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This paper presents a new spectral element based on the dynamic stiffness matrix of a prestressed cylindrical shell. The dynamic stiffness matrix is built using first-order shear deformation theory, and natural frequencies are processed easily. Vibration analyses are performed with numerical examples to determine the performance of this approach and the effect of prestressing on frequency response functions. This element has many advantages over the finite element method in terms of accuracy, model size and computing time. [ABSTRACT FROM AUTHOR]

This paper describes a procedure for taking into account distributed loads in the calculation of the harmonic response of a cross-ply laminated circular cylindrical shell using the dynamic stiffness method. This work is a direct continuation of a previous work concerning isotropic materials. Equivalent loads are established on element boundaries to determine the response of the system. Therefore, the vibration analysis is solved with numerical examples in order to determine the performances of this approach. The method allows reducing both the size of the model and computing time, and ensures higher precision compared to the finite element method. [ABSTRACT FROM AUTHOR]

The aim of this paper is to describe a procedure for computing the dynamic stiffness matrix relative to the in-plane effect for an orthotropic rectangular plate. The dynamic stiffness matrix is calculated for free edge boundary conditions. The formulation is based on strong solutions for the equations of motion for an orthotropic plate obtained with the Levy series and a Gorman decomposition of the free boundary conditions. The results obtained for the in-plane harmonic response are validated by the Finite Element Method. [ABSTRACT FROM AUTHOR]

Abstract: This paper describes a procedure for taking into account distributed loads in the dynamic stiffness matrix formulation, also known as the continuous element method. In that formulation, concentrated or linearly distributed loads are taken into account by considering the necessary number of elements in such a way that these loads are applied on element boundaries. As for distributed loads such as pressure and surface forces, they were not provided for in the formulation. The validation is achieved by comparison of accuracy and computational time of harmonic response calculations performed by the continuous element model and a finite element model. [Copyright &y& Elsevier]

Abstract: This paper describes a procedure for calculating the dynamic stiffness matrix of tubular shells with free edge boundary conditions. Such an analysis forms the basis for the Continuous Element Method. The method is used to formulate a thick axisymmetric shell element which takes into account rotatory inertia, transverse shear deformation and non-axisymmetric loadings. [Copyright &y& Elsevier]

A novel Lévy series for developing a dynamic stiffness matrix for a completely free orthotropic Kirchhoff plate is presented in this paper. The bending behavior is based on the Kirchhoff–Love thin-plate theory. The dynamic stiffness matrix is derived using the new Lévy series without classical symmetry decomposition, simplifying the building procedure. Harmonic responses obtained by this method and the finite element method are compared to establish the rate of convergence and the degree of precision of the current formulation. [Display omitted] • We present new Lévy series for calculating the dynamic stiffness matrix of free orthotropic plates. • Free boundary conditions are required for plate assemblies. • Modal analysis and harmonic analysis are presented. • The numerical validation is achieved thanks to comparisons with FE results. [ABSTRACT FROM AUTHOR]