Analysis of Wave Propagation in Elastic Cylindrical Shells by the Perturbation Method

1972 ◽  
Vol 39 (2) ◽  
pp. 385-389 ◽  
Author(s):  
T. L. Geers
Keyword(s):  
Cylindrical Shell ◽  
Wave Propagation ◽  
Perturbation Method ◽  
Cylindrical Shells ◽  
Stress Waves ◽  
Elastic Cylindrical Shell ◽  
Series Solutions ◽  
Perturbation Solutions

Simple perturbation solutions are given for the propagation of stress waves in an elastic cylindrical shell subjected to transient, axisymmetric, longitudinal excitations. The solutions are shown to be accurate even at rather large distances from the boundary at which the excitation is applied. Convergence of the series solutions is examined and application of the technique to related problems is discussed.

scholarly journals Elastic Response of Acoustic Coating on Fluid-Loaded Rib-Stiffened Cylindrical Shells

2018 ◽  
Vol 141 (1) ◽  
Author(s):  
Christopher Gilles Doherty ◽  
Steve C. Southward ◽  
Andrew J. Hull
Keyword(s):  
Cylindrical Shell ◽  
Cylindrical Shells ◽  
Coupled System ◽  
Elastic Response ◽  
System Response ◽  
Elastic Cylindrical Shell ◽  
Fluid Environment ◽  
Reinforcing Ribs ◽  
Double Index ◽  
Stress Boundary Conditions

Reinforced cylindrical shells are used in numerous industries; common examples include undersea vehicles, aircraft, and industrial piping. Current models typically incorporate approximation theories to determine shell behavior, which are limited by both thickness and frequency. In addition, many applications feature coatings on the shell interior or exterior that normally have thicknesses which must also be considered. To increase the fidelity of such systems, this work develops an analytic model of an elastic cylindrical shell featuring periodically spaced ring stiffeners with a coating applied to the outer surface. There is an external fluid environment. Beginning with the equations of elasticity for a solid, spatial-domain displacement field solutions are developed incorporating unknown wave propagation coefficients. These fields are used to determine stresses at the boundaries of the shell and coating, which are then coupled with stresses from the stiffeners and fluid. The stress boundary conditions contain double-index infinite summations, which are decoupled, truncated, and recombined into a global matrix equation. The solution to this global equation results in the displacement responses of the system as well as the exterior scattered pressure field. An incident acoustic wave excitation is considered. Thin-shell reference models are used for validation, and the predicted system response to an example simulation is examined. It is shown that the reinforcing ribs and coating add significant complexity to the overall cylindrical shell model; however, the proposed approach enables the study of structural and acoustic responses of the coupled system.

The Effect of Plate Curvature on the Influence of Macroscale Geometric Voids in Controlling Stress Wave Propagation

2020 ◽  
Author(s):  
C. S. Florio
Keyword(s):  
Wave Propagation ◽  
Stress Wave ◽  
Plane Stress ◽  
Cylindrical Shells ◽  
Reaction Force ◽  
Stress Waves ◽  
Stress Wave Propagation ◽  
Axial Impact ◽  
Plate Curvature ◽  
Metal Plates

Abstract Much work has been done to create and understand means to control the propagation of acoustic and light waves through materials and structures. The ability to perform similar studies on the control of stress waves has implications not only for the development of capabilities to disrupt stress waves in order to limit their damage, but also to direct stress waves in order to tailor the behavior of a structure for a specific functional goal. Recent studies have demonstrated the use of voids and inclusions of varying size, geometry, arrangement, and composition in structures to attenuate impact forces or cloak stress waves in thin, flat, plane stress plates. However, many structures that may benefit from these wave modification methods are comprised of cylindrical shells. It is not currently known how well the techniques to control wave propagation and trends identified in plane stress plates can be applied to structures with cylindrical shells. Therefore, this study develops and uses computational modeling methods to examine the modification and control of stress waves induced by an axial impact load in metal plates of varying curvature through the inclusion of macroscale voids. Methods are developed and used in this work to study the response of metal plates of varying curvature with and without voids of different shapes and arrangement to axial impact loads. The response is quantified through the magnitude of the fixed end reaction force and through normal oscillations of discrete points along the length of the plate. Fast Fourier transformation and wavelet coherence techniques are used to understand both the time-averaged and time-dependent oscillation behavior. Correlations are drawn between plate curvature and void design on the control of the propagation of stress waves. The knowledge gained can help guide the understanding design of these stress wave modification features.

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).

Rails Deformation Pattern in Frontal Impact

2002 ◽  
Author(s):  
Joseph Hassan ◽  
Guy Nusholtz ◽  
Ke Ding
Keyword(s):  
Wave Propagation ◽  
Real World ◽  
Stress Waves ◽  
Stress Wave Propagation ◽  
Deformation Pattern ◽  
Frontal Impact ◽  
Rigid Barrier ◽  
Final Deformation ◽  
Deformation Patterns ◽  
The Impact

During a vehicle crash stress waves can be generated at the impact point and propagate through the vehicle structure. The generation of these waves is dependent, in general, on the crash type and, in particular, on the impact contact characteristics. This has consequences with respect to different crash barrier interfaces for vehicle evaluation. The two barriers most commonly used to evaluate the response of a vehicle in a frontal impact are the rigid barrier and the offset deformable barrier. They constitute different crash modes, full frontal and offset. Consequently it would be expected that there are different deformation patterns between the two. However, an additional possible contributor to the difference is that an impact into a rigid barrier generates waves of significantly greater stress than impacts with the deformable one. If stress waves are a significant component of real world final deformation patterns then, the choice of barrier interface and its effective stiffness is critical. To evaluate this conjecture, models of two types of rails each undergoing two different types of impacts, are analyzed using an explicit dynamic finite element code. Results show that the energy perturbation along the rail depends on the barrier type and that the early phase of wave propagation has very little effect on the final deformation pattern. This implies that in the real world conditions, the stress wave propagation along the rail has very little effect on the final deformed shape of the rail.

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