Nonlinear Solitary Wave In Elastic Wave Metamaterials With Discrete Particles

In recent years,phononic crystals and elastic wave metamaterials have received a lot of attention.Besides the linear cases,there is the interaction between nonlinear parameters and waves in nonlinear phononic crystals and metamaterials,which can result in more complex wave properties.As a typical periodic structure with nonlinear characteristics,descrete granular elastic wave metamaterials are an important topic in the field of elastic wave metamaterials and the main research object of this thesis.Solitary waves have good stability during their transmission,which results in that their waveform can be kept and propagation speed is unchanged.The research on solitary waves in the discrete particle chain is very important.This work studies about the propagation characteristics of solitary waves in discrete granular nonlinear elastic wave metamaterials.The main contents and conclusions of this thesis include:1.Based on the assumptions of small deformation and long-wavelength,the wave equation of the pre-compressed particle chain is converted into the KdV form by the introduction of space movable coordinate and slow-time variable.And the expressions of incident,reflected and transmitted solitary waves are obtained.By the numerical method with the finite difference derivation,it is found that the collision of solitary waves at the interface does not affect the transmission characteristics of each other.Moreover,the adjustment of collision and transmission of nonlinear solitary waves in the granular chain are realized.2.With the introduction of several variables,the uncoupled equations of nonlinear wave equations are derived and expressions of the bright,dark and peaked solitary wave solutions of the pre-compressed particle chain with local resonators are obtained.The influences of the pre-pressure and wave speed on three solitary waves are also discussed,which further show that the propagation characteristics of solitary waves can be tuned by changing the pre-pressure.The Runge-Kutta method is used during the numerical simulation and experiments are performed to support theoretical results.3.Two non-destructive test devices are designed by nonlinear elastic wave metamaterial with solitary waves.The curved cavity and vertical cavity tracks,as well as scattered,impact and signal acquisition particles are included.These devices apply the signal transmission in several tracks to achieve the non-destructive test at different points and one location with constitutive testing.It shows the superior properties because the efficiency and accuracy of non-destructive testing are enhanced.