微结构固体中孤立波的动力稳定性

DYNAMICAL STABILITY OF SOLITARY WAVE IN MICROSTRUCTURED SOLIDS

描述微结构固体中波传播的一种KdV类方程作为控制方程并利用积分因子方法,对微结构固体中传播孤立波的动力学稳定性进行了数值模拟研究.主要以高斯波、Ricker子波以及双曲正割波扰动作为初始扰动,考察了不同小扰动下孤立波能否较长时间保持波形结构和传播速度而稳定传播问题.结果表明,不同的小扰动对孤立波的影响不同,孤立波的稳定传播与扰动幅度和宽度都有关系,只有受到幅度和宽度都非常小的扰动下在弱微尺度非线性效应的微结构固体中传播的孤立波才能显现出一定程度的抗干扰性和动力学稳定性,能够在微结构固体中较长时间稳定传播.

A KdV-like equation describing wave propagation in microstructured solids as governing equation,the dy⁃namical stability of solitary waves propagating in microstructured solids was numerical simulated using the method of in⁃tegrating factors.Taking Gaussian wave,Ricker wavelet and Hyperbolic secant wave as initial disturbances,stable prop⁃agation keeping structure of waveform and propagation speed of solitary wave for a long time was investigated,under those three small disturbances.The simulation results show that different small disturbances have different effects on soli⁃tary wave,the stable propagation of solitary wave is related to the amplitude and width of the disturbances.Only under disturbances of very small amplitude and width,the solitary waves can exhibit a certain degree of anti-interference and dynamical stability,and can stably propagate in microstructural solids with weak microscale nonlinear effects for a long time.