复杂支承边界梁结构振动特性分析方法与应用  

Analysis Method and Application of Free Vibration Characteristics of Complex Supported Boundary Beam Structure

作　　者：田瑞 韩涛[1,2] 常亮 聂小华[1,2] TIAN Rui;HAN Tao;CHANG Liang;NIE Xiaohua(Aviation Industry Aircraft Strength Research Institute,Xi'an 710065,China;National Key Laboratory of Strength and Structural Integrity,Xi'an 710065,China)

机构地区：[1]中国飞机强度研究所,西安710065 [2]强度与结构完整性全国重点实验室,西安710065

出　　处：《强度与环境》2025年第1期9-16,共8页Structure & Environment Engineering

基　　金：民机科研:飞机结构强度试验数字化:国家自然科学基金(51975470)。

摘　　要：研究了基于微分变换法(DTM)求解典型梁、复杂弹性边界梁及跨中含附加弹性支承梁结构固有频率和振型的问题,详细推导了多种不同支承类型梁结构固有频率的计算方程,并分别采用微分变换法和理论方法计算了四种典型支承边界梁结构的固有频率和振型,验证了DTM方法的计算精度。同时,结合具体算例研究了边界支承刚度、跨中附加弹性支承刚度及位置对梁结构固有频率的影响规律。研究表明:采用DTM求解梁结构自由振动微分方程不仅计算简便、精度高,而且还具有广泛地适用性,尤其在复杂弹性边界和跨中含附加弹性支承梁结构固有频率和振型求解问题上具有明显的优势。The method of differential transformation method(DTM) for solving the natural frequencies and modes of typical beams,elastic boundary beams and beams with additional elastic supports is studied.The equations for calculating the natural frequencies of beam structures with different supports are derived in detail.The natural frequencies and modes of four typical boundary beams are calculated by differential transform method and theoretical method respectively,and the calculation accuracy of DTM method is verified.The effects of the stiffness of the boundary support,the stiffness and the position of the additional elastic support on the natural frequency of the beam structure are analyzed with examples.The results show that the differential transformation method is not only simple and accurate,but also widely applicable,especially in solving the natural frequency and mode of beam structures with complex elastic boundaries and additional elastic supports.

关 键 词：微分变换法 梁结构 固有频率和振型 弹性边界 附加弹性支承 

分 类 号：O321[理学—一般力学与力学基础] O327[理学—力学]