等方性弾性平板における非線形三波相互作用の数値解析

抄録

The three-dimensional dynamic finite element analysis of nonlinear wave propagation in an isotropic elastic plate is performed to investigate the non-collinear interaction of guided elastic waves. The material nonlinearity of the plate is accounted as a hyperelastic material with the second- and third-order elastic constants. It is shown that a third wave (scattered wave) is nonlinearly generated when two identical lowest-order antisymmetric plate waves (primary waves) with the frequency of 500 kHz intersect in the plate. By carrying out the two-dimensional Fourier transform, the scattered wave is found to be the lowest-order symmetric Lamb mode with the frequency of 1 MHz, corresponding to the sum frequency of the primary waves. Furthermore, the amplitude of the scattered wave is shown to be significantly influenced by the intersection angle of two primary waves. In particular, the scattered wave is found to have the larger amplitude when the resonance condition is nearly met, i.e., the wavevector of scattered wave approximately coincides with the sum of those of primary waves.