Free vibration analysis of free rectangular plate on one side of three-sided support

elastic sheets;  Free vibration;  Orthogonality of the shape of the shape

The plate free vibration shape must have orthogonality, and the expression of the free rectangular plate vibration function expression of the three-sided support side can meet the vibration differential equation and all boundary conditions by using the main vibration direction ordering method, and has the orthogonality of the mode shape. The number of vibration waveforms in this shape curve is unique in the direction of the main oscillation and not unique in the other direction, and the shape of the shape curve conforms to the deformation form that can be defined by the boundary conditions of the plate. By proving the existence of mode shape orthogonality, analyzing the structural form of the mode function expression, deriving the frequency equation of rectangular plates with different boundary conditions, calculating the self-resonance frequency of the plate and the corresponding mode shape, and comparing it with the results of predecessors, the correctness of the method is theoretically explained.