摘要
研究受面内载荷影响作轴向变速运动正交各向异性薄板横向振动的稳定性。通过Hamilton原理得到板横向振动的运动微分方程。将多尺度法直接应用于运动微分方程,利用可解性条件得到次谐波共振和组合共振的稳定边界。给出数值算例说明轴向平均速度、激励幅值对稳定性边界的影响。
The stability is investigated for transverse vibration of an axially moving orthotropic plate under in-plane loading. The axially moving velocity is assumed as small periodic variation about a constant value. The governing equation of the system is obtained by Hamilton＇ s principle and then the method of multiple scales is applied directly to the governing partial differential equation without trun- cation. Based on the solvability condition derived from eliminating secular terms, the stability boundaries are obtained for the change of frequency and amplitude of speed variation in the cases of subharmonic resonance and combination resonance. Numerical examples are presented to show the contributions of axially moving speed and excitation magnitude to the stability boundaries. Furthermore, the critical axially moving speed where instability range becomes minimum is found for both the subharmonic and combination resonance.
出处
《机械强度》
CAS
CSCD
北大核心
2010年第4期531-535,共5页
Journal of Mechanical Strength
基金
国家自然科学基金资助项目(10702045)~~
关键词
正交各向异性板
次谐共振
组合共振
多尺度法
Orthotropic plate
Subharmonic resonance
Combination resonance
Method of multiple scales
