Shock wave structure in a strongly nonlinear lattice with viscous dissipation

作     者：E. B. Herbold V. F. Nesterenko 

作者机构：Department of Mechanical and Aerospace Engineering University of California at San Diego La Jolla California 92093-0411 USA Materials Science and Engineering Program University of California at San Diego La Jolla California 92093-0418 USA 

出 版 物：《Physical Review E》 (物理学评论E辑：统计、非线性和软体物理学)

年 卷 期：2007年第75卷第2期

页      面：021304-021304页

核心收录：

学科分类：07[理学] 070203[理学-原子与分子物理] 0702[理学-物理学] 

主　　题：SOLITARY WAVES CHAINS PROPAGATION SPHERES 

摘      要：The shock wave structure in a one-dimensional lattice (e.g., granular chain of elastic particles) with a power law dependence of force on displacement between particles (F∝δn) with viscous dissipation is considered and compared to the corresponding long wave approximation. A dissipative term depending on the relative velocity between neighboring particles is included to investigate its influence on the shape of a steady shock. The critical viscosity coefficient pc, defining the transition from an oscillatory to a monotonic shock profile in strongly nonlinear systems, is obtained from the long-wave approximation for arbitrary values of the exponent n. The expression for the critical viscosity is comparable to the value obtained in the numerical analysis of a discrete system with a Hertzian contact interaction (n=3∕2). The expression for pc in the weakly nonlinear case converges to the known equation for the critical viscosity. An initial disturbance in a discrete system approaches a stationary shock profile after traveling a short distance that is comparable to the width of the leading pulse of a stationary shock front. The shock front width is minimized when the viscosity is equal to its critical value.