Application of flügge thin shell theory to the solution of free vibration behaviors for spherical-cylindrical-spherical shell: A unified formulation

Pang, Fuzhen; Li, Haichao; Cui, Jie; Du, Yuan; Gao, Cong

doi:10.1016/j.euromechsol.2018.12.003

Cited by 75 publications

(12 citation statements)

References 42 publications

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“…Panda et al [29][30][31][32] investigated the nonlinear free vibration characteristics of laminated composite shallow spherical shell using the variational method, and the analytical model was established on the basis of Green-Lagrange nonlinear kinematics. For space reasons, other papers on rotating cylindrical and spherical shells can be found in references [33][34][35].…”

Section: Introductionmentioning

confidence: 99%

Free Vibration Characteristics of Moderately Thick Spherical Shell with General Boundary Conditions Based on Ritz Method

Gao

Zhang

et al. 2020

Shock and Vibration

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In this paper, the Ritz method is adopted to investigate the vibration characteristics of isotropic moderately thick annular spherical shell with general boundary conditions. The energy expressions of the annular spherical shell were established based on the first-order shear deformation theory (FSDT). The spring stiffness method is introduced to guarantee continuity and simulate various boundary conditions on the basis of the domain decomposition method. Under the current framework, the displacement admissible function along axial direction and circumferential direction of the shell structure are, respectively, expanded as the unified Jacobi polynomials and Fourier series. The final solutions can be obtained according to the Ritz method. The validity of the proposed method is proved by comparing the results of the same condition with those obtained by the finite element method (FEM) and published literatures. The results show that the current method has fast convergence and delightful accuracy through the comparative study. On this basis, the vibration characteristics of isotropic moderately thick annular spherical shell are further studied by a series of numerical examples.

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Section: Introductionmentioning

confidence: 99%

Free Vibration Characteristics of Moderately Thick Spherical Shell with General Boundary Conditions Based on Ritz Method

Gao

Zhang

et al. 2020

Shock and Vibration

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“…For the wave-based method, it is an unfamiliar semianalytical method to investigate the dynamic characteristics of the engineering structure in some applications such as cylindrical shell structure [33][34][35], coupled structure [36][37][38][39][40], coupled vibroacoustic problem [41], composite structure [42][43][44][45], and so on.…”

Section: Introductionmentioning

confidence: 99%

Wave‐Based Method for Free Vibration Analysis of Orthotropic Cylindrical Shells with Arbitrary Boundary Conditions

Pang

Huo

et al. 2019

Mathematical Problems in Engineering

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The wave-based method (WBM) is a feasible method which investigates the free vibration characteristics of orthotropic cylindrical shells under general boundary conditions. Based on Reissner–Naghid’s shell theory, the governing motion equation is established, and the displacement variables are transformed into wave functions formed to satisfy the governing equations. On the basis of the kinematic relationship between the force resultant and displacement vector, the overall matrix of the shell is established. Comparison studies of this paper with the solutions in the literatures were carried out to validate the accuracy of the present method. Furthermore, by analyzing some numerical examples, the free vibration characteristics of orthogonal anisotropic cylindrical shells under classical boundary conditions, elastic boundary conditions, and their combinations are studied. Also, the effects of the material parameter and geometric constant on the natural frequencies for the orthotropic circular cylindrical shell under general boundary conditions are discussed. The conclusions obtained can be used as data reference for future calculation methods.

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“…The adaptability and exactness of the method were verified by the results published in the literature and 3D finite element analysis. Pang and colleagues [5][6][7][8] used a semianalytical method to analyze free vibration characteristics of single and combined shells of revolution. Ye et al 9,10 investigated the vibration behaviors of functionally graded (FG) and composite laminated spherical shells with arbitrary boundary conditions.…”

Section: Introductionmentioning

confidence: 99%

Free vibration of spherical cap subjected to various boundary conditions

Huo

Pang

et al. 2019

Advances in Mechanical Engineering

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In this article, the free vibration characteristics of spherical caps with different thickness distribution subjected to general boundary conditions are investigated using a semi-analytical approach. Based on the theory of thin shell, the theoretical model of spherical cap is established. Spherical caps are partitioned into sections along the meridional orientation. The displacement components of spherical caps along the meridional direction are represented by Jacobi polynomials. Meanwhile, Fourier series are utilized to express displacement components in the circumferential direction. Various boundary conditions can be easily achieved by the penalty method of the spring stiffness technique. The vibration characteristics of spherical caps are derived by means of the Rayleigh–Ritz energy method. Reliability and validity of the current method are verified by convergence studies and numerical verification. The comparison of results between the current method, finite element method, and those published in the literature prove that the current method works well when handling free vibration of spherical caps. More results of spherical caps with different geometric specifications and edge conditions are displayed in the form of table and graphic, which may serve as a reference for future studies.

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Application of flügge thin shell theory to the solution of free vibration behaviors for spherical-cylindrical-spherical shell: A unified formulation

Cited by 75 publications

References 42 publications

Free Vibration Characteristics of Moderately Thick Spherical Shell with General Boundary Conditions Based on Ritz Method

Free Vibration Characteristics of Moderately Thick Spherical Shell with General Boundary Conditions Based on Ritz Method

Wave‐Based Method for Free Vibration Analysis of Orthotropic Cylindrical Shells with Arbitrary Boundary Conditions

Free vibration of spherical cap subjected to various boundary conditions

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