Curvature Effects on the Vibration Characteristics of Doubly Curved Shallow Shells with General Elastic Edge Restraints

Shi, Hui; Yang, Tianhang; Jiang, Shiliang; Li, W. L.; Liu, Zhigang

doi:10.1155/2015/435903

Cited by 4 publications

(3 citation statements)

References 29 publications

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“…In this article the GEM will be adapted to this purpose. It is to be noted that trigonometric shape functions have been extensively and successfully used to reproduce the vibration field of uniform and rib reinforced cylinders [45,46]. Unfortunately, thin cuneate ABH areas are very challenging and pose limits to the precision one could obtain with trigonometric functions [44].…”

Section: Introductionmentioning

confidence: 99%

Vibration of cylindrical shells with embedded annular acoustic black holes using the Rayleigh-Ritz method with Gaussian basis functions

Deng

Guasch

Maxit

et al. 2021

Mechanical Systems and Signal Processing

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The numerical simulation of beams and plates with embedded acoustic black holes (ABHs) is computationally demanding because of the very thin thickness attained at the ABH central area. Semi-analytical approaches relying on the Rayleigh-Ritz method with wavelet or Gaussian basis functions have thus revealed as an accurate and fast alternative to determine the ABH vibration field in parametric studies. To date however, the vast majority of works on ABHs have only dealt with ABH indentations on straight beams and flat plates. It would be also worth exploring the feasibility of ABHs to control the vibrations of curved shells, typically found in aerospace and naval structures. In this work, we address this issue and extend the Gaussian expansion method (GEM) to characterize annular ABHs embedded on cylindrical shells. First, we show how the GEM can be modified to make Gaussian shape functions satisfy periodic boundary conditions in the circumferential direction of the cylinder. The GEM is then used to determine the vibration field of the ABH cylindrical shell and gets validated by comparison with finite element simulations. A thorough analysis of the performance of the annular ABH follows, which stresses the differences with the behavior of ABHs on flat surfaces. In particular, we show the influence that waves propagating in the circumferential direction have on the operational frequency range of the ABH. The effects of the viscoelastic layer and the inclusion of longitudinal stiffeners to strengthen the cylinder rigidity are also analyzed by means of the proposed GEM approach. This work broadens previous semi-analytical methods to start investigating the ABH effect on curved structures.

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Section: Introductionmentioning

confidence: 99%

Vibration of cylindrical shells with embedded annular acoustic black holes using the Rayleigh-Ritz method with Gaussian basis functions

Deng

Guasch

Maxit

et al. 2021

Mechanical Systems and Signal Processing

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“…Shi et al [19] detected and studied the effects of curvature on the vibration characteristics of doubly curved shallow shells with general elastic edge constraints. A unified novel solution was proposed and validated by numerous tabular and graphical results illustrating the influence of curvature on the shell material frequencies for different boundary conditions.…”

Section: Introductionmentioning

confidence: 99%

Chaotic vibrations of flexible shallow axially symmetric shells

et al. 2018

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In this work, chaotic dynamics of flexible spherical axially symmetric shallow shells subjected to sinusoidal transverse load is studied with emphasis put on the vibration modes. Chaos reliability is verified and validated by solving the implemented mathematical model by partial nonlinear equations governing the dynamics of flexible spherical shells and by estimating the signs of the largest Lyapunov exponents with the help of qualitatively different approaches. It is shown how the scenario of transition of the investigated shells from regular to chaotic vibrations depends on the boundary condition. The following cases are considered: (1) movable and fixed simple supports along the shell contours, taking into account shell stiffness (Feigenbaum scenario) and shell damping (RuelleTakens-Newhouse scenario), and (2) movable clamping (regular shell vibrations). The presence of dents, the location and character of which essentially depend on the shell geometric parameters, boundary conditions, and the external load parameters, is detected in some regions of the shell surface and discussed.

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“…Shi et al [44] investigated the effect of the ratio of two principal radii of curvature on frequencies of free vibration of monolithic isotropic doubly curved shells using the LFAT. They found that natural frequencies increase with an increase in the R 2 /R 1 ratio for a given R 2 /l 2 ratio and decrease with an increase in the R 2 /l 2 ratio for a given R 2 /R 1 ratio, where l 1 and l 2 are the two planform lengths.…”

Section: Introductionmentioning

confidence: 99%

Stretching and bending deformations due to normal and shear tractions of doubly curved shells using third-order shear and normal deformable theory

Shah

Batra

2016

Mechanics of Advanced Materials and Structures

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We analyze static infinitesimal deformations of doubly curved shells using a third-order shear and normal deformable theory (TSNDT) and delineate effects of the curvilinear length/thickness ratio, R/a, a/h, radius of curvature/curvilinear length, and the ratio of the two principal radii on through-the-thickness stresses, strain energies of the in-plane and the transverse shear and normal deformations, and strain energies of stretching and bending deformations for loads that include uniform normal tractions on a major surface and equal and opposite tangential tractions on the two major surfaces. In the TSNDT the three displacement components at a point are represented as complete polynomials of degree three in the thickness coordinate. Advantages of the TSNDT include not needing a shear correction factor, allowing stresses for monolithic shells to be computed from the constitutive relation and the shell theory displacements, and considering general tractions on bounding surfaces. For laminated shells we use an equivalent single layer TSNDT and find the in-plane stresses from the constitutive relations and the transverse stresses with a onestep stress recovery scheme. The in-house developed finite element software is first verified by comparing displacements and stresses in the shell computed from it with those from either analytical or numerical solutions of the corresponding 3D problems. The strain energy of a spherical shell is found to approach that of a plate when R/a exceeds 10. For a thick clamped shell of aspect ratio 5 subjected to uniform normal traction on the outer surface, the in-plane and the transverse deformations contribute equally to the total strain energy for R/a greater than 5. However, for a cantilever shell of aspect ratio 5 subjected to equal and opposite uniform tangential tractions on the two major surfaces, the strain energy of in-plane deformations equals 95-98% of the total strain energy. Numerical results presented herein for several problems provide insights into different deformation modes, help designers decide when to consider effects of transverse deformations, and use the TSNDT for optimizing doubly curved shells.

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Curvature Effects on the Vibration Characteristics of Doubly Curved Shallow Shells with General Elastic Edge Restraints

Cited by 4 publications

References 29 publications

Vibration of cylindrical shells with embedded annular acoustic black holes using the Rayleigh-Ritz method with Gaussian basis functions

Vibration of cylindrical shells with embedded annular acoustic black holes using the Rayleigh-Ritz method with Gaussian basis functions

Chaotic vibrations of flexible shallow axially symmetric shells

Stretching and bending deformations due to normal and shear tractions of doubly curved shells using third-order shear and normal deformable theory

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