摘要
板结构与其他构件的装配关系可用不同的边界条件进行模拟,然而针对不同边界条件的板结构进行动力学特性分析,目前缺乏统一的数学建模方法。以混合弹性边界条件下加筋、开孔的板类结构的横向振动为例,利用Rayleigh-Ritz法和模态叠加法求解矩形加筋多孔板在简谐激励下的动力学响应问题。采用将开孔板与加强筋沿交界面进行分离,结合改进的傅里叶级数设定开孔板的横向振动位移函数,利用不同刚度弹簧模拟混合弹性边界,推导加筋矩形开多孔板和边界弹簧系统的动能与势能,求解其在简谐激励下的动力学响应。经对比,理论计算结果与有限元(Finite Element Method,FEM)结果吻合良好。此外,用同样的方法分析不同孔尺寸对结构固有频率和响应的影响。研究发现,可通过改变加筋板的开孔形状、尺寸对结构的振动特性进行调整。研究成果可为混合弹性边界板结构动力分析提供一种新的技术途径,可以简化加筋开孔板结构动力分析的步骤。
The assembly relationship between plate structures and other components can be simulated by different boundary conditions.However,there is a lack of unified mathematical modeling method for dynamic characteristics analysis of plate structures with different boundary conditions.In this paper,the transverse vibration of plate structures with reinforcement and open holes under mixed elastic boundary conditions was studied.The dynamic response of rectangular reinforced perforated plates under harmonic excitation is solved by Rayleigh-Ritz method and modal superposition method.The perforated plate and the stiffener were separated along the interface,and the transverse vibration displacement function of the perforated plate was set by using the improved Fourier series.The mixed elastic boundary was simulated by springs with different stiffness,and the kinetic energy and potential energy of the system of the stiffened rectangular perforated plate and the boundary spring were derived to solve the dynamic response of the system under harmonic excitation.By comparison,it was found that the theoretical calculation results are in good agreement with those of the FEM analysis.In addition,the effects of different hole sizes on the natural frequency and response of the structure were analyzed by the same method.It is shown that the vibration characteristics of the structure can be adjusted by changing the shape and size of the openings of the stiffened plates.This paper provides a new technical approach for dynamic analysis of plate structures with hybrid elastic boundaries.
作者
刘鹏
张保成
邓子伟
张凯
彭磊
孙启航
LIU Peng;ZHANG Baocheng;DENG Ziwei;ZHANG Kai;PENG Lei;SUN Qihang(College of Engineer,Ocean University of China,Qingdao 266100,Shandong,China)
出处
《噪声与振动控制》
CSCD
北大核心
2024年第2期16-21,266,共7页
Noise and Vibration Control
基金
国家自然科学基金资助项目(U2006229)。
