摘要
基于修正Timoshenko梁理论,结合波动法,建立了适用于黏弹性地基的周期性梁结构振动特性分析模型。通过将位移表示为波函数形式,构建梁单元的位移与力参数矩阵,并结合相邻单元间的连续性条件与边界条件,形成了一维周期梁在黏弹性地基上的波动分析框架。将该模型与有限元频率响应结果对比,验证了其准确性与可靠性。在此基础上,系统分析了材料属性、几何特征及地基黏弹性参数对结构传输特性的影响规律。结果表明:材料刚度差和几何不均性可显著调节带隙范围与损耗强度;地基刚度与剪切刚度可推动带隙频率向高频移动;结构阻尼主要增强能量耗散能力而对带隙频率影响较小。所构建模型具备良好的适用性与预测能力,适用于工程周期结构的定向隔振设计。
A vibration analysis model for periodic beam structures on viscoelastic foundations was developed based on the modified Timoshenko beam theory and the wave-based method.By representing displacements in the form of wave functions,the displacement and force parameter matrices of beam elements were formulated.Considering the continuity conditions between adjacent units and boundary constraints,a one-dimensional wave propagation framework was established for periodic beams on viscoelastic foundations.The model’s accuracy and reliability were validated through comparison with frequency response results from finite element simulations.On this basis,a parametric study was conducted to investigate the influence of material properties,geometric characteristics,and foundation viscoelastic parameters on the wave transmission behavior.The results demonstrate that the proposed model exhibits strong applicability and predictive capability.The stiffness contrast and geometric asymmetry between periodic units significantly affect the band gap width and transmission loss.Increasing foundation stiffness and shear resistance shifts the band gaps toward higher frequencies and enhances attenuation performance,while increase of structural damping primarily suppresses resonance peaks without notably altering band gap positions.These findings provide theoretical support for vibration isolation design in periodic structures.
作者
何东泽
杜爽
黄世军
HE Dongze;DU Shuang;HUANG Shijun(School of Mechanical Engineering,Yanshan University,Qinhuangdao 066000,China;Hebei Innovation Center for Equipment Lightweight Design and Manufacturing,Qinhuangdao 066000,China)
出处
《振动与冲击》
北大核心
2025年第24期77-84,共8页
Journal of Vibration and Shock
基金
国家自然科学基金青年基金(52405133)
河北省自然科学基金青年科学基金项目(A类)(E2024203033)。
关键词
黏弹性地基
修正Timoshenko梁理论
周期梁结构
波动法
传输特性
viscoelastic foundations
modified Timoshenko beam theory
periodic beam structures
wave based method
transmissibility characteristics
