一种预变形周期刚架结构振动带隙特性分析

Analysis of the vibration band gap characteristics of a pre-deformed periodic rigid frame structure

针对减振需求,本文在X型刚架结构的基础上,采用谱元法,分析了一种预变形刚架结构的振动带隙特性。根据梁/杆小变形理论,建立梁/杆谱单元刚度矩阵,针对刚架结构组装得到整体刚度阵,从而建立预变形平面刚架动力学模型。采用有限元方法验证了谱元法的有效性,在谱元法有效的前提下,计算结构的固有频率和频域响应,获得振动带隙结果,结果证明:预变形周期刚架结构可以实现更加低频的振动带隙。通过与无预变形周期刚架X型结构进行比较,揭示了本文所设计结构具有更低固有频率的原因。利用有限元方法计算频响透射率,验证理论模型的有效性。通过观察模态,进一步证明带隙的存在以及结果正确性。在结论基础上,提出可以考虑改变变形角,以满足工程需要。

Aiming at the vibration reduction needs,the vibration band gap characteristics of a pre-deformation rigid frame structure are analyzed based on an X-type rigid frame structure using the spectral element method.The spectral element stiffness matrix is established using the small deformation theory of beams and rods,and the overall stiffness matrix for the rigid frame structure is assembled.Thus,the dynamic model of a pre-deformed plane rigid frame structure is established.The validity of the spectral element method is verified using the finite element method,and the vibration band gap results are obtained by calculating the natural frequency and the frequency domain response of the structure,considering the validity of the spectral element method.The results show that the pre-deformed periodic rigid frame structure can achieve a lower-frequency vibration band gap,the reason for which is revealed by comparison with the X-type structure of the periodic rigid frame without pre-deformation.Finally,the frequency response transmittance is calculated via the finite element method to verify the validity of the theoretical model.The band gap existence and the result accuracy are further demonstrated by observing the modes.Based on these conclusions,it is proposed that the deformation angle can be changed to meet the engineering needs.