Fan Jiashen. Analytical Solution for Mode Ⅱ Dynamic Rupture of Standard Linear Viscoelastic Solid With Nonlinear Damping[J]. Applied Mathematics and Mechanics, 2000, 21(4): 415-423.
Citation: Fan Jiashen. Analytical Solution for Mode Ⅱ Dynamic Rupture of Standard Linear Viscoelastic Solid With Nonlinear Damping[J]. Applied Mathematics and Mechanics, 2000, 21(4): 415-423.

Analytical Solution for Mode Ⅱ Dynamic Rupture of Standard Linear Viscoelastic Solid With Nonlinear Damping

  • Received Date: 1998-11-23
  • Rev Recd Date: 1999-04-20
  • Publish Date: 2000-04-15
  • 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 order three is obtained.Then,applying the small parameter expansion method,linearized asymptotic governing equation for each order of the small parameter is obtained.Dividing the order three 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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