The Interaction Between The Highly Nonlinear Solitary Waves And Viscoelastic Medium

The stress waves can form and propagate stably when one-dimensional granular chains without pre-compression is impacted by a particle with a initial velocity.These waves reflect just until encounter the boundary and their propagation velocity and particle velocity,the stress perturbation is nonlinear,called highly nonlinear solitary waves(HNSWS).The HNSWS's good information transfer function and stable equilibrium make it applicable to the field of non-destructive testing.It uses the coupling effect of the one-dimensional particle chain and the measured structure to achieve the detection purpose through the analysis of the rebound stress wave.In this paper,we study the interaction between highly nonlinear solitary waves and viscoelastic media based on one-dimensional particle chains and takes the collision of one-dimensional particle chain and viscoelastic medium as the research object.Through numerical analysis,we use the analysis of incident wave and rebound wave to demonstrate whether one-dimensional particle chain is sensitive to the inherent properties of viscoelastic medium.The main research contents are as follows::1.Research on the motion characteristics of one-dimensional particle chain:Through the Hertz's contact law,the relationship between the contact force of two particles after contact and the amount of compression is deduced.Using this relationship and Newton's law,we deduce the differential equations of motion of particles in granular chains,except for the end particles.2.Research on the coupling of HNSWS and viscoelastic half-space:First,the viscoelastic medium is simplified as a viscoelastic half-space model with only a few parameters,and the most important thing is to solve the contact problem between the end particle and the viscoelastic half-space.Then the integral differential equation of the HNSWS and viscoelastic half-space is established.By solving the equations numerically and obtaining perturbation velocity curves and displacement curves of particles,the effects of elastic modulus and viscous coefficient of viscoelastic half-space on solitary waves are analyzed and whether the solitary wave is sensitive to the elastic modulus and viscosity coefficient of the viscoelastic half-space is explored.1.Research on the coupling of HNSWS and viscoelastic large plates:The inelastic theory of the elastic plates is extended to the viscoelastic large plates,and then the deflection differential equations of the viscoelastic large plates are established.Then a complete differential equation for the coupling of HNSWS and viscoelastic large plate is established.By solving the equations numerically and obtaining perturbation velocity curves and displacement curves of particles,the influence of the thickness,density,Poisson's ratio,modulus of elasticity and viscosity of the viscoelastic large plate on the rebound solitary wave are analyzed and whether the solitary wave is sensitive to these parameters of the viscoelastic large plate is explored.The research results of this paper provide a theoretical basis for the non-destructive testing of viscoelastic materials with highly nonlinear solitary waves,and provide a broad application prospect for the practical application of solitary waves.