任意形状固支板横向振动的边界保角映射解法  

Boundary conformal mapping method for transverse vibration of clamped plates with arbitrary shapes

作　　者：袁运博 李宏亮[2] 刘洪达 郭宜斌[1] 王东华 率志君[1] YUAN Yun-bo;LI Hong-liang;LIU Hong-da;GUO Yi bin;WANG Dong-hua;SHUAI Zhi-jun(College of Power and Energy Engineering,Harbin Engineering University,Harbin 150001,China;College of Aerospace and Civil Engineering,Harbin Engineering University,Harbin 150001,China;Harbin Marine Boiler&Turbine Research Institute(No.703 Research Institute of CSSC),Harbin 150001,China)

机构地区：[1]哈尔滨工程大学动力与能源工程学院,黑龙江哈尔滨150001 [2]哈尔滨工程大学航天与建筑工程学院,黑龙江哈尔滨150001 [3]哈尔滨船舶锅炉涡轮机研究所(中国船舶集团有限公司第703研究所),黑龙江哈尔滨150001

出　　处：《振动工程学报》2020年第5期921-929,共9页Journal of Vibration Engineering

基　　金：船用低速机工程一期(MC-201501-D01-01);国家自然科学基金资助项目(51805106)。

摘　　要：基于边界保角映射法建立了任意形状固支板横向振动特性分析的半解析方法。在极坐标系下,以一般弹性薄板横向振动的位移解析函数为基础,引入边界保角映射的概念,将任意形状板中面的外边界线映射为映射平面内的单位圆周线,在映射平面内推导了任意形状板横向振动转角函数的统一表达式。根据固支边界条件,在映射平面内建立了用于确定任意形状固支板横向振动固有频率和模态振型的特征方程。椭圆板、矩形板和马蹄形板3个算例分析结果与现有公开发表结果及有限元结果的对比表明,所提方法能高精度地获得任意形状固支板横向振动的固有频率和模态振型。A general semi-analytic method based on boundary conformal mapping method is proposed to investigate the transverse vibration characteristics of arbitrarily shaped plates with clamped edges.The boundary conformal mapping method is introduced to map the outer edge of the mid-plane of an arbitrary shaped plate to a unit circumference of the mapping plane.According to the analytic deflection function in the polar coordinates and the boundary conformal mapping function,the unified rotation function is derived in the mapping plane.With the clamped boundary condition,characteristic equations for arbitrarily shaped plates are derived to determine the natural frequencies and the corresponding mode shapes.The results of three clamped plates,viz.,elliptical plate,rectangular plate and horseshoe plate,are compared with the available results between the published and the FEM results.It indicates that the natural frequencies and the corresponding mode shapes of the transverse vibration of clamped plates with arbitrary shapes can be obtained accurately by the proposed method.

关 键 词：横向振动 任意形状板 边界保角映射法 固支边界 

分 类 号：O326[理学—一般力学与力学基础] O327[理学—力学]