Transverse Wave Propagation in a Thin Isotropic Plate Part I

This article deals with the propagation of a transverse wave in a thin rectangular isotropic plate, which is fixed around the perimeter. The transverse wave is generated by an impact falling on the geometric center of the plate. The solution is performed analytically in the MATLAB software environment for Kirchhoff and Rayleigh geometric models and Hooke’s model. The introduction to the article outlines a very brief history of the solution, followed by a general analytical solution. The basic relations for displacements and velocities in the direction of the x, y, z axes are derived. Under the defined assumptions, the deformations in the individual axes and the rotation of the axes are also solved. Part of the general solution is the derivation of relations for normal and shear stresses, as well as the magnitudes of shear and normal forces and bending moments. Attention is also paid to determining the relationships for different types of excitation loads of the board. The relations for Kirchhoff’s and Rayleigh’s model are derived, as well as the results of the analytical solution at selected points of the plate. A comparison of the results of the solution of both models, i.e., Kirchhoff’s and Rayleigh’s, is performed, both in terms of displacements, velocities, and normal stresses.