Natural characteristics of rectangular plates clamped at 4 corner points

The natural characteristics of a rectangular plate clamped at 4 corner points are of importance in its application and fault diagnosis. Firstly, its Lagrange equation of transverse vibration based on the principle of energy conservation under constraint conditions of support locations was established to analyze its free vibration problem. Secondly, the frequency equation of the rectangular plate was obtained using Rayleigh-Ritz method with simple polynomials as its modal functions. Finally, the fundamental frequencies were gained for different side ratios according to the theoretical results of the rectangular plates, they were compared with those obtained using the finite element method. In order to get the fundamental frequencies conveniently, approximate expressions were deduced for a typical plate with certain geometrical parameters and material constants in practical engineering. It was shown that the theoretical results agree well with those obtained using the finite element method and the test data. ©, 2015, Chinese Vibration Engineering Society. All right reserved.