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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