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This article presents an inverse formulation of the eigenvalue problem for computing the required changes in laminated composite plates in order to achieve desired dynamic characteristics in the structure. The stiffness and mass matrices of the plated structure are first derived using the finite element formulation based on the first-order shear deformation theory (FSDT) for laminated composite plates with arbitrary angle-ply stacking sequence. Based on this formulation and using the first- and second-order Taylor expansion both the direct and inverse eigenvalue problems are formulated to find the changes in eigenvalues due to an arbitrary change in physical or geometrical properties of the structure. An initial sensitivity analysis is conducted to identify the layer in which modification of design variables have the most influence on the structures dynamic characteristics. The design variables in this context are defined as the fiber angles in each layer and the layer thickness. The proposed algorithm is applied to several case studies to demonstrate the application and the accuracy of the proposed formulation in solving the direct and the inverse eigenvalue problems with one and two design variables. Dynamic behavior modification of a plate is performed using the inverse approach, and the required modified stacking sequence is obtained to shift the natural frequencies to desired values. [ABSTRACT FROM AUTHOR]

This paper investigates the effect of cut-outs on the dynamic behaviour of cylindrical panels, using a newly developed strain based finite element. The developed element is based on assumed strains and has only five necessary degrees of freedom at each corner node. The displacement fields of the element satisfy the exact requirement of rigid body displacements. The efficiency of the element is tested by applying it to the calculation of natural frequencies of shells. Investigations are first carried out to test the convergence of the element and to establish the mesh size to be used. The element is further applied to analyse cylindrical panels with cut-outs. Simply supported as well as clamped panels on their edges were considered and the effects of the size and location of the openings on the natural frequencies are investigated. The subspace iteration technique which is shown to have an economising effect, is used to obtain the natural frequencies and the associated modes of vibration. [Copyright &y& Elsevier]

Abstract: This paper proposes a new method for performing predefined simultaneous modification of natural frequencies and buckling loads of composite cylindrical panels. The method is based on the fact that both natural frequencies and buckling loads are eigenvalues of an algebraic system of simultaneous equations. First- and second-order derivatives of these eigenvalues are calculated and the first two terms in Taylor expansion are used for developing a modification procedure that is defined as an inverse eigenvalue problem. A four-layered composite cylindrical panel with an arbitrary angle-ply stacking sequence is considered as a case study and several simultaneous modifications for natural frequencies and buckling loads are carried out. It is shown that the proposed method can perform the predefined modification with an acceptable accuracy even for large perturbations in objective functions. [Copyright &y& Elsevier]

Abstract: In this paper, the first and second order derivatives of natural frequencies and buckling loads with respect to an arbitrary geometrical or physical property of a plate structure are calculated. Based on these eigenderivatives, and by using first and second order Taylor expansions, an approximate method is presented for simultaneous modification of natural frequencies and buckling loads. In the proposed method, the structural modification is considered as an inverse eigenvalue problem and calculated eigenderivatives are used for transforming this inverse problem to solving a system of algebraic equations. By solving this set of equations, the necessary changes in design parameters are calculated, in order to achieve predefined simultaneous shifts in natural frequencies and buckling loads. A plate with two boundary conditions is considered as a case study. The plate is divided into eight regions and the plate thickness in each region is considered as a design parameter. By considering several case studies, the required modification in design variables is calculated for achieving a predefined change in natural frequencies, buckling loads or simultaneous change of both. In each case, the calculated changes in design variables are implemented on the initial structure, and the changes in eigenvalues are computed using FE method. It is shown that the results from presented method compare very well with those obtained from a direct optimization procedure. [Copyright &y& Elsevier]