摘要
提出一种统一、有效的数值方法分析Winkler地基上矩形薄板的振动响应问题。采用Winkler地基模型,用横向弹簧和扭转弹簧的组合表示矩形薄板边界,用改进的傅里叶级数形式表示横向位移函数,用瑞利-里兹方法推导出拉格朗日函数的振动响应矩阵。通过计算Winkler地基上矩形薄板的振动响应并将之与有限元法结果相比较,验证了该方法的正确性和有效性。进一步探究了不同激励点、不同响应点处共振峰值数目的变化。
A unified and effective numerical method is proposed to analyze the vibration response of thin rectangular plates on Winkler foundations.Using Winkler foundation model,the rectangular thin plate boundary is expressed as a combination of transverse springs and torsional springs,and the transverse displacement function is expressed as an improved Fourier series form.The vibration response matrix of Lagrange function is derived by Rayleigh-Ritz method.By calculating the vibration response of the rectangular thin plate on Winkler foundation,and comparing the results with those of the finite element method,the correctness and effectiveness of the proposed method are verified.Furthermore,the variation of the number of resonance peaks at different excitation points and different response points is explored.
作者
郑双星
高芳清
丁凯文
ZHENG Shuangxing;GAO Fangqing;DING Kaiwen(College of Mechanics and Engineering,Southwest Jiaotong University,Chengdu 610031,China;Key Laboratory of Applied Mechanics and Structural Safety of Sichuan Province,Southwest Jiaotong University,Chengdu 610031,China)
出处
《噪声与振动控制》
CSCD
北大核心
2021年第6期19-23,共5页
Noise and Vibration Control
关键词
振动与波
WINKLER地基
改进傅里叶级数
矩形薄板
振动响应
vibration and wave
Winkler foundation
improved Fourier-series
rectangular thin plate
vibration response
