基于辛空间波的正交各向异性圆柱壳随机振动分析方法

doi:10.7527/S1000-6893.2025.32322

Abstract

Abstract:

A symplectic-wave-based method is proposed for the random vibration analysis of orthotropic cylindrical shells under turbulent boundary layer. Firstly， based on the semi-empirical model of turbulent boundary layer， the random vibration response of orthotropic cylindrical shells under turbulent boundary layer is transformed into harmonic response. Then， according to Kirchhoff-Love theory and Legendre transformation， the unified governing equation is obtained from the fundamental equations for orthotropic cylindrical shells under axial compression in the Lagrangian system transferring into the Hamiltonian system. And， the harmonic response of orthotropic cylindrical shells is solved through wave propagation analysis. Finally， both the state vector and excitation are expanded to obtain circumferential superposition form of the solution by applying the superposition principle of linear differential equation solutions. By combining symplectic orthogonality with the solution for first-order linear differential equations， the harmonic response is obtained. Compared with the modal superposition method， the proposed method can analytically handle arbitrary boundary conditions with higher convergence speed and computational accuracy. Numerical examples validate the convergence and effectiveness of the method， and the influence of axial compression variations on the random vibration response of orthotropic cylindrical shells is analyzed.

Key words: turbulent boundary layer, orthotropic cylindrical shells, random vibration, symplectic-wave-based method, axial compression

CLC Number:

Jiaqi MI, Yongping JIANG, Ruxin GAO. A symplectic-wave-based method for random vibration analysis of orthotropic cylindrical shells[J]. Acta Aeronautica et Astronautica Sinica, 2026, 47(3): 232322.

Figures/Tables 10

Fig.1

Table 1

Geometric and material parameters of orthotropic cylindrical shells

参数	数值
$L$ /m	10
$h$ /m	0.02
$R$ /m	0.5
$ρ$ /（kg∙m^-3）	1 532
$E 1$ /GPa	124.5
$E 2$ /GPa	10.2
$G 12$ /GPa	6.3
μ₁₂	0.34
η	0.05

Table 1

Fig.2

Table 2

Computation time of the presented method and modal superposition method

方法	m_max	计算时间/s
方法	m_max	M=1，N=2	M=4，N=4
模态叠加法	$8$	0.50	0.51
	$16$	1.00	0.99
	$24$	1.55	1.52
	$32$	2.01	2.02
本文方法		0.85	0.81

Table 2

Fig.3

Fig.4

Fig.5

Fig.6

Fig.7

Fig.8

References 28

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A symplectic-wave-based method for random vibration analysis of orthotropic cylindrical shells

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