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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 extends the first order formulations presented in Part I to second order methods for relocation of structural natural frequencies from their initial design values to new modified frequencies. The method is based on an inverse formulation and solution algorithm of the eigenvalue problem. Using the second order Taylor''s expansion series, the required parameter variation to achieve a desired natural frequency shift for the structure is computed through second order differential or binomial equations. The proposed technique can also incorporate the design constraints or objective functions in the system equations. The formulations are quite generic and applicable to all finite element structures. The accuracy of the proposed methods is tested by conducting several case studies, the results of which demonstrate the validity of the technique for a wide range of practical problems. [Copyright &y& Elsevier]

This paper proposes an inverse strategy for relocation of structural natural frequencies using first order formulation and solution algorithm. In the proposed method a sensitivity analysis of the systems eigenvalues with respect to material or geometrical parameters of the structure is conducted initially. The required parameter variation to achieve a desired frequency shift for the structure is then computed. The proposed technique incorporates the design constraints or objective functions in the system equations in such a way that a square system of equations is always preserved. The formulations are general and applicable to all finite element structures because the sensitivity analysis is based on the stiffness and mass matrices regardless of the type of elements used. An algorithm suitable for implementation of the technique for practical purposes is developed. The accuracies of the proposed methods are tested conducting several case studies and the results are validated against exact solutions. [Copyright &y& Elsevier]

This paper presents formulations for inverse optimisation of vibration behaviour of finite element models of both truss and continuous structures. The proposed algorithms determine the required modifications on truss and continuous structures to achieve specified natural frequencies. The modification can be carried out globally or locally on the structures stiffness and matrices and the formulation can also be used to add new structural members to achieve the desired response. Numerical examples and finite element implementation of the developed method are provided to demonstrate the feasibility of the formulations. [Copyright &y& Elsevier]

An efficient relationship between geometric and material properties of pin-jointed truss structures and their eigenvalues is established. The problem is formulated as an inverse eigenvalue problem. This formulation allows the determination of the required modifications on the structural members to achieve specified eigenfrequencies. In addition to the modification of the existing structural elements, the formulation also allows addition of new structural elements to obtain the desired frequencies. Using the proposed inverse method, two cases of plane as well as space truss structures are studied and the results are compared with those obtained using the conventional optimization techniques adopted by commercial finite element codes. [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]