Vibration Characteristics of Cylindrical Membrane

doi:10.16183/j.cnki.jsjtu.2022.396

Abstract

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

CLC Number:

V274

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