考虑裂纹效应的弹性板振动分析模型  

Vibration analysis model of an elastic plate with cracked effects

作　　者：刘文光[1] 严铖 

机构地区：[1]南昌航空大学航空制造工程学院,南昌330063

出　　处：《振动与冲击》2014年第7期133-137,共5页Journal of Vibration and Shock

基　　金：江西省自然科学基金(20122BAB216027);国家自然科学基金(51265040)资助

摘　　要：针对含裂纹板的动力学问题,提出了一种耦合裂纹效应的弹性板动力学建模方法。该方法依据变形等效原则用虚拟外部载荷代替裂纹作用,并通过力学平衡原理建立了耦合裂纹项的弹性板运动方程,且基于Rice和Levy应力关系式推导出裂纹项表达式;在此基础上,结合Galerkin法和Berger经验,把含裂纹弹性板振动系统简化成一单自由度非线性振动模型进行动力学特性分析。通过算例探讨了裂纹尺度、阻尼以及激励力位置对弹性板振动特性的影响。结论表明,裂纹尺度和板尺寸对振动非线性作用明显,动应力幅值受阻尼与激励力位置的控制。A modeling method of an elastic plate vibration with cracked effects was proposed aiming at dynamic problems of cracked plates. The crack was replaced with a virtual external force approximately according to the deformation equivalence principle.The motion equation of an elastic plate considering cracked effects was derived via the principle of mechanical equilibrium,and the crack terms were derived with the stress relations introduced by Rice and Levy.Then,Galerkin method and Berger＇s experience were used to simplify the cracked plate into a one-DOF nonlinear vibration system.The dynamic characteristics of a simply supported plate were analyzed.A case study was performed for studying the effects of crack size,plate dimension,damping and loading point on the vibration behavior of an elastic plate.Results indicated that the plate＇s nonlinear vibration behavior is affected by plate dimension and crack size obviously;the dynamic stress response amplitude is controlled by damping and loading point location.

关 键 词：振动分析模型 裂纹效应 弹性板 

分 类 号：V216.3[航空宇航科学与技术—航空宇航推进理论与工程] V224