynomials as admissible functions is used to obtain a simple analysis of the free vibration problem of slender beams subject to various complicating effects these effects are the presence of concentrated masses and or concentrated moments of inertia intermediate supports axial loading and non uniformity of cross section such may exist separately or in any combination numerical results are presented for several example beams illustrating the accuracy and versatility of the approach

modified stieltjes polynomials and gauss kronrod quadrature rules modified stieltjes polynomials are defined and used to construct suboptimal extensions of gaussian rules with one or two degrees less of polynomial exactness than the corresponding kronrod extension we prove that for wide classes of weight functions and a sufficiently large number of nodes the extended quadratures have positive weights and simple nodes on the interval 1 1 the classes of weight functions considered complement those for which the gauss kronrod rule is known to exist also strong asymptotic representations on the whole interval 1 1 are given for the modified stieltjes polynomials which prove that they behave asymptotically as orthogonal polynomials finally we provide some numerical examples

free vibration analysis of a rectangular plate carrying any number of point masses and translational springs by using the modified and quasi analytical and numerical combined methods the natural frequencies and the corresponding mode shapes of a uniform rectangular plate carrying any number of rigidly attached or elastically mounted point masses and translational springs with various magnitudes and arbitrary locations are determined by using the modified analytical and numerical combined method or modified ancm and the quasi ancm instead of seeking the closed form solution analytically for the natural frequencies and normal mode shapes of the unconstrained rectangular plate without any concentrated elements attached required for the pure ancm the normal mode shapes for the modified ancm and the natural frequencies together with the normal mode shapes for the quasi ancm are obtained numerically however then the characteristic equation of the constrained rectangular plate with any number of concentrated elements attached is derived basing on the natural frequencies and normal mode shapes of the unconstrained plate and applying the mode superposition theory finally the natural frequencies and mode shapes of the constrained plate are obtained numerically the pure ancm is originally available only for the problems that the closed form solution for the natural frequencies and normal mode shapes of the constrained system is obtainable now the modified ancm and quasi ancm presented in this paper break the limitation of the pure ancm and extend the area of problems solvable by the ancm 1997 john wiley sons ltd

hermite and hermite fejer interpolation for stieltjes polynomials let x 1 x 2 1 2 and p n be the ultraspherical polynomials with respect to x then we denote by e n 1 the stieltjes polynomials with respect to x satisfying in this paper we show uniform convergence of the hermite fejer interpolation polynomials h n 1 and h 2n 1 based on the zeros of the stieltjes polynomials e n 1 and the product e n 1 p n for 0 1 and 0 a 1 2 respectively to prove these results we prove that the lebesgue constants of hermite fejer interpolation operators for the stieltjes polynomials e n 1 and the product e n 1 p n are optimal that is the lebesgue constants h n 1 0 a 1 and h 2n 1 0 a 1 2 have optimal order o 1 in the case of the hermite fejer interpolation polynomials h 2n 1 for 1 2 1 we prove weighted uniform convergence moreover we give some convergence theorems of hermite fejer and hermite interpolation polynomials for 0 1 in weighted lp norms

on the free transverse vibration of annular and circular thin sectorial plates subject to certain complicating effects abstract the rayleigh ritz method with orthogonally generated polynomials as admissible functions is used to obtain an eigenvalue equation for the free transverse vibration of thin annular sectorial plates circular sectorial plates are treated with this equation by permitting the inner radius to become negligibly small the plates may be of isotropic or polar orthotropic material of uniform or radially and or circumferentially varying thickness and may include interior circumferential or radial line supports numerical values for the natural frequency parameters of several different plates are presented and compared with previously published values where available

transverse vibrations of a rotating uniform cantilever beam with tip mass as predicted by using beam characteristic orthogonal polynomials in the rayleigh ritz method abstract natural frequencies and mode shapes of a rotating uniform cantilever beam with a tip mass are studied by using beam characteristic orthogonal polynomials in the rayleigh ritz method the set of orthogonal polynomials which satisfy the geometrical boundary conditions are generated by using the gram schmidt process the results are compared with those obtained by the myklestad method the extended galerkin method and finite element methods the variation of natural frequencies with the speed of rotation is plotted for several parameter combinations such as setting angle tip mass moment of inertia of tip mass etc mode shapes at different rotational speeds are also plotted use of orthogonal polynomials for the deflection shapes enables the computation of higher natural frequencies of any order to be accomplished without facing any numerical difficulties which is not the case when arbitrary polynomial expressions are used

introducing the use of positive and negative inertial functions in asymptotic modelling the work presented here shows that the natural frequencies of constrained systems may be obtained from asymptotic models of corresponding systems where the constraints are replaced by artificial mass or moment of inertia of very large positive and negative values this offers a convenient alternative to the current practice of using artificial elastic restraints of large stiffness a concept introduced by courant in 1943 to remove a limitation on the choice of admissible functions recent publications show that in order to control the error caused by approximating constraints with restraints of large stiffness it is necessary to use both positive and negative stiffness values however the negative stiffness introduces instability near the lower modes of vibration and the magnitude of negative stiffness parameter used must be greater than the highest critical stiffness to ensure bounded results are obtained the use of positive and negative artificial inertial parameters overcomes this problem as they do not introduce instability near the lower modes allowing the natural frequencies of constrained systems to be delimited to any desired accuracy

stieltjes polynomials and gauss kronrod quadrature for jacobi weight functions let w beta t 1 t 1 t 1 denote the jacobi weight function for 0 5 2 the stieltjes polynomial has only few real zeros and that gauss kronrod quadrature is not possible so far results of the above type have been known only for ultraspherical weight functions w lambda t big 1 t 2 big lambda 1 2 for 0 2 for 3 the impossibility of gauss kronrod quadrature has been proved by the authors recently

a family of gauss kronrod quadrature formulae etude d une famille de formules de quadrature de gauss kronrad formules explicites des poids

vibrations of rectangular plates with elastically restrained edges abstract the rayleigh ritz method is used to determined natural frequencies in transverse vibration of rectangular plates with elastically restrained edges by treating an elastically restrained edge as intermediate between an appropriate pair of classical boundary conditions and using the corresponding vibration mode shapes of beams with classical boundary conditions as assumed functions a relatively small number of functions is required consequently only a modest quantity of computation is necessary the good accuracy of the method is demonstrated by solving test problems the method can be applied to a wide range of elastic restraint conditions any aspect ratio and for higher modes in addition to the fundamental the usefulness and accuracy of existing simplified approaches to the problem are assessed the effect of in plane forces on the natural frequencies and the determination of critical loads for plates with these restraint conditions are considered also

numerical treatment of stochastic differential equations we define general runge kutta approximations for the solution of stochastic differential equations sde these approximations are proved to converge in quadratic mean to the solution of an sde with a corrected drift the explicit form of the correction term is given concerning the order of convergence we show that in general it is impossible for the quadratic mean of the one step error to be of an order greater than o h 3 this order is attained e g by the stochastic analogue of heun s method in the n dimensional case the highest order of convergence is in general only o h 2 attained by euler s method the order o h 3 can only be reached if nabla x sigma r sigma s nabla x sigma s sigma r for the diffusion matrix

correction gauss kronrod integration rules for cauchy principal value integrals math comp 41 1983 no 1 63 78 mr0701624 84i 65029

the use of asymptotic modelling in vibration and stability analysis of structures abstract the use of springs with very large stiffness to model constraints in vibratory systems has been a popular approach to overcome the limitations on the choice of admissible functions in the rayleigh ritz method the maximum possible error resulting from this asymptotic modelling can be determined by using positive and negative stiffness values or in general terms using positive and negative penalty functions this paper illustrates how this method could be used to determine the critical loads of structures

estimation of carbon transfer coefficients using duke forest free air co2 enrichment data a compartmental carbon model is presented in which there are parameters quantifying the transfer between various carbon pools these parameters are estimated using two co 2 data sets elevated and ambient from the duke forest face data set a quadratic objective criterion is used to compare closeness of fit of system output co 2 flux to the observed co 2 flux data adjoint equations are developed based on the system of difference equations approximating the solution of the model equations the data and the criterion parameter estimation algorithms are developed using minimization techniques it is found that the estimated parameters obtained using the two different data sets agree closely

a semi analytical method for the free vibration of doubly curved shells of revolution abstract in this paper a semi analytical method is used to investigate the free vibration of doubly curved shells of revolution with arbitrary boundary conditions the doubly curved shells of revolution are divided into their segments in the meridional direction and the theoretical model for vibration analysis is formulated by applying flugge s thin shell theory regardless of the boundary conditions the displacement functions of shell segments are composed by the jacobi polynomials along the revolution axis direction and the standard fourier series along the circumferential direction the boundary conditions at the ends of the doubly curved shells of revolution and the continuous conditions at two adjacent segments were enforced by the penalty method then the natural frequencies of the doubly curved shells are obtained by using the rayleigh ritz method for arbitrary boundary conditions this method does not require any changes to the mathematical model or the displacement functions and it is very effective in the analysis of free vibration for doubly curved shells of revolution the credibility and exactness of proposed method are compared with the results of finite element method fem and some numerical results are reported for free vibration of the doubly curved shells of revolution under classical and elastic boundary conditions results of this paper can provide reference data for future studies in related field

use of lagrange multipliers with polynomial series for dynamic analysis of constrained plates part ii lagrange multipliers abstract the eigenvalues modal shapes and response of constrained plates loaded by vibrating single degree of freedom machinery are derived the results for the complete system are obtained by application of lagrange equations and lagrange multipliers the coefficients of the solution are found with the aid of polynomial series and are explicity given in the appendices to part i 1 of this work the variants considered are an unstiffened and a beam stiffened plate

ultraspherical stieltjes polynomials and gauss kronrod quadrature behave nicely for lambda 0 we show that the zeros of the stieltjes polynomials associated with the ultraspherical weight function with parameter lambda 0 are real and simple and except for two of them belong to 1 1 we also prove that they strictly interlace with the zeros of the corresponding ultraspherical polynomials consequently a gauss kronrod quadrature formula with two nodes outside the interval 1 1 is obtained we prove that the coefficients of such quadrature rules are positive finally an asymptotic representation of stieltjes polynomials which converges uniformly on the whole interval 1 1 is provided

frequency window method for forced vibration of structures with connected substructures a novel method is presented to analyze the harmonic forced vibration of a main structure with multiple connected substructures the response of the combined system is represented in terms of the uncoupled modes of the system components then the response equations are given in terms of rational polynomial expansions for the main structure mobility substructure impedances and the forcing function next the uncoupled modes with natural frequencies closest to the excitation frequency are isolated by a frequency window the essential idea of the frequency window method is to retain full mathematical detail for these modes and to retain only the essential effects from all remaining modes this results in both a reduction of complexity and computation effort the method differs fundamentally from mode truncation and taylor s series methods furthermore the method gives parameters which provide insight into the coupling effects between the main structure and the substructures