轴向运动黏弹性梁横向非线性受迫振动

运用微分求积法数值研究不同边界条件下轴向运动黏弹性梁受到简谐外激励的横向受迫

Transverse non-linear forced vibration of axially moving viscoelastic beam

Forced vibration of axially moving viscoelastic beams constrained by simple supports with torsional springs was investigated by using differential quadrature method. Under certain conditions,the boundary conditions of the hybrid supports may degenerate into the conditions of simply supports or fixed supports.It is assumed that the excitation is spatially uniform and temporally harmonic. The time derivatives of material properties were used in the viscoelastic constitutive relations. The differential quadrature schemes were developed to solve numerically the steady state responses of a nonlinear partial-differential equation model and also of a nonlinear integro-partial-differential equation model. Numerical examples results demonstrate the amplitudes of steady-state responses decrease with the increase of torsional stiffness. The amplitudes predicted by the fixed supported conditions are smaller than those by the simply supported conditions,and the two models yield the same trend of amplitude variation,but the amplitudes predicted by nonlinear integro-partial-differential equation are bigger than those by nonlinear partial-differential equation.