Acoustic Radiation From Thick Laminated Cylindrical Shells With Sparse Cross Stiffeners

2013 ◽  
Vol 135 (3) ◽  
Author(s):  
Xiongtao Cao ◽  
Chao Ma ◽  
Hongxing Hua
Keyword(s):  
Cylindrical Shell ◽  
Radial Displacement ◽  
Acoustic Radiation ◽  
Periodic Structures ◽  
Cylindrical Shells ◽  
Acoustic Power ◽  
Acoustic Energy ◽  
Parallel Plates ◽  
Wavenumber Domain ◽  
Laminated Cylindrical Shells

A general method for predicting acoustic radiation from multiple periodic structures is presented and a numerical solution is proposed to find the radial displacement of thick laminated cylindrical shells with sparse cross stiffeners in the wavenumber domain. Although this method aims at the sound radiation from a single stiffened cylindrical shell, it can be easily adapted to analyze the vibrational and sound characteristics of two concentric cylindrical shells or two parallel plates with complicated periodic stiffeners, such as submarine and ship hulls. The sparse cross stiffeners are composed of two sets of parallel rings and one set of longitudinal stringers. The acoustic power of large cylindrical shells above the ring frequency is derived in the wavenumber domain on the basis of the fact that sound power is focused on the acoustic ellipse. It transpires that a great many band gaps of wave propagation in the helical wave spectra of the radial displacement for stiffened cylindrical shells are generated by the rings and stringers. The acoustic power and input power of stiffened antisymmetric laminated cylindrical shells are computed and compared. The acoustic energy conversion efficiency of the cylindrical shells is less than 10%. The axial and circumferential point forces can also produce distinct acoustic power. The radial displacement patterns of the antisymmetric cylindrical shell with fluid loadings are illustrated in the space domain. This study would help to better understand the main mechanism of acoustic radiation from stiffened laminated composite shells, which has not been adequately addressed in its companion paper (Cao et al., 2012, “Acoustic Radiation From Shear Deformable Stiffened Laminated Cylindrical Shells,” J. Sound Vib., 331(3), pp. 651-670).

Relationships Between Acoustic Radiation Modes, Complex Acoustic Power, and Radiation Efficiency

1997 ◽  
Author(s):  
Pei-Tai Chen
Keyword(s):  
Acoustic Radiation ◽  
Acoustic Power ◽  
Radiation Efficiency ◽  
Acoustic Energy ◽  
Normal Velocity ◽  
Far Field ◽  
Surface Complex ◽  
Surface Integral ◽  
Complex Power ◽  
Mass Spring

Abstract The paper explores the physical meaning underlying the surface complex acoustic power of a vibrating body, and its relationship to radiation efficiency under mono-frequency oscillations. The vibrating can be the entire wetted surface, or only a part of the surface with the remaining surface being held rigid. The surface complex acoustic power can be computed by the surface integral of pressure multiplying the complex conjugate of normal velocity. Based on the Gaussian Divergence theorem, it is shown that the real part of the complex power is the power radiated into a far field, while that the imaginary part pertains to the volume integral of the difference between the acoustic kinetic energy density with the potential energy density over the volume between the vibrating surface and the far field. The dynamical behavior of the acoustic field can be viewed as an infinite degree of freedom mass/spring/dashpot system, where the mass and spring are the inertia effects and acoustic compression effects of the acoustic particles and the dashpot is due to the plane wave relationship of the pressure waves at the far field that the acoustic energy propagates away from the acoustic field. By the model of the mass /spring/dashpot system, the phase angle of the complex acoustic power is identified as an indication of the ability of the vibrating surface to radiate acoustic power. The phase angle of the complex power depends on the distribution of the surface normal velocity. In order to study the normal velocity profile in relation to the ability to radiate acoustic energy, the previously established radiation mode (Chen and Ginsberg, 1995) is introduced and extended to situations in which a part of the surface is held rigid. An orthogonal condition for the velocity radiation modes is also established such that arbitrary velocity profiles can be decomposed into radiation modes. The acoustic modal radiation efficiency, defined as the radiated modal acoustic power divided by the surface integral of mean square normal velocity, is investigated in terms of the acoustic eigenvalue of that mode. Several different geometries of vibrating bodies are used to demonstrate the correlation of radiation efficiencies to eigenvalues of radiation modes, which include a rectangular baffled vibrating membrane, a box with only one of the six surfaces vibrating, a slender spheroidal body, and a spherical body. This correlation of acoustic radiation characteristics for different geometries is also demonstrated for a spheroidal body vibrating at some areas with other areas being held rigid.

Influence of Boundary Conditions on the Active Control of Vibration and Sound Radiation for a Circular Cylindrical Shell

2011 ◽  
Vol 66-68 ◽  
pp. 1270-1277
Author(s):  
Lu Dai ◽  
Tie Jun Yang ◽  
Yao Sun ◽  
Ji Xin Liu
Keyword(s):  
Cylindrical Shell ◽  
Boundary Conditions ◽  
Active Control ◽  
Structural Engineering ◽  
Acoustic Radiation ◽  
Circular Cylindrical Shell ◽  
Acoustic Power ◽  
Fourier Series Method ◽  
Vibration And Sound Radiation ◽  
Elastically Restrained

Vibration and acoustic radiation of circular cylindrical shells are hot topics in the structural engineering field. However for a long period, this sort of problems is only limit to classical homogeneous boundary conditions. In this paper, the vibration of a circular cylindrical shell with elastic boundary supports is studied using modified Fourier series method, and the far-field pressure for a baffled shell is calculated by Helmholtz integral equation. Active control of vibration and acoustic radiation are carried out by minimizing structural kinetic energy and radiated acoustic power respectively. The influence of boundary conditions on the active control is investigated throughout several numerical examples. It is shown that the active control of vibration and acoustic for an elastically restrained shell can exhibit unexpected and complicated behaviors.

Analysis of Acoustic Radiation Characteristics of an Infinitely Long Half-Filled Cylindrical Shell

2018 ◽  
Author(s):  
Shuai Zhang ◽  
Tianyun Li ◽  
Xiang Zhu ◽  
Wenjie Guo
Keyword(s):  
Cylindrical Shell ◽  
Numerical Method ◽  
Radial Displacement ◽  
Acoustic Radiation ◽  
Surface Boundary ◽  
Acoustic Structure ◽  
Fluid Structure ◽  
Finite Element Software ◽  
Fluid Load ◽  
Control Equation

The acoustic radiation analysis of a fully-submerged infinitely long half-filled cylindrical shell coupling with fluid field is a typical acoustic-structure problem in the infinite domain, the solution of which is currently mainly based on numerical method. The analytic or semi-analytical method is indispensable for the numerical method and the mechanism to reveal the acoustic-structure coupling characteristics. In this paper, an analytic solution is presented that can calculate the acoustic radiation of infinitely long half-filled cylindrical shell. The displacement of the shell, the fluid load and the excitation force are expressed as the combination of trigonometric series and Fourier series, and displacements of the other two directions are removed by orthogonalizing, only the radial displacement is retained. The control equation of the fluid-structure interaction can be obtained from the relationship between the amplitude of fluid load and the amplitude of radial displacement which can be established by orthogonalizing the continuous conditions of the fluid-structure coupled contact surface and the free surface boundary condition. Solving the control equation, the vibration and acoustic radiation of the coupling system can be determined. Compared with the finite element software Comsol, the results of forced vibration and underwater radiated noise show that the presented method is accurate and reliable. A new way to solve acoustic-vibration problem with partial coupling of elastic structure and sound field is provided in this study.

scholarly journals Research on nonlinear vibration control of laminated cylindrical shells with discontinuous piezoelectric layer

2021 ◽  
Author(s):  
Chaofeng Li ◽  
Peiyong Li ◽  
Xueyang Miao
Keyword(s):  
Cylindrical Shell ◽  
Vibration Control ◽  
Nonlinear Vibration ◽  
Piezoelectric Layer ◽  
Cylindrical Shells ◽  
Harmonic Balance Method ◽  
Amplitude Response ◽  
Nonlinear Vibration Control ◽  
Laminated Cylindrical Shell ◽  
Laminated Cylindrical Shells

Abstract In this paper, the nonlinear vibration control of the piezoelectric laminated cylindrical shell with point supported elastic boundary condition is analyzed, in which the geometric nonlinearity is considered by the first-order shear nonlinear shell theory. In the model, different boundary conditions are simulated by introducing a series of artificial springs. The elastic-electrically coupled differential equations of piezoelectric laminated cylindrical shells are obtained based on the Chebyshev polynomials and Lagrange equation, and decoupled by using the negative velocity feedback adjustment. Later, the Incremental Harmonic Balance Method (IHBM) is deduced, and the frequency-amplitude response of the piezoelectric laminated cylindrical shell is obtained by IHBM. Finally, the influence of the constant gain, size and position of the piezoelectric layer on frequency-amplitude response are investigated. The results show that the position, size and constant gain of the piezoelectric layer have a significant influence on its nonlinear vibration control.

POSTBUCKLING OF SHEAR-DEFORMABLE ANISOTROPIC LAMINATED CYLINDRICAL SHELLS UNDER AXIAL COMPRESSION

2008 ◽  
Vol 08 (03) ◽  
pp. 389-414 ◽  
Author(s):  
ZHI-MIN LI ◽  
HUI-SHEN SHEN
Keyword(s):  
Cylindrical Shell ◽  
Axial Compression ◽  
Perturbation Technique ◽  
Cylindrical Shells ◽  
Anisotropic Shell ◽  
Equilibrium Path ◽  
Singular Perturbation Technique ◽  
Initial Geometric Imperfections ◽  
Shear Deformable ◽  
Laminated Cylindrical Shells

A postbuckling analysis is presented for a shear-deformable anisotropic laminated cylindrical shell of finite length subjected to axial compression. The material of each layer of the shell is assumed to be linearly elastic, anisotropic and fiber-reinforced. The governing equations are based on a higher order shear-deformable shell theory with the von Kármán–Donnell type of kinematic nonlinearity and including the extension/twist, extension/flexural and flexural/twist couplings. The nonlinear prebuckling deformations and initial geometric imperfections of the shell are both taken into account. A singular perturbation technique is employed to determine the buckling loads and postbuckling equilibrium paths. The numerical illustrations concern the postbuckling response of perfect and imperfect, moderately thick, anisotropic laminated cylindrical shells with different values of shell parameters and stacking sequence. The results confirm that there exists a compressive stress along with an associate shear stress and twisting when the anisotropic shell is subjected to axial compression. The postbuckling equilibrium path is unstable for the moderately thick cylindrical shell under axial compression and the shell structure is imperfection-sensitive.

Acoustic Radiation From Stiffened Cylindrical Shells With Constrained Layer Damping

2013 ◽  
Vol 135 (1) ◽  
Author(s):  
Xiongtao Cao ◽  
Hongxing Hua ◽  
Zhenguo Zhang
Keyword(s):  
Cylindrical Shell ◽  
Sound Pressure ◽  
Acoustic Radiation ◽  
Equations Of Motion ◽  
Cylindrical Shells ◽  
Phase Method ◽  
Stationary Phase Method ◽  
Constrained Layer Damping ◽  
Acoustic Characteristics ◽  
Stiffened Cylindrical Shell

Acoustic radiation from cylindrical shells stiffened by two sets of rings, with constrained layer damping (CLD), is investigated theoretically. The governing equations of motion for the cylindrical shell with CLD are described on the basis of Sanders thin shell theory. Two sets of rings interact with the host cylindrical shell only through the normal line forces. The solutions are derived in the wavenumber domain and the stationary phase method is used to find an analytical expression of the far-field sound pressure. The effects of the viscoelastic material core, constrained layer and multiple loadings on sound pressure are illustrated. The helical wave spectra of sound pressure and the radial displacement clearly show the vibrational and acoustic characteristics of the stiffened cylindrical shell with CLD. It is shown that CLD can effectively suppress the radial vibration and reduce acoustic radiation.

Vibration Characteristics Research of Finite Cylindrical Shells Semi-Submerged

2017 ◽  
Vol 863 ◽  
pp. 163-169
Author(s):  
Wen Jie Guo ◽  
Tian Yun Li ◽  
Yu Yue Miao ◽  
Xiang Zhu
Keyword(s):  
Cylindrical Shell ◽  
Radial Displacement ◽  
Cylindrical Shells ◽  
Energy Functional ◽  
Vibration Characteristics ◽  
New Thought ◽  
Fluid Load ◽  
Vibration And Sound Radiation ◽  
Control Equation ◽  
Solid Liquid

A significant amount of research on the vibration and sound radiation of the cylindrical shell has been carried out and reported. The cylindrical shell was usually assumed to be submerged in an infinite fluid. However, the fluid region surrounding the cylindrical shell is bounded. Free vibration and forced vibration characteristics of finite cylindrical shells semi-submerged are studied in this paper, based on energy functional variational principle. The combined form of the triangular series and the Fourier series is used for the displacement of the cylindrical shell, then the orthogonality can be used to eliminate the other two directions after the variation, and only the radial displacement is kept. The relationships between the amplitudes of fluid load and the amplitudes of the radial displacement are established by the orthogonal processing of the continuous conditions of the solid-liquid coupling contact surface and the boundary conditions of the free liquid surface. Finally, the fluid structure coupling control equation is obtained. The results show that the method is correct and effective, in addition, providing a new thought for solving similar problem.

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