Winkler地基上四边自由矩形薄板的亚谐共振与奇异性分析  

SUBHARMONIC RESONANCE OF RECTANGULAR THIN PLATE WITH FOUR SIDES FREE ON WINKLER FOUNDATION AND ITS SINGULARITY ANALYSIS

作　　者：杨志安[1] 李文兰[2] 

机构地区：[1]唐山学院 [2]天津大学图书馆,天津300072

出　　处：《机械强度》2007年第2期329-333,共5页Journal of Mechanical Strength

摘　　要：研究Winkler地基上四边自由矩形薄板的亚谐共振问题。按照弹性力学理论建立Winkler地基上四边自由受简谐激励作用矩形薄板的动力学方程。利用Galerkin方法将其转化为非线性振动方程。应用非线性振动的多尺度法求得系统满足1/3次亚谐共振情况时的一次近似解,并进行数值计算。分析激励、阻尼等对系统响应曲线的影响。应用奇异性理论对1/3次亚谐共振幅频响应方程进行奇异性分析,得到选取不同分岔参数时开折参数平面的转迁集和分岔图。Subharmonic vibration of a rectangular thin plate with four sides free on the Winkler foundation is studied. Based on elasto-dynamics, the governing equation of a rectangular thin plate with four sides free on the Winkler foundation subjected to harmonic excitation is derived. The governing equation is further reduced into an ordinary nonlinear differential equation by Galerkin＇ s method. By applying the method of multiple scales to the reduced system, the first approximation solution for 1/3 subharmonic resonance of the system is obtained. The influence of excitation and damping on the system response is analyzed numerically. Then singularity analysis of amplitude frequency response equation of the system is carried out by means of singularity theory. Transition sets and bifurcation diagrams of the unfolding parameter plane for different bifurcation parameters are obtained.

关 键 词：矩形薄板 WINKLER地基 Galerlfin方法 多尺度法 非线性振动 奇异性 

分 类 号：O321[理学—一般力学与力学基础]