基于Mindlin理论多阶梯厚圆盘弯曲振动特性研究

Study on bending vibration characteristics of the multi-step thick disc based on the Mindlin theory

实际应用中为了获得大辐射声功率,通常采用多阶梯圆盘作为辐射体。从声学工程应用角度,基于Mindlin厚板理论结合连接处的连续性条件和边界条件推导了自由边界条件下的多阶梯厚弯振圆盘的弯振频率方程,利用数值计算法对多阶梯厚圆盘振动特性和频率特性进行研究,并结合有限元法进行模态分析,其结果与试验测试及理论计算基本一致;研究了各结构参数对振动频率的影响规律,结果表明各阶频率随阶梯圆盘节线半径r1的增加而增大,随阶梯圆环外半径r2的增大而减小,随圆盘高度和基底高度的增加而增加;各部分的材料对多阶梯圆盘的频率影响不同,其中材料的弹性模量影响最大,研究结果为多阶梯弯振厚圆盘和大功率弯曲振动辐射器的设计提供理论参考和频率调试依据。

Multi-step disks are usually used as radiators,in order to obtain the high-radiation sound power in practical application. From the perspective of acoustic engineering and application, the bending-vibration frequency equation of the multistep thick bending-vibration disk under the free-boundary condition is derived, based on the Mindlin thick-plate theory, as well as combined with the continuity and boundary conditions of the joints. The multi-step thick disk's vibration and frequency characteristics are explored by means of the numerical method;the modal analysis is conducted with the aid of the finite element method. The results are in good agreement with those obtained from the experimental test and theoretical calculation. The influence of structural parameters on vibration frequency is identified. The results show that the frequency of each step increases as the radius r1 of the step disk increases,decreases as r2 increases,and increases as both the height of the disk and the height of the substrate grows. Different parts exert different influence on the frequency of the multi-step disk, and the elastic modulus exerts the most influence. The results provide theoretical reference and basis of frequency adjustment for the design of multi-step thick bending-vibration disks and high-power bending-vibration radiators.