Solving hybrid support boundary condition of an axially accelerating viscoelastic beam via Differential Quadrature scheme
Wang Bo 1; Chen Liqun 2,3
1. School of Mechanical Engineering, Shanghai Institute of Technology, Shanghai 201418, China;2. Department of Mechanics, Shanghai University, Shanghai 200444, China;3. Shanghai Institute of Applied Mathematics and Mechanics, Shanghai University, Shanghai 200072, China
Abstract:A methodology that to solve hybrid support boundary condition of nonlinear axially accelerating viscoelastic beam via Differential Quadrature scheme is presented. Differential Quadrature scheme is employed to solve numerically nonlinear governing differential equation of an axially accelerating viscoelastic beam under hybrid support. The procedure how hybrid support boundary condition is built to the Differential Quadrature weighting coefficients matrices themselves is explained. Steady-state response is investigated when the principal parameter resonance of axially accelerating viscoelastic beam occurs. Numerical and analytical solutions are compared in numerical examples.