弹性支撑下金字塔点阵夹芯梁结构的动力学研究  

DYNAMIC STUDY OF THE PYRAMID LATTICE SANDWICH BEAM STRUCTURE UNDER ELASTIC SUPPORT

作　　者：曹义军 孙方旭[2] 方兆波 CAO Yijun;SUN Fangxu;FANG Zhaobo(East Lake Laboratory of Hubei Province,Wuhan 430205,China;Naval University of Engineering,Wuhan 430033,China)

机构地区：[1]湖北东湖实验室,武汉430205 [2]海军工程大学,武汉430033

出　　处：《力学与实践》2025年第2期347-353,共7页Mechanics in Engineering

基　　金：国家自然科学基金项目(12102031)资助。

摘　　要：提出一种针对弹性支撑下金字塔点阵夹芯梁动力学特性的有效研究方法。推导了夹芯梁的位移函数,建立了上下梁和金字塔芯层的应力-应变关系。采用Rayleigh-Ritz法结合正交多项式推导出弹性支撑夹芯梁的模态函数。利用Hamilton原理推导了结构的运动方程,采用特征值法和Newmark积分法完成对弹性支撑金字塔夹芯梁的动力学分析。将理论方法计算的结构固有频率与有限元仿真结果进行比较,验证了理论模型的正确性并讨论了弹性支撑对结构幅频响应的影响。This paper proposes an effective research method for the dynamic characteristics of pyramid lattice sandwich beams on elastic support.The displacement function of the sandwich beam is derived and the stress-strain relationship of the upper and lower beams and the pyramid core is established.The Rayleigh-Ritz method combined with orthogonal polynomials is used to derive the modal function of the sandwich beam under elastic support.The Hamilton principle is used to derive the motion equation of the structure,and the eigenvalue method and Newmark integral method were used to complete the dynamic analysis of the pyramid sandwich beam structure under elastic support.The natural frequency of the structure calculated by the theoretical method is compared with the finite element simulation results to verify the correctness of the theoretical model and discuss the influence of the elastic support on the amplitude-frequency response of the structure.

关 键 词：夹芯梁 固有频率 HAMILTON 原理 Rayleigh-Ritz 法 弹性支撑 

分 类 号：O326[理学—一般力学与力学基础]