Abstract

Nonlinear Generation and Propagation of Lamb Waves

M.Deng (Department of Physics, Logistics Engineering University, Chongqing, China)

e-mail: hgwldmx@cta.cq.cn

In this article we have developed a technique for analyzing the nonlinear generation and propagation of Lamb waves in a solid plate. The nonlinearity is treated as a second-order perturbation of the linear elastic response. Some interesting features of the physics of the second harmonics of Lamb waves are given. The analyses are performed for these cases in which the phase velocities of fundamental Lamb modes are exactly and approximatively equal to those of double frequency Lamb modes, respectively. The formation process of the second harmonics with cumulative growth effects and the corresponding solutions are presented. It is found that the phases of partial waves of the second harmonics are proportional to the propagation distance for the case in which the phase velocities of fundamental and duple frequency Lamb modes are approximately equal. The range of propagation distance of the second harmonics with cumulative growth effects is given. Numerical results show that the appropriate dispersion of Lamb modes may cause the accretion of normal displacement components of the second harmonics on the solid plate surface. This effect may be of significance in practical measurement of nonlinear effects of Lamb waves.

Section : 2