Effect of radial loads on the natural frequencies of thin-walled circular cylindrical shells

Kumar, Anish; Das, Sovan Lal; Wahi, Pankaj

doi:10.1016/j.ijmecsci.2016.12.024

Cited by 9 publications

(4 citation statements)

References 26 publications

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“…The integration of the partial differential equations rarely leads to an exact closed-form solution, which, however, is rather convoluted [1]. More frequently, the resolution is achieved by finite element analysis, numerical approaches [1][2][3][4][5][6][7] or simplified analytical models [8][9][10][11][12]. Nonetheless, the finite element method (FEM) may require a convergence analysis and lacks intelligibility.…”

Section: Introductionmentioning

confidence: 99%

A simple tool to forecast the natural frequencies of thin-walled cylinders

Cammalleri

2023

Theoretical and Applied Mechanics - AIMETA 2022

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Abstract. This paper presents an approximate method to predict the natural frequencies of thin-walled cylinders. By taking inspiration from a previous work of one of the authors, the starting point of the proposed approach is a proper construction of reasonable eigenfunctions. However, a new simple tool based on the principle of virtual work has been developed to estimate the natural frequencies and the amplitude of vibration without complex numerical resolution. Moreover, the applicability of the model is extended to all the most common constraint conditions. The identification of the natural frequencies of a continuous cylinder is reduced to an eigenvalue problem based on a matrix whose elements depend only on the geometric characteristics of the cylinder, the mechanical properties of the material and known numerical parameters. The latter are precalculated for given boundary conditions, covering clamped or pinned end constraints. Although the proposed formulation can address any constraints combination, only a pinned-pinned cylinder is analyzed here for brevity. The reliability of the model was tested against FEM analysis results. These comparisons showed that the maximum error versus the exact solutions for the lowest natural frequency is around 2% for all the mode shapes of the pinned-pinned case, offering an excellent trade-off between accuracy and ease of use.

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Section: Introductionmentioning

confidence: 99%

A simple tool to forecast the natural frequencies of thin-walled cylinders

Cammalleri

2023

Theoretical and Applied Mechanics - AIMETA 2022

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“…A similar approach was used by Fakkaew et al [34]. Lastly, the latest contributions focus on the finite element method (FEM) using the block Lanczos iteration method [35], the reverberation-ray matrix approach [36], Galerkin projections of the partial differential equations governing the shell equations of motion [37], the symplectic approach [38,39], and the isogeometric analysis [40] to extend the theory of natural vibrations to various thin-walled structures, also in composite materials [41].…”

Section: Introductionmentioning

confidence: 99%

A Dynamic Matrix for the Study of Free Vibrations of Thin Circular Cylindrical Shells under Different Boundary Conditions

Cammalleri,

Castellano

2023

Designs

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Although free vibrations of thin-walled cylinders have been extensively addressed in the relevant literature, finding a good balance between accuracy and simplicity of the procedures used for natural frequency assessment is still an open issue. This paper proposes a novel approach with a high potential for practical application for rapid esteem of natural frequencies of thin-walled cylinders under different boundary conditions. Starting from Donnell–Mushtari’s shell theory, the differential problem is simplified by using the principle of virtual work and introducing the flexural waveforms of a beam as constrained as the cylinder. Hence, the formulation is reduced to the eigenvalue problem of an equivalent 3 × 3 dynamic matrix, which depends on the cylinder geometry, material, and boundary conditions. Several comparisons with experimental, numerical, and analytical approaches are presented to prove model reliability and practical interest. An excellent balance between fast usability and accuracy is achieved. The user-friendliness of the model makes it suitable to be implemented during the design stage without requiring any deep knowledge of the topic.

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“…Kumar et al [4] stated that the derived equations are of importance in predicting the correct static buckling pressure. The variation of natural frequencies for thin-walled circular cylindrical shells subjected to external radial load are also studied with the help of these developed equations [17]. On the other hand, the governing equations are often predominant by radial displacements while the influence of the axial and circumferential displacements and their derivatives are often ignored during the applications [18][19][20].…”

Section: Introductionmentioning

confidence: 99%

The Significance of Nonlinear Terms in the Governing Equations to Describe the Large Deformation of Thin-Walled Cylindrical Shell Under Transient Pressures

Qian

et al. 2022

Preprint

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The significance of the nonlinear terms in the governing equations to describe the transiently large deformation of a thin-walled cylindrical shell under impact pressures is discussed in this paper. Firstly, the first P-K stress tensor is adopted to depict the motion equations of the shell with respect to the original configuration. More nonlinear terms are retained when the first P-K stress is transformed into the symmetrical second P-K stress. Moreover, the Green strain tensor is employed in the geometrical equation to describe the nonlinearly large deformation of shell, and the curvature change is expressed to involve large deformation as well. Without considering all these nonlinear terms, the governing equation can degenerate to that in references. The circumferential displacement is kept in the motion equations, and the wall thickness change is taken into account. Dividing these nonlinear terms into two parts according to their affiliations, four groups of governing equations involving different nonlinear terms are obtained. Then, the deformation behavior of a shell subjected to a specified loading is solved using different governing equations and compared with FEM results to reveal the significance of these nonlinear terms. It is found that the nonlinear terms from geometrical equations should be kept while the nonlinear terms in equilibrium equations can be ignored.

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Effect of radial loads on the natural frequencies of thin-walled circular cylindrical shells

Cited by 9 publications

References 26 publications

A simple tool to forecast the natural frequencies of thin-walled cylinders

A simple tool to forecast the natural frequencies of thin-walled cylinders

A Dynamic Matrix for the Study of Free Vibrations of Thin Circular Cylindrical Shells under Different Boundary Conditions

The Significance of Nonlinear Terms in the Governing Equations to Describe the Large Deformation of Thin-Walled Cylindrical Shell Under Transient Pressures

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