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Application of an analytical method for solving the problems of vibrations of sandwich shell with damping

Cabańska-Płaczkiewicz K.

Journal of Technical Physics

2008

Vol. 49, no 2

113-128

This paper deals with implementation of the generalized-exact method for solving the problems of vibrations of the cylindrical sandwich shell with damping. The essential procedures of this paper are based on a set of generalized principles of the analytical method. The primary operation is the variables separation in the homogeneous system of partial differential equations describing free vibrations of this shell. The effect of this separation is a single homogeneous ordinary differential equation concerning the complex modal function with respect to the time-variable, and a homogeneous system of the ordinary differential equations concerning the complex modes with respect to the spatial variable. The following basic procedure is imposition of the assumed boundary conditions on the solution of the system of the ordinary differential equations, i.e. formulation of the boundary-value problem. The results of the solution of the boundary-value problem are two infinite complex sequences, i.e. eigen-frequencies and eigenvectors of eigenfunctions corresponding to the eigenfrequencies and satisfying the fundamental principle of orthogonality. The above-mentioned results are then used in other procedures. The penultimate procedures refer to solving the free vibrations problem. The essence of these procedures is determination of the integration constants appearing in the modal function by means of a generalized formula with respect to the initial conditions. The last, also significant procedures relate to solving the forced vibrations by means of a certain set of generalized formulae assigned to the analytical method.