计及剪切变形的复合材料薄壁梁的阻尼分析模型

Analytic Model of Modal Damping for Thin-walled Composite Beams with Shear Deformation

为精确描述阻尼对复合材料薄壁结构动力学特性的影响,提出一个计及剪切变形的复合材料薄壁梁的结构阻尼分析模型。基于改进的变分渐进法(VAM)描述复合材料薄壁梁的位移和应变,采用Hamilton原理导出Timoshenko梁的自由振动偏微分方程,采用Galerkin法将偏微分方程化为常微分方程,通过求解复特征值问题得到梁的模态阻尼。将阻尼计算结果与现有文献的有限元阻尼计算结果进行比对,验证了本文模型的有效性。通过算例分析得到圆截面薄壁复合材料梁的阻尼数值计算结果。研究表明,不考虑剪切变形将会得到偏高的阻尼预测结果。此外,采用的铺层方式不同,产生最大阻尼的纤维铺层角也将有所不同。

In order to accurately predict the ef fect of damping on the dynamical behavior of composi te thin-wal led beams,this paper presents an analytic model of modal damping for thin-walled composite beams with shear deforma-tion. The displacement and strain of the beams were firstly described by using a momethod （VAM） and the partial diiferential equations of Timoshenko beam’s free motion were derived by usingHamilton？s principle. Then the partial differential equations were transformed into ordinary ditferential equations by using Galerkin method and the modal damping was obtained by solving the complex eigenvalues of effectiveness of the model was veri fied by comparing the damping computation results with those avai lable in current literature and the numerical results of damping were presented for circular cross-section composite thinby analysis of examples. The study shows that higher damping will be predicted without takinto consideration and that diiferent laminate configurations yield diiferent fiber laminate angles for the largest damp-ing.