transverse shear modulus identification by an inverse method using measured flexural resonance frequencies from beams abstract many papers have already been presented about identification of 2d in plane elastic engineering constants e1 e2 v12 and g12 by inverse methods most of the described methods are based on measured resonance frequencies on plate specimens less attention has been paid to the identification of transverse shear moduli especially validation of the obtained results and error bound estimations are often lacking this paper presents an inverse method for the identification of the transverse moduli of test beams by measured flexural resonance frequencies the procedure is first illustrated with numerically generated test data and next applied on experimentally measured results the sensitivity of the flexural resonance frequencies for variations of the shear modulus is discussed as well as an estimation of the uncertainty intervals on the obtained moduli the results are validated by using the obtained shear moduli for the prediction of torsional resonance frequencies

single layer plate theories applied to the flexural vibration of completely free thick laminates two different refined single layer plate theories are used to analyze the flexural vibration of thick symmetrically laminated rectangular plates with all edges free both theories account for parabolic distribution of the transverse shear strains through the thickness of the plate the first theory includes the transverse normal effect and employs a three dimensional constitutive law whereas the second neglects this effect and employs plane stress reduced stiffnesses numerical results are obtained by using the ritz method characteristic orthogonal polynomials are used in the series representing the displacement functions convergence studies are shown to verify the accuracy of the approximate method the accuracy of the results is further assessed by comparison with results from three dimensional finite element analyses numerical results are presented for various plates including cross ply and angle ply laminated plates the effect of transverse shear and normal deformation on the plate natural frequencies is illustrated by comparing the frequencies of the two higher order theories and the classical plate theory for decreasing length to thickness ratio

grammian solutions and pfaffianization of a non isospectral and variable coefficient kadomtsev petviashvili equation abstract in this paper we first present the grammian determinant solutions to the non isospectral and variable coefficient kadomtsev petviashvili vckp equation then by using the pfaffianization procedure of hirota and ohta a new non isospectral and variable coefficient integrable coupled system is generated moreover gramm type pfaffian solutions of the pfaffianized system are proposed

free vibration of laminated composite and sandwich plates using global local higher order theory abstract in this paper the global local higher order theory is used to study the free vibration of laminated composite and sandwich plates this global local theory can satisfy the free surface conditions and the geometric and stress continuity conditions at interfaces and the number of unknowns is independent of the layer numbers of the laminate based on the higher order theory a refined three noded triangular element satisfying c1 weak continuity conditions is presented for general laminated composite plates results obtained from present global local higher order theory have been found in good agreement with those obtained from three dimensional elasticity theories moreover this theory is still suitable for analysis of laminated plates with arbitrary layouts and soft core sandwich plates whereas numerical results show that the global higher order and first order theory overestimate natural frequency for these special structures this theory cannot only calculate the natural frequencies but can accurately predict the modal stress distributions in the thickness direction without any smooth techniques

a variable kinematic ritz formulation for vibration study of quadrilateral plates with arbitrary thickness a new variable kinematic ritz method applied to free vibration analysis of arbitrary quadrilateral thin and thick isotropic plates is presented carrera s unified formulation and the versatile pb 2 ritz method are properly combined to build a powerful yet simple modeling and solution framework the proposed technique allows to generate arbitrarily accurate ritz solutions from a large variety of refined two dimensional plate theories by expanding so called ritz fundamental nuclei of the plate mass and stiffness matrices theoretical development of the present methodology is described in detail convergence and accuracy of the method are examined through several examples on thin moderately thick and very thick plates of rectangular skew trapezoidal and general quadrilateral shapes with an arbitrary combination of clamped free and simply supported edges present results are compared with existing three dimensional solutions from open literature maximum and average differences of various higher order plate theories and three dimensional results are also presented with the aim of providing useful guidelines on the choice of appropriate plate theory to get a desired accuracy on frequency parameters

exponential stability for a class of state dependent delay equations via the crandall liggett approach abstract in this paper we are concerned with the exponential asymptotic stability of the solution of a class of differential equations with state dependent delays our approach is based on the crandall liggett approximation and the properties of semigroups

theory and experiments for nonlinear vibrations of imperfect rectangular plates with free edges abstract large amplitude vibrations of completely free rectangular plates are investigated for the first time nonlinear higher order shear deformation theory is used and the nonlinear response to transverse harmonic excitation in the frequency neighborhood of the fundamental mode is studied geometric imperfections are taken into account the numerical analysis is carried out in two steps first the plate displacements and rotations are expanded in terms of chebyshev polynomials and a linear analysis is conducted to obtain the natural frequencies and modes of vibration then the energy functional is discretized by using the natural modes of vibration and a system of nonlinear ordinary differential equations with cubic and quadratic nonlinear terms is obtained a pseudo arc length continuation and collocation scheme is used for bifurcation analysis of periodic solutions moreover to validate the numerical results experimental tests have been conducted for the fundamental vibration mode at several harmonic excitation amplitudes by using a laser doppler vibrometer to characterize the nonlinear response of the plate with imperfections and closed loop control of the excitation the effects of geometric imperfections on the trend of nonlinearity and on natural frequencies are fully discussed and the convergence of the numerical solutions has been verified

on shear deformable beam theories the frequency and normal mode equations of the homogeneous orthotropic bickford beam abstract this paper provides a step forwards the construction and documentation of the frequency equations and the characteristic functions of a general three degrees of freedom theory that describes the plane motion of shear deformable elastic beams the governing equations of this shear deformable beam theory g3dofbt involve a general shape function of the transverse beam co ordinate parameter the a posteriori choice of which specifies the distribution of the transverse shear strain or stress along the beam thickness different choices of this shape function produce as particular cases the corresponding governing equations of different beam theories these include the differential equations of the euler bernoulli beam theory as well as the corresponding equations of the shear deformable theories due to timoshenko and bickford other examples can also be found by considering the shear deformable beam theories produced as one dimensional versions of relevant refined plate theories since corresponding developments of the timoshenko beam theory are already available in the literature the bickford theory is considered as the pilot beam theory in this study the frequency equations the characteristic functions and the orthogonality conditions of this theory which assumes a through thickness parabolic distribution of the transverse shear strain or stress are constructed analytically for all the classical sets of boundary conditions applied at the beam ends some preliminary numerical results are also presented and discussed for beams having both their ends simply supported or clamped

linearized stability in periodic functional differential equations with state dependent delays in this paper we study stability of periodic solutions of a class of nonlinear functional differential equations fdes with state dependent delays using the method of linearization we show that a periodic solution of the nonlinear fde is exponentially stable if the zero solution of an associated linear periodic linear homogeneous fde is exponentially stable

free vibrations of multilayered plates based on a mixed variational approach in conjunction with global piecewise smooth functions abstract this paper presents a two dimensional model for the analysis of freely vibrating laminated plates the governing differential equations associated boundary conditions and constitutive equations are derived from reissner s mixed variational theorem both the governing differential equations and the related boundary conditions are presented in terms of resultant stresses and displacements the model is able to provide the results for the corresponding three dimensional theory such a performance is guaranteed from an appropriate expansion of relevant kinetic and stress quantities through the thickness of the multilayered plate the expansion is realized by using a novel selection of global piecewise smooth functions gpsfs the number of gpsfs can be arbitrarily increased to achieve a two dimensional plate theory which is at least as accurate as that of a full layerwise theory it is also shown that gpsfs permit to deal a multilayered plate as if it was virtually made of a single layer indeed the theory need not explicitly introduce continuity conditions for both displacements and relevant stresses the performance of the present two dimensional model in conjunction with the global piecewise smooth functions is tested and discussed by comparing its resulting eigen parameters for a class of simply supported plates with those of other two dimensional models and with those existing of the exact three dimensional theory

pfaffianization of the two dimensional toda lattice pfaffianization procedure due to hirota and ohta is applied to the two dimensional toda lattice as a result a pfaffianized version of the two dimensional toda lattice is found

a semi discrete kadomtsev petviashvili equation and its coupled integrable system we establish connections between two cascades of integrable systems generated from the continuum limits of the hirota miwa equation and its remarkable nonlinear counterpart under the miwa transformation respectively among these equations we are mainly concerned with the semi discrete bilinear kadomtsev petviashvili kp equation which is seldomly studied in literature we present both of its casorati and grammian determinant solutions through the pfaffianization procedure proposed by hirota and ohta we are able to derive the coupled integrable system for the semi discrete kp equation

global hopf bifurcation for differential equations with state dependent delay abstract we develop a global hopf bifurcation theory for a system of functional differential equations with state dependent delay the theory is based on an application of the homotopy invariance of s 1 equivariant degree using the formal linearization of the system at a stationary state our results show that under a set of mild conditions the information about the characteristic equation of the formal linearization with frozen delay can be utilized to detect the local hopf bifurcation and to describe the global continuation of periodic solutions for such a system with state dependent delay

global attractivity of nonautonomous stage structured population models with dispersal and harvest the nonautonomous stage structured single species dispersal model with harvesting of mature individuals in an n patch environment is considered in which the individual members of the population have a life history that takes them through two stages immature and mature by using the theory of monotone and concave operators to functional differential equations we establish conditions under which this population dynamical system admits a positive periodic solution which attracts all positive solutions

on state dependent delay partial neutral functional integro differential equations in this paper the existence of mild solutions for a class of abstract neutral integro differential equations with state dependent delay is studied

the effect of state dependent delay and harvesting on a stage structured predator prey model we propose and analyze a stage structured predator prey model in which the time from birth to maturity is directly related to the number of individuals present individuals mature more quickly when there are fewer of them around the state dependent time delay is taken to be an increasing differentiable bounded function in this research we study the dynamics of our model analytically we present results on positivity and boundedness of all populations criteria for the existence of all equilibria and uniqueness of a positive equilibrium are given in order to observe the effect of state dependent maturation delay local stability analysis around all equilibria of the proposed model is discussed due to variation of maturation delay also global stability of trivial and the boundary equilibria is investigated using liapunov functional and lasalle invariant principle to investigate the effect of state dependent maturation delay and the harvesting effort of all species we carried out numerical simulations

parameter uncertainty and design of optimal experiments for the estimation of elastic constants abstract this paper investigates an inverse technique for the identification of orthotropic elastic constants from measured plate natural frequencies in general the accuracy of the identified parameters depends on the method of estimation modelling errors and measurement errors the paper addresses the parameter uncertainty due to errors in the measurements based on assumptions of the measurement errors second order statistics of parameters are approximated by linearization schemes the main focus is on the possibility of designing the experiment to minimize the uncertainty of the estimated parameters the uncertainty of each estimate as function of the experimental design variables is investigated also the overall optimality of the experimental design defined as the hypervolume of the confidence region is considered the results show that not all parameters are estimated with a sufficient precision in the general case but by carefully designing the experiment the parameter uncertainties can be greatly reduced both thin and thick plates are considered with focus on single layer plates but the results for laminated plates are also discussed

two generalized higher order theories in free vibration studies of multilayered plates this paper presents an extension of two dimensional models for the analysis of freely vibrating laminated plates the extension concerns the enlargement of higher order theories recently introduced by different authors in several forms to encompass higher order terms over the cubic one usually taken into consideration higher order effects such as rotatory inertia and transverse shear stress are naturally included without any shear correction factors namely two different models are introduced by expanding on different functional bases displacements d2d and transverse shear stresses in conjunction with displacements m2d the expansion is considered to be consistent with the traction type boundary condition on the external surfaces of the plate the governing equations and associated boundary conditions are consistently obtained by the classical hamilton s variational principle and reissner s mixed variational theorem both models are equivalent single layer type and therefore differ according to the layer wise descriptions preserve the independence of the number of unknown variables on the number of layers however this feature is presented together with intrinsic physical violations for both models model d2d violates the interlaminar stress continuity requirement and model m2d violates in a weaker from the same requirement derivatives are not piecewise continuous besides neglecting the transverse normal stress the importance of completely fulfilling the mentioned continuity is then discussed once the relevant governing equations are tailored for the cylindrical bending condition the effectiveness of the models is indicated by making numerical comparisons with the exact three dimensional theory of the elasticity for several lamination schemes angle cross ply lay ups and characteristic geometric ratios for low and higher frequencies

on the general variable coefficient kp equation with self consistent sources a new general variable coefficient kp equation with self consistent sources and its grammian solutions is obtained by using the source generation procedure moreover by applying the pfaffianization procedure a new coupled variable coefficient kp equation is constructed its wronski type pfaffian solution and gramm type pfaffian solution are given at last a new integrable system of the general variable coefficient kp equation with self consistent sources is established

on the 2 1 dimensional gardner equation determinant solutions and pfaffianization in this paper we first present the casorati and grammian determinant solutions to the 2 1 dimensional gardner equation then by using the pfaffianization procedure of hirota and ohta a new integrable coupled system is generated from the gardner equation moreover gramm type pfaffian solutions to the pfaffianized system are proposed

on the nonisospectral kadomtsev petviashvili equation in this paper we first present the grammian determinant solutions to the nonisospectral kadomtsev petviashvili kp equation then by using the pfaffianization procedure of hirota and ohta an integrable coupled system is generated moreover gramm type pfaffian solutions to the pfaffianized system are proposed

matrix integral solutions to the discrete kp hierarchy and its pfaffianized version matrix integrals used in random matrix theory for the study of eigenvalues of hermitian ensembles have been shown to provide functions for several hierarchies of integrable equations in this article we extend this relation by showing that such integrals can also provide functions for the discrete kp hierarchy and a coupled version of the same hierarchy obtained through the process of pfaffianization to do so we consider the first equation of the discrete kp hierarchy the hirota miwa equation we write the wronskian determinant solutions to the hirota miwa equation and consider a particular form of matrix integrals which we show is an example of those wronskian solutions the argument is then generalized to the whole hierarchy a similar strategy is used for the pfaffianized version of the hierarchy except that in that case the solutions are written in terms of pfaffians rather than determinants

stability and hopf bifurcation analysis of an eco epidemic model with a stage structure abstract in this paper an eco epidemiological model with a stage structure is considered the asymptotical stability of the five equilibria the existence of stability switches about positive equilibrium is investigated it is found that hopf bifurcation occurs when the delay passes though a critical value some explicit formulae determining the stability and the direction of the hopf bifurcation periodic solutions bifurcating from hopf bifurcations are obtained by using the normal form theory and center manifold theory some numerical simulations for justifying the theoretical analysis are also provided finally biological explanations and main conclusions are given

on the pfaffianized kp equation with self consistent sources abstract a new procedure called source generation is applied to the pfaffianized kp equation as a result the pfaffianized kp equation with self consistent sources escs is obtained this coupled system cannot only be reduced to the pfaffianized kp equation but also reduced to the kp equation with self consistent sources kpescs so the pfaffianized kp escs can be viewed as a pfaffian version of the kpescs which indicates the commutativity of the source generation procedure and pfaffianization

analysis of a model representing stage structured population growth with state dependent time delay a stage structured model of population growth is proposed where the time to ma turity is itself state dependent it is shown that under appropriate assumptions all solutions are positive and bounded criteria for the existence of positive equilibria and further conditions for the uniqueness of the equilibria are given the stability of the equilibria are also discussed in addition an attracting region is determined for solutions such that this region collapses to the unique positive equilibrium in the state independent case

on the non isospectral kadomtsev petviashvili equation with self consistent sources abstract a new procedure called source generation is applied to construct non isospectral soliton equations with self consistent sources as results the non isospectral kadomtsev petviashvili equation with self consistent sources kpescs and its gramm type determinant solutions are obtained furthermore the non isospectral pfaffianized kp equation with self consistent sources is constructed this coupled system can not only be reduced to the non isospectral pfaffianized kp equation but also reduced to the non isospectral kpescs

a pfaffian version of the modified discrete kp equation we first present casorati determinant and gram type determinant solutions to a modified discrete kp equation and then produce a pfaffianized version of modified discrete kp equations by using hirota and ohta s pfaffianization procedure the solutions to a coupled modified discrete kp equation are expressed by two types of pfaffians

pfaffianization of the three dimensional three wave equation a pfaffianized version of the three dimensional three wave equation is found using hirota and ohta s pfaffianization procedure in addition n lump solutions to the pfaffianized system are presented

pfaffianization of the discrete three dimensional three wave interaction equation we first present the discrete gram type determinant solution to the discrete three dimensional three wave interaction equation then a pfaffianized version of the discrete three dimensional three wave interaction equation is produced by using hirota and ohta s pfaffianization procedure the gram type pfaffian solution to the resulting system is also given in addition we obtain the soliton solutions of the resulting system as an example of the gram type pfaffian solution

existence results for an impulsive abstract partial differential equation with state dependent delay in this paper we establish the existence of mild solutions for a class of impulsive abstract partial functional differential equation with state dependent delay

backlund darboux transformations for the coupled kp hierarchy using the geometry of the infinite isotropic grassmannian related to the hirota ohta coupled kp hierarchy we construct its elementary backlund darboux transformations

on the integrable discrete versions of the leznov lattice determinant solutions and pfaffianization in this paper we present the casorati form of the n soliton solution for an integrable fully discrete version and two integrable semi discrete versions of the leznov lattice which arise from the integrable discretization of the two dimensional leznov lattice by using the pfaffianization procedure of hirota and ohta a new integrable coupled system is generated from the semi discrete version of the leznov lattice in the y direction

the non isospectral modified kadomtsev petviashvili equation with self consistent sources and its coupled system abstract a new algebraic method called source generation procedure is applied to construct non isospectral soliton equations with self consistent sources as results the non isospectral modified kadomtsev petviashvili equation with self consistent sources mkpescs and its gramm type determinant solutions are obtained by using the source generation procedure furthermore a new coupled system of the non isospectral mkpescs and its pfaffian solutions are constructed

pfaffianization of the discrete kp equation we use the procedure of ohta and hirota to generate an integrable coupled system of discrete equations from the discrete kp equation

gram type pfaffian solution to the coupled discrete kp equation in this paper we first prove the grammian determinant solution to the discrete kp dkp equation by the algebraic identity of pfaffian instead of laplace expansion for determinants then we present the gram type pfaffian solution to the pfaffianized dkp system as an example the n soliton solution for the system is obtained

the asymptotic behavior of the strong solutions for a non autonomous non local pde model with delay abstract in this paper we study the asymptotic behavior of the strong solutions of a non autonomous non local pde model with time delay we present the existence and structure of the uniform attractor by constructing the skew product flow of the family of processes generated by the strong solutions in order to obtain the existence of the uniform attractor we prove the family of processes satisfies uniform condition c by using some special technique of phase space decomposition additionally it is shown that all the bounded complete trajectories are globally asymptotic stable under some assumptions as the application of our result we obtain a globally asymptotic stable nontrivial strong periodic solution of a non local pde model

existence results for fractional neutral integro differential equations with state dependent delay in this paper we study the existence of mild solutions for a class of abstract fractional neutral integro differential equations with state dependent delay the results are obtained by using the leray schauder alternative fixed point theorem an example is provided to illustrate the main results