放置變壓器彈性邊界薄板振動(dòng)分析*
晏致濤1，王靈芝1,李正良1，戴志勇2，鄧璞3
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(1 重慶大學(xué)土木工程學(xué)院, 重慶 400045； 2 深圳市供電規(guī)劃設(shè)計(jì)院有限公司, 深圳 518054；3 重慶建筑工程職業(yè)學(xué)院, 重慶 400072)
［摘要］放置在樓面上的變壓器的周期振動(dòng)不僅降低了設(shè)備的動(dòng)態(tài)精度和使用性能，而且降低了樓面的振動(dòng)舒適性。利用瑞利.里茲能量法，將矩形薄板體系的位移振型函數(shù)代入哈密頓變分方程，推導(dǎo)出以整體體系的自由振動(dòng)固有頻率為特征值、以位移振型函數(shù)中的傅里葉系數(shù)組成的向量為特征向量的標(biāo)準(zhǔn)特征方程。將附加分布質(zhì)量矩形薄板的橫向位移函數(shù)變量分離為空間函數(shù)（振型）和時(shí)間函數(shù)（廣義坐標(biāo)）的積，并利用振型的正交性推導(dǎo)出強(qiáng)迫振動(dòng)作用下的振動(dòng)位移響應(yīng)的表達(dá)式。以典型的附加變壓器的矩形薄板為例，分析了彈性邊界剛度4個(gè)參數(shù)對(duì)薄板體系的振動(dòng)特性的影響。［關(guān)鍵詞］變壓器; 薄板; 自由振動(dòng); 強(qiáng)迫振動(dòng); 彈性邊界中圖分類號(hào)：TU33+9 文獻(xiàn)標(biāo)識(shí)碼：A 文章編號(hào)：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
*國(guó)家自然科學(xué)基金資助項(xiàng)目（51178489，51478069）。作者簡(jiǎn)介：晏致濤，博士，教授，博士生導(dǎo)師，Email：yanzhitao@cqu.edu.cn。
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