境界要素法による種々の形状の膜の非線形振動解析

抄録

The nonlinear vibrations of membranes with various shapes are analyzed by the boundary element method. In order that the application of the boundary element method may be practical in such nonlinear dynamic problems, a treatment that produces modal equations from the governing nonlinear partial differential equations is employed. In this way, it is shown that the original problem is reduced to solving successively several easier problems, and that the modal equations derived thus enable the treatment of various nonlinear oscillations. As an example of the application of this treatment, rectangular and circular membranes are first analyzed, the results of which are compared with other published data to confirm the validity of the treatment. Then, trapezoidal and elliptical membranes are analyzed, and some typical nonlinear oscillations such as subharmonic and summed-and differential harmonic oscillations are shown to occur.