周辺固定矩形板のランダム加振に対する非線形応答の実験と解析

抄録

Probabilistic property of a nonlinear vibration of a rectangular panel is studied analytically and experimentally. The test model of a rectangular panel with clamped edges was clamped on an electromagnetic shaker and was randomly excited under approximately band-limited white noise of acceleration. In order to prevent thermal effect on the inplane stress condition of the panel, super-invar whose thermal expansion coefficient is 1×10^-7 was used as the materials of the test plate and clamping block. Probabilistic quantities of a center deflection and an edge strain were measured through a real time auto-correlator and a FOURIER transformer. The deflection is expanded in the series of independent modes, and a set of nonlinear equations of vibration of multi-degree of freedom, having nonlinear damping terms, are derived in the frame work of the linear viscoelastic stress-strain relation and the large deflection theory of a thin plate. The solution of the equation of three mode approximation are numerically obtained by using a simulation method. A good agreement is observed between the experiment results and the simulation solution. Besides, statistical linearization technique is used to calculate the root mean square and is found to give fairly good approximate solution. It is clarified that the three-mode approximation and nonlinear damping force are required to get a good agreement between theory and experiment.