The Interaction Bewteen The Highly Nonlinear Solitary Waves And Functionally Graded Material

One-dimensional(1-D) granular chain is a special medium. In chain of the particles, the dynamic response encompass linear, weakly nonlinear, and strongly nonlinear regimes. The strongly nonlinear dynamic response supports the formation and propagation of highly nonlinear solitary waves. The solitary waves is a superior information carrier with a highly stability and controllability.Functionally graded materials(FGM) is a new material. The material attribute(composition, structure)change gradually along a direction. Thus, the properties also change gradient along the same direction. The most work are focused on the mechanical property and optimization design. Based on the research on structural health monitoring and nondestructive evaluation of elastic plate applying highly nonlinear solitary waves, we comprehensively explore the sensitivity of reflected solitary wave on material properties, geometric configuration.Based on the highly nonlinear solitary waves in granular chain, we investigate the coupling mechanism between 1-D granular chain with FGM and conduct finite element analysis. The main contents are described as follows:1 .Briefly introducing the properties of particle and particle chain: Based on the Newton's cradle,we introduce the special medium——the particle granular chain. And we describe the content we will present in this paper. Secondly, Based on the Hertz's contact law we get the relationship between the compression and contact force when particle chain interacting with the structure. When we confirm the number of particles and the properties of particle chain, we will get the coupling differential equations by Newton's second law.2.Studying the coupling mechanics between granular chain and semi-infinite functionally graded materials: Based on the Hertz's contact law and the relationship between load and indentation depth in semi-infinite FGM, we obtain the differential equation system numerically and use fourth-order Runge-Kutta method to solve the equation. The curves of the velocity and displacement of the middle particle under different elastic and gradient parameters are obtained. Ultimately, it is demonstrated whether the granular chain is sensitive to the material attributes of FGM.3. Studying the granular chain with functional graded thin plate: Considering the Hertz law?the relationship between load and indentation depth in semi-infinite FGM and the intrinsic inelasticity of large plates, we get the differential equation system numerically and use Runge-Kutta method to solve the equation. The curves of the velocity and displacement under different Physical parameters are obtained. Finally we explore whether the granular chain is sensitive to the material attributes and geometry dimension of FGM.4?Modeling and simulation with finite element: analyze the interaction between single granular and semi-infinite homogeneous material; analyze the interaction between 1-D granular chain and semi-infinite homogeneous material.