摘要
运用微分算子形式推导出了时域内同时考虑拉伸与剪切粘性及转动惯量的粘弹性梁在切向均布随从力作用下的统一屈曲运动微分方程,该方程具有广泛的通用性,适合于任一粘弹性模型。进而得到三参量模型粘弹性非保守梁的屈曲运动微分方程。采用幂级数法建立两端简支、两端固定和左端简支右端固定等支承条件下三参量模型粘弹性梁离散化的动力方程——复特征方程。通过拟牛顿法,得到了一阶复特征值的负实部(衰减系数)及虚部(衰减振动频率)与切向均布随从力的变化曲线。
The unified differential equation of buckling and motion of viscoelastic beams under uniformly distributed follower forces in time domain is established by differential operators. The equation has extensive applicability and is suitable for various viscoelastic models. The governing equation of a three-parameter viscoelastic model is obtained. The dynamic descretization equation (complex eigenvalue) of viscoelastic beams of three-parameter model under follower forces is derived by power series method. Boundary conditions such as simply-simply, clamped-clamped and simply-clamped ends are considered. The curves of negative real part (decaying coefficient) and imaginary part (decaying vibration frequency) versus uniformly distributed follower forces are obtained using quasi-Newton method.
出处
《工程力学》
EI
CSCD
北大核心
2005年第3期26-30,38,共6页
Engineering Mechanics
关键词
粘弹性梁
动力稳定性
幂级数法
随从力
微分算子
Buckling
Differential equations
Dynamics
Equations of motion
Stability
Viscoelasticity
