Free and Forced Vibration Characteristics Analysis of a Multispan Timoshenko Beam Based on the Ritz Method

The uniform formulation of dynamic vibration analysis of multispan beams is presented by using an efficient domain decomposition method in this paper. Firstly, the structure is divided into several equal sections based on domain decomposition method. Next, the artificial spring is used to simulate complex boundaries and continuity condition of multispan beam. Finally, the admissible displacement functions are expanded through Jacobi orthogonal polynomials, and the free and forced vibration characteristics of multispan beam structures can be obtained by using Rayleigh–Ritz method. Results for various boundary conditions, ratios of thickness to length (h/L), numbers, and stiffness of supporting springs are presented. It is clearly shown that accurate solutions can be obtained by using the proposed method, and this study extends the application range of the Jacobi polynomials-Ritz method. In addition, the research results of this paper can provide data support for engineers such as bridge designers to design multispan bridges.

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Free and forced vibration analysis of uniform and stepped circular cylindrical shells using a domain decomposition method

Applied Acoustics ◽

10.1016/j.apacoust.2012.09.002 ◽

2013 ◽

Vol 74 (3) ◽

pp. 425-439 ◽

Cited By ~ 58

Author(s):

Yegao Qu ◽

Yong Chen ◽

Xinhua Long ◽

Hongxing Hua ◽

Guang Meng

Keyword(s):

Domain Decomposition ◽

Forced Vibration ◽

Vibration Analysis ◽

Decomposition Method ◽

Domain Decomposition Method ◽

Cylindrical Shells ◽

Circular Cylindrical Shells ◽

Forced Vibration Analysis

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Vibration characteristics of a spherical–cylindrical–spherical shell by a domain decomposition method

Mechanics Research Communications ◽

10.1016/j.mechrescom.2013.01.002 ◽

2013 ◽

Vol 49 ◽

pp. 17-26 ◽

Cited By ~ 29

Author(s):

Shihao Wu ◽

Yegao Qu ◽

Hongxing Hua

Keyword(s):

Spherical Shell ◽

Domain Decomposition ◽

Decomposition Method ◽

Domain Decomposition Method ◽

Vibration Characteristics

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A Domain Decomposition Method for Forced Vibration Analysis of Joined Conical-Cylindrical-Spherical Shell

Applied Mechanics and Materials ◽

10.4028/www.scientific.net/amm.184-185.3 ◽

2012 ◽

Vol 184-185 ◽

pp. 3-10

Author(s):

Shi Hao Wu ◽

Ye Gao Qu ◽

Hong Xing Hua

Keyword(s):

Boundary Conditions ◽

Spherical Shell ◽

Domain Decomposition ◽

Forced Vibration ◽

Decomposition Method ◽

Domain Decomposition Method ◽

Double Series ◽

Longitudinal Direction ◽

Energy Functional ◽

Finite Element Software

Based upon the Reissner-Naghdi-Berry shell theory, a semi-analytical domain decomposition method is presented to analyze the forced vibration of a joined conical-cylindrical-spherical shell with general boundary conditions. The joined shell was divided into some conical, cylindrical and spherical shell segments along the axis of revolution. The constraint equations derived from interface continuity conditions between two adjacent shell segments were introduced into the energy functional of the joined shell. Displacement variables of each shell segment are expressed as a mixed double series in the forms of Fourier series in the circumferential direction and Chebyshev orthogonal polynomial in the longitudinal direction. The forced vibration response of the joined shells subjected to various harmonic excitations and boundary conditions was calculated and compared with those FEM results obtained by finite element software ANSYS to confirm the reliability and accuracy of this analytical solution.

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

Shock and Vibration ◽

10.1155/2020/4130103 ◽

2020 ◽

Vol 2020 ◽

pp. 1-20

Author(s):

Bing Hu ◽

Cong Gao ◽

Hang Zhang ◽

Haichao Li ◽

Fuzhen Pang ◽

...

Keyword(s):

Boundary Conditions ◽

Spherical Shell ◽

Jacobi Polynomials ◽

Domain Decomposition Method ◽

Ritz Method ◽

Admissible Function ◽

Shear Deformation Theory ◽

Vibration Characteristics ◽

General Boundary ◽

General Boundary Conditions

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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