圆柱薄膜振动特性

doi:10.16183/j.cnki.jsjtu.2022.396

摘要/Abstract

摘要：

根据达朗贝尔原理建立圆柱状薄膜非线性振动方程并对其展开分析与试验验证.建立圆柱膜振动问题的控制方程组,依据薄膜振动物理方程与边界条件简化方程组并求解;得到圆柱膜非线性振动频率解析解,并通过有限元仿真对其线性解析解进行验证.结果表明,理论计算与数值仿真结果误差较小,有限元方法适用于柔性薄膜结构模态分析.采用三维激光扫描式测振系统测试圆柱膜在空气环境中的振动频率,利用有限元分析软件获得圆柱膜干模态和湿模态振动频率并提取空气附加质量系数.结果表明,圆柱膜振动湿模态测试结果与数值分析结果具有良好的一致性,地面空气附加质量对圆柱膜振动的影响与薄膜自身质量处于同一量级.

关键词: 非线性振动, 湿模态, 空气附加质量, 曲率薄膜

Abstract:

Based on the principle of D’Alembert, the nonlinear vibration equation of cylindrical membrane is established, and the analysis and experimental verification of it are conducted. The control equation system for cylindrical membrane vibration problems is established, and the equation system according to the physical equations and boundary conditions of thin diaphragms is simplified and solved, the analytical solution of nonlinear vibration frequency of cylindrical membrane is obtained, and the linear analytical solution is verified by finite element simulation, which shows that the error between theoretical calculation and numerical simulation is small, and the applicability of finite element method to the modal analysis of flexible membrane structure is verified. A 3D laser scanning vibration measurement system is used to test the vibration frequency of cylindrical membranes in the air environment. The finite element analysis software is used to obtain the dry mode and wet mode vibration frequencies of cylindrical membranes and extract the additional mass coefficients of air. The results showed that the test results of the vibration in wet mode have a good consistency with the numerical analysis results, and the influence of the additional quality of the ground air on the cylindrical membrane is in the same order of magnitude as its own mass.

Key words: nonlinear vibration, wet modal, additional mass of air, curvature membrane

中图分类号:

V274

黄涛, 何泽青, 宋林. 圆柱薄膜振动特性[J]. 上海交通大学学报, 2024, 58(4): 428-437.

HUANG Tao, HE Zeqing, SONG Lin. Vibration Characteristics of Cylindrical Membrane[J]. Journal of Shanghai Jiao Tong University, 2024, 58(4): 428-437.

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模态	m, n	计算值/Hz	仿真值/Hz	相对误差/%
一阶	m=1, n=2	163.74	152.34	7.483
二阶	m=1, n=3	231.96	232.18	0.094
三阶	m=1, n=4	320.63	320.88	0.078
四阶	m=1, n=5	409.24	408.97	0.066
五阶	m=1, n=6	496.90	496.03	0.042

模态	m, n	计算值/Hz	仿真值/Hz	相对误差/%
一阶	m=1, n=2	10.747	10.879	1.21
二阶	m=1, n=3	18.069	18.173	0.57
三阶	m=1, n=4	25.305	25.340	0.14
四阶	m=1, n=5	32.352	32.346	0.02
五阶	m=1, n=6	39.292	39.248	0.11

模态	频率/Hz
模态	A=0 m	A=0.01 m	A=0.02 m	A=0.03 m	A=0.04 m	A=0.05 m
一阶	161.63	174.58	187.58	199.59	226.47	257.25
二阶	230.47	248.43	270.33	301.57	340.73	384.99
三阶	319.56	340.28	368.75	409.48	461.72	519.75
四阶	408.39	429.12	463.29	515.36	579.01	651.85
五阶	496.21	519.27	561.48	625.50	697.39	784.62

p/kPa	一阶频率/Hz		二阶频率/Hz		三阶频率/Hz		四阶频率/Hz
p/kPa	试验	仿真	试验	仿真	试验	仿真	试验	仿真
3	49.3	64.5	81.3	87.5	122.6	125.3	165.1	166.5
5	62.1	73.9	104.2	110.6	155.9	160.8	212.4	214.3
7	71.3	81.7	121.3	128.8	182.7	188.7	249.5	252.0
9	79.1	89.2	137.6	145.4	207.1	213.8	283.1	285.7

p/kPa	C_a
p/kPa	一阶	二阶	三阶	四阶
3	2.640	2.254	1.989	1.810
5	2.650	2.266	1.998	1.817
7	2.692	2.254	2.024	1.838
9	2.697	2.300	2.024	1.838