Precise solution for free vibration of rectangular plates supported on four sides

elastic sheets;  Free vibration;  Exact solution

The concept of the main vibration direction of rectangular plate vibration is proposed, and the vibration waveform of rectangular plate is unique in the main vibration direction, so that the unified vibration function expression of the four-sided supporting rectangular plate is established, and the frequency equation of the free vibration of the plate and the corresponding mode shape curve are derived, except for a pair of side simple branches, a pair of side fixed rectangular plates and three-sided simple branches, and one side fixed rectangular plate only occurs a pair of side simple branch directions of vibration in the main vibration direction, the rest of the plates have two main vibration directions.