Applied Mathematics and Mechanics (English Edition) ›› 2000, Vol. 21 ›› Issue (4): 461-470.

• 论文 • 上一篇    下一篇

ANALYTICAL SOLUTION FOR MODE Ⅲ DYNAMIC RUPTURE OF STANDARD LINEAR VISCOELASTIC SOLID WITH NONLINEAR DAMPING

范家参   

  1. Department of Civil Engineering, Yunnan Polytechnic University, Kunming 650061, P. R. China
  • 收稿日期:1998-11-23 修回日期:1999-04-20 出版日期:2000-04-18 发布日期:2000-04-18
  • 基金资助:
    the Science Research Foundation of Yunnan Provincial Education Committee (9712063)

ANALYTICAL SOLUTION FOR MODE Ⅲ DYNAMIC RUPTURE OF STANDARD LINEAR VISCOELASTIC SOLID WITH NONLINEAR DAMPING

Fan Jiashen   

  1. Department of Civil Engineering, Yunnan Polytechnic University, Kunming 650061, P. R. China
  • Received:1998-11-23 Revised:1999-04-20 Online:2000-04-18 Published:2000-04-18
  • Supported by:
    the Science Research Foundation of Yunnan Provincial Education Committee (9712063)

摘要: Introducing the nonlinear Rayleigh damping into the governing equation of the Mode Ⅲ dynamic rupture for standard viscoelastic solid, this equation is a partial differential and integral equation. First, eliminating the integral term, a PDE of third-order is obtained. Then, applying the small parameter expansion method, linearized asymptotic governing equation for each order of the small parameter is obtained. Dividing the third-order PDE into an elastic part with known solution, the rest part pertains to viscous effect which is neither a Mathieu equation nor a Hill one. The WKBJ method is still adopted to solve it analytically.

Abstract: Introducing the nonlinear Rayleigh damping into the governing equation of the Mode Ⅲ dynamic rupture for standard viscoelastic solid, this equation is a partial differential and integral equation. First, eliminating the integral term, a PDE of third-order is obtained. Then, applying the small parameter expansion method, linearized asymptotic governing equation for each order of the small parameter is obtained. Dividing the third-order PDE into an elastic part with known solution, the rest part pertains to viscous effect which is neither a Mathieu equation nor a Hill one. The WKBJ method is still adopted to solve it analytically.

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