Analyses of Chaotic Motion of Pre-Existing Microvoid in Hyperelastic Sphere Under Damping Force Interference
This paper investigated the dynamic characteristics of pre-existing microvoid in the center of sphere composed of a class of transversely isotropic incompressible Varga hyper-elastic materials.A mathematical model is established based on the equilibrium differential equation to describe the radially symmetric motion of the microvoid,and considers the load and damping force acting on the surface of the sphere through the initial and boundary con-ditions of the differential equations.The analyses and conclusions are as follows:1)Under the effect of constant load,qualitative analyses are conducted on the system,with a focus on discussing the impact of material parameters and structural parameters on system's equi-librium points and nonlinear response.Owing to the the strong nonlinearity of the system,the microvoid motion within the hyperelastic sphere exhibites asymmetric"∞"homoclinic or-bits.2)Under the influence of periodic load and damping force,using methods like the phase trajectory curves,amplitude-frequency curves,Melnikov method,bifurcation diagrams,and Poincaré sections,the paper reveals dynamic phenomena such as superharmonic resonance,quasi-periodic motion,and chaotic motion of the system.
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