Vibrations of multilayer plates under the effect of impulse loads. Three-dimensional theory
In the case of relative thickness, two-dimensional theories of multilayer plates yield incorrect results by the investigation of wave processes. The behavior of multilayer plates can be described more accurately by using the three-dimensional theory of elasticity. In the reviewed paper, the authors propose an analytical numerical approach to the study of transient vibrations of a multilayer plate under impulsive loading by employing the three-dimensional theory of elasticity. The behavior of plate is described by Lamé's equations. The solution for displacement functions are expressed as double Fourier series in direction of plane coordinates, satisfying boundary conditions on the plate contour. The partial derivatives of these functions in the direction of the normal coordinate are replaced by their finite-difference approximations. As a result, the problem is reduced to the integration of a system of ordinary differential equations with constant coefficients. The procedure described in this paper allows to obtain the solution of the title problem without large computational difficulties.
system of ordinary differential equations with constant coefficients
scientific article; zbMATH DE number 1341404