Dynamic Behavior of Reinforced Cylindrical Shells in a Vacuum and in a Fluid

1954 ◽  
Vol 21 (1) ◽  
pp. 35-41
Author(s):  
Miguel C. Junger
Keyword(s):  
Cylindrical Shell ◽  
Wave Equation ◽  
Sound Field ◽  
Dynamic Equations ◽  
Lagrange Equations ◽  
Fluid Medium ◽  
Load Distributions ◽  
Inertial Component ◽  
Modes Of Vibration ◽  
Infinite Cylindrical Shell

Abstract The vibrations of an infinite cylindrical shell reinforced with periodically spaced septa and stiffening rings are studied in a vacuum and in a fluid medium. Lagrange equations are used to derive the dynamic equations; the fluid reaction is obtained from the solution of the wave equation. The solution gives the dynamic characteristics of the shell, the amplitude of forced vibration, and the sound field generated thereby. The theory can be extended to shells embodying complex stiffening structures and load distributions. Certain features of the fluid reaction suggest interesting applications: Its inertial component becomes extremely large under certain conditions, thus tending to eliminate some modes of vibration; also, the resistive, i.e., damping, component may vanish for certain modes, which therefore do not radiate any sound.

Inelastic Response of an Infinite Cylindrical Shell to Transient Acoustic Waves

1989 ◽  
Vol 56 (4) ◽  
pp. 900-909 ◽  
Author(s):  
Thomas L. Geers ◽  
Chi-Lin Yen
Keyword(s):  
Cylindrical Shell ◽  
Acoustic Waves ◽  
Nonlinear Response ◽  
Circular Cylindrical Shell ◽  
Pressure Profile ◽  
Response Analysis ◽  
Fluid Medium ◽  
Convolution Integrals ◽  
Infinite Cylindrical Shell ◽  
Incident Waves

The geometrically and constitutively nonlinear response of an infinite, circular, cylindrical shell submerged in an infinite fluid medium to a transverse, transient acoustic wave is analyzed. Circumferential Fourier series solutions are obtained through the numerical integration of coupled ordinary differential equations and convolution integrals. Numerical results are presented in the form of response histories, response snapshots, and iso-damage curves for incident waves of rectangular pressure profile. Response solutions obtained with the first-order doubly asymptotic approximation are compared with their “exact” counterparts. It is found that doubly asymptotic approximations are unsuitable for two-dimensional, shock-response analysis of yielding submerged structures.

Power Flow and Sound Radiation of a Submerged Cylindrical Shell with Internal Structural

2011 ◽  
Vol 105-107 ◽  
pp. 321-325 ◽  
Author(s):  
Jin Yan ◽  
Juan Zhang
Keyword(s):  
Cylindrical Shell ◽  
Power Flow ◽  
Coupled System ◽  
Engineering Practice ◽  
Coupling Condition ◽  
Space Harmonics ◽  
In Series ◽  
Infinite Cylindrical Shell ◽  
Radiated Sound ◽  
Vibrational Power Flow

The vibrational power flow in a submerged infinite cylindrical shell with internal rings and bulkheads are studied analytically. The harmonic motion of the shell and the pressure field in the fluid is described by Flügge shell theory and Helmholtz equation, respectively. The coupling condition on the outer surface of the shell wall is introduced to obtain the vibrational equation of this coupled system. Both four kinds of forces (moments) between rings and shell and between bulkheads and shell are considered. The solution is obtained in series form by expanding the system responses in terms of the space harmonics of the spacing of both ring stiffeners and bulkheads. The vibrational power flow and radiated sound power are obtained and the influences of various complicating effects such as the ring, bulkhead and fluid loading on the results are analyzed. The analytic model is close to engineering practice, which will be valuable to the application on noise and vibration control of submarines and underwater pipes.

Vibration Power Flow Analysis of a Submerged Constrained Layer Damping Cylindrical Shell

2012 ◽  
Author(s):  
Yun Wang ◽  
Gangtie Zheng
Keyword(s):  
Cylindrical Shell ◽  
Power Flow ◽  
Axial Direction ◽  
Input Power ◽  
Exciting Force ◽  
Dynamic Equations ◽  
Constrained Layer Damping ◽  
Vibration Power Flow ◽  
Constrained Damping ◽  
Mode Order

The vibration power flow in a submerged infinite constrained layer damping (CLD) cylindrical shell is studied in the present paper using the wave propagation approach. Dynamic equations of the shell are derived with the Hamilton principle in conjunction with the Donnell shell assumptions. Besides, the pressure field in the fluid is described by the Helmholtz equation and the damping characteristics are considered with the complex modulus method. Then, the shell-fluid coupling dynamic equations are obtained by using the coupling between the shell and the fluid. Vibration power flows inputted to the coupled system and transmitted along the shell axial direction are both studied. Results show that input power flow varies with driving frequency and circumferential mode order, and the constrained damping layer will restrict the exciting force inputting power flow into the shell, especially for a thicker viscoelastic layer, a thicker or stiffer constraining layer (CL), and a higher circumferential mode order. Cut-off frequencies do not exist in the CLD cylindrical shell so that the exciting force can input power flow into the shell at any frequency and for any circumferential mode order. The power flow transmitted in the CLD cylindrical shell exhibits an exponential decay form along its axial direction, which indicates that the constrained damping layer has a good damping effect especially at middle or high frequencies.

Nonlinear Response of an Elastic Cylindrical Shell to a Transient Acoustic Wave

1981 ◽  
Vol 48 (1) ◽  
pp. 15-24 ◽  
Author(s):  
T. L. Geers ◽  
C.-L. Yen
Keyword(s):  
Cylindrical Shell ◽  
Acoustic Wave ◽  
Nonlinear Response ◽  
Circular Cylindrical Shell ◽  
Elastic Cylindrical Shell ◽  
Fluid Medium ◽  
Energy Functionals ◽  
Potential Formulation ◽  
Rigorous Treatment ◽  
Residual Potential

Governing equations are developed for the nonlinear response of an infinite, elastic, circular cylindrical shell submerged in an infinite fluid medium and excited by a transverse, transient acoustic wave. These equations derive from circumferential Fourier-series decomposition of the field quantities appearing in appropriate energy functionals, and from application of the “residual potential formulation” for rigorous treatment of the fluid-structure interaction. Extensive numerical results are presented that provide understanding of the phenomenology involved.

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