摘要
建立了小挠度矩形薄板在非线性弹性地基上受均布横向简谐激励作用的动力学方程,利用Galerkin方法将其转化为非线性振动方程。应用多尺度法求得了系统主共振情况的一次近似解,并进行了数值计算。得到了系统主共振稳态响应的转迁集和分岔图。分析了阻尼系数,地基系数,板厚等对系统主共振影响。结果表明,随着地基系数和阻尼系数的增加,振幅减小;随着薄板厚度的增加,振幅增大。
A nonlinear dynamical equation of the small deformation thin rectangular plates on nonlinear elastic foundation subjected to harmonic excitation is established. It is transferred to be a nonlinear vibration equation by Galerkin＇s method. By means of the method of the multiple scales the first approximate solution of the primary resonance of the system is acquired, and numerical calculation is carried out. The transition variety and bifurcation diagram of the unfolding parametric plane are given. The response curves of the primary resonance are affected by damping parameter, foundation parameter and geometry parameter. It is pointed out that with the increasing of foundation coefficient and damping coefficient, the amplitude reduces. With the increasing of the thickness of thin plate, the amplitude increases.
出处
《岩石力学与工程学报》
EI
CAS
CSCD
北大核心
2005年第A02期5745-5750,共6页
Chinese Journal of Rock Mechanics and Engineering
关键词
岩土力学
非线性弹性地基
GALERKIN方法
多尺度法
非线性振动
矩形薄板
rock and soil mechanics
nonlinear elastic foundation
Galerkin＇s method
the method of multiplescales
nonlinear vibration
thin rectangular plate
