非线性兰姆波在阶梯板中传播的有限元仿真

Finite element simulation of nonlinear Lamb wave propagation in a plate with step discontinuities

在非线性兰姆波检测中,累积二次谐波是重要的检测信号。该文利用有限元法仿真了非线性兰姆波在阶梯板中的产生和传播过程,通过二维离散傅里叶变换分析了兰姆波的传播模态和各个模态通过波导横截面的能流大小,给出了各个模态在阶梯板中的反射、透射系数,总结了其随阶梯板厚度的变化规律。研究发现,随着台阶增高,散射效应使得兰姆波更难入射波导的薄端,使兰姆波的总透射能量降低,但是随着非线性兰姆波累积效应的增强,更多的能量会从基波馈入高次谐波,两种效应共同决定了非线性兰姆波的透射和反射系数,随着阶梯板厚度差的增加,向薄端传播的二次谐波能量先增加后减小,存在一个极大值。该文研究结果对深入研究非线性导波传播理论和发展非线性导波检测技术提供了借鉴。

In the application of nonlinear Lamb waves,amplitude of cumulative second harmonics is an important indicator.This paper analyzes the generation and propagation of nonlinear Lamb waves in a plate with step discontinuities,uses 2D discrete Fourier transform to identify the propagating Lamb modes and their power flow past the cross-sections of the plate,quantifies their reflection and transmission coefficients and their variation with respect to the height of the step.It is found that,as the height of the step increases,the scattering of Lamb waves will reduce the power flux transmitted to the thinner side of the plate and therefore reduces the total transmitted energy.However,as the accumulation of nonlinear Lamb waves becomes stronger,more energy will be transmitted from fundamental waves to higher harmonics.The scattering and accumulation of nonlinear Lamb waves determine the transmission and reflection coefficient of different Lamb modes.As the height of the step becomes larger,the energy of second harmonics transmitted to the thinner side of the plate will first increase and then decrease,reaching a maximum at a certain step thickness.This paper provides guidance to a deeper understanding of nonlinear guided wave propagation and the development of nonlinear guided wave testing.