放置变压器弹性边界薄板振动分析*
- 摘 要
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(1 重庆大学土木工程学院, 重庆 400045； 2 深圳市供电规划设计院有限公司, 深圳 518054；3 重庆建筑工程职业学院, 重庆 400072)
［摘要］放置在楼面上的变压器的周期振动不仅降低了设备的动态精度和使用性能，而且降低了楼面的振动舒适性。利用瑞利.里兹能量法，将矩形薄板体系的位移振型函数代入哈密顿变分方程，推导出以整体体系的自由振动固有频率为特征值、以位移振型函数中的傅里叶系数组成的向量为特征向量的标准特征方程。将附加分布质量矩形薄板的横向位移函数变量分离为空间函数（振型）和时间函数（广义坐标）的积，并利用振型的正交性推导出强迫振动作用下的振动位移响应的表达式。以典型的附加变压器的矩形薄板为例，分析了弹性边界刚度4个参数对薄板体系的振动特性的影响。［关键词］变压器; 薄板; 自由振动; 强迫振动; 弹性边界中图分类号：TU33+9 文献标识码：A 文章编号：1002-848X(2015)19-0067-05
Vibration analysis of a thin plate carrying a transformer based on elastic boundary conditionYan Zhitao1, Wang Lingzhi1, Li Zhengliang1, Dai Zhiyong2, Deng Pu3
(1 School of Civil Engineering, Chongqing University, Chongqing 400045, China; 2 Shenzhen Power Planning and Design Institute Limited, Shenzhen 518054, China; 3 Chongqing Jianzhu College, Chongqing 400072, China)Abstract: The periodic excitation generated by the transformer placed on the floor reduces the dynamic accuracy and service performance of the device as well as the floor vibration comfort. Using the Rayleigh Ritz method, the displacement mode shape function of the rectangular thin plate system was substituted into the Hamilton variable equation to obtain standard characteristic equation, which was composed of characteristic value of free vibration natural frequency of the overall system, and characteristic vectors composed of Fourier coefficient vectors of displacement mode shape function. The variables of the transverse displacement function of the rectangular thin plate with additional distributed mass were separated into the product of space function (vibration mode) and time function (generalized coordinates). An expression of the vibration displacement response under forced vibration was derived by using the orthogonality of the vibration mode. Taking the typical rectangular thin plate with an additional transformer as an example, the influences of 4 elastic boundary stiffness parameters on vibration characteristics of the thin plate system were analyzed.Keywords:transformer; thin plate; free vibration; forced vibration; elastic boundary
*国家自然科学基金资助项目（51178489，51478069）。作者简介：晏致涛，博士，教授，博士生导师，Email：yanzhitao@cqu.edu.cn。
