scholarly journals Wave Based Method for Free Vibration Analysis of Ring Stiffened Cylindrical Shell with Intermediate Large Frame Ribs

2013 ◽  
Vol 20 (3) ◽  
pp. 459-479 ◽  
Author(s):  
Meixia Chen ◽  
Jianhui Wei ◽  
Kun Xie ◽  
Naiqi Deng ◽  
Guoxiang Hou
Keyword(s):  
Cylindrical Shell ◽  
Free Vibration ◽  
Boundary Conditions ◽  
Natural Frequencies ◽  
Free Vibration Analysis ◽  
Structure Type ◽  
Vibration Characteristics ◽  
Mode Shapes ◽  
Arbitrary Boundary ◽  
Stiffened Cylindrical Shell

Wave based method which can be recognized as a semi-analytical and semi-numerical method is presented to analyze the free vibration characteristics of ring stiffened cylindrical shell with intermediate large frame ribs for arbitrary boundary conditions. According to the structure type and the positions of discontinuities, the model is divided into different substructures whose vibration field is expanded by wave functions which are exactly analytical solutions to the governing equations of the motions of corresponding structure type. Boundary conditions and continuity equations between different substructures are used to form the final matrix to be solved. Natural frequencies and vibration mode shapes are calculated by wave based method and the results show good agreement with finite element method for clamped-clamped, shear diaphragm – shear diaphragm and free-free boundary conditions. Free vibration characteristics of ring stiffened cylindrical shells with intermediate large frame ribs are compared with those with bulkheads and those with all ordinary ribs. Effects of the size, the number and the distribution of intermediate large frame rib are investigated. The frame rib which is large enough is playing a role as bulkhead, which can be considered imposing simply supported and clamped constraints at one end of the cabin and dividing the cylindrical shell into several cabins vibrating separately at their own natural frequencies.

scholarly journals A Unified Approach of Free Vibration Analysis for Stiffened Cylindrical Shell with General Boundary Conditions

2019 ◽  
Vol 2019 ◽  
pp. 1-14 ◽  
Author(s):  
Xue-Qin Li ◽  
Wei Zhang ◽  
Xiao-Dong Yang ◽  
Lu-Kai Song
Keyword(s):  
Cylindrical Shell ◽  
Free Vibration ◽  
Boundary Conditions ◽  
Vibration Analysis ◽  
Natural Frequencies ◽  
Free Vibration Analysis ◽  
General Boundary ◽  
General Boundary Conditions ◽  
Unified Approach ◽  
Stiffened Cylindrical Shell

A unified approach of free vibration analysis for stiffened cylindrical shell with general boundary conditions is presented in this paper. The vibration of stiffened cylindrical shell is modeled mathematically involving the first-order shear deformation shell theory. The improved Fourier series is selected as the admissible displacement function while the arbitrary boundary conditions are simulated by adjusting the equivalent spring stiffness. The natural frequencies and modal shapes of the stiffened shell are obtained by solving the dynamic model with the Rayleigh-Ritz procedure. Various numerical results of free vibration analysis for stiffened cylindrical shell are obtained, including natural frequencies and modes under simply supported, free, and clamped boundary conditions. Moreover, the effects of stiffener on natural frequencies are discussed. Compared with several state-of-the-art methods, the feasibility and validity of the proposed method are verified.

FREE VIBRATION ANALYSIS OF DISCRETELY STIFFENED SKEW PLATES

2001 ◽  
Vol 01 (01) ◽  
pp. 125-144 ◽  
Author(s):  
HUAN ZENG ◽  
CHARLES W. BERT
Keyword(s):  
Free Vibration ◽  
Boundary Conditions ◽  
Natural Frequencies ◽  
Ritz Method ◽  
Free Vibration Analysis ◽  
Vibration Characteristics ◽  
Skew Angle ◽  
Various Boundary Conditions ◽  
Skew Plate ◽  
Convergence Study

Stiffened skew plates find application in various engineering fields. The free vibration characteristics of such plates have been studied by various methods. An orthogonally stiffened skew plate is a skew plate with stiffeners running orthogonal to two opposite edges. To the best knowledge of the present investigators, no previous work has been done for free vibration characteristics of skew plates of such stiffening geometry. The present work studies the free vibration of such plates. The pb-2 Rayleigh–Ritz method was employed due to its accuracy and computational efficiency. The conventional finite element method was also used as a comparative check. A convergence study was first performed for various boundary conditions. Then the vibration of orthogonally stiffened skew plates with different boundary conditions was studied. Close agreement was found between these two methods. The variations of natural frequencies with different parameters, including skew angle ϕ, edge ratio b/a, and height-thickness ratio f/h, were investigated for three types of boundary conditions.

Free vibration analysis of a rectangular plate carrying multiple various concentrated elements

2003 ◽  
Vol 217 (2) ◽  
pp. 171-183 ◽  
Author(s):  
J-S Wu ◽  
H-M Chou ◽  
D-W Chen
Keyword(s):  
Finite Element ◽  
Free Vibration ◽  
Boundary Conditions ◽  
Rectangular Plate ◽  
Normal Mode ◽  
Vibration Analysis ◽  
Natural Frequencies ◽  
Free Vibration Analysis ◽  
Equation Of Motion ◽  
Mode Shapes

The dynamic characteristic of a uniform rectangular plate with four boundary conditions and carrying three kinds of multiple concentrated element (rigidly attached point masses, linear springs and elastically mounted point masses) was investigated. Firstly, the closed-form solutions for the natural frequencies and the corresponding normal mode shapes of a rectangular ‘bare’ (or ‘unconstrained’) plate (without any attachments) with the specified boundary conditions were determined analytically. Next, by using these natural frequencies and normal mode shapes incorporated with the expansion theory, the equation of motion of the ‘constrained’ plate (carrying the three kinds of multiple concentrated element) were derived. Finally, numerical methods were used to solve this equation of motion to give the natural frequencies and mode shapes of the ‘constrained’ plate. To confirm the reliability of previous free vibration analysis results, a finite element analysis was also conducted. It was found that the results obtained from the above-mentioned two approaches were in good agreement. Compared with the conventional finite element method (FEM), the approach employed in this paper has the advantages of saving computing time and achieving better accuracy, as can be seen from the existing literature.

An exact solution for free vibration of thin functionally graded rectangular plates

2010 ◽  
Vol 225 (3) ◽  
pp. 526-536 ◽  
Author(s):  
A Hasani Baferani ◽  
A R Saidi ◽  
E Jomehzadeh
Keyword(s):  
Free Vibration ◽  
Boundary Conditions ◽  
Natural Frequencies ◽  
Equations Of Motion ◽  
Vibration Characteristics ◽  
Functionally Graded ◽  
Mode Shapes ◽  
Rectangular Plates ◽  
Functionally Graded Plates ◽  
Different Boundary Conditions

The aim of this article is to find an exact analytical solution for free vibration characteristics of thin functionally graded rectangular plates with different boundary conditions. The governing equations of motion are obtained based on the classical plate theory. Using an analytical method, three partial differential equations of motion are reformulated into two new decoupled equations. Based on the Navier solution, a closed-form solution is presented for natural frequencies of functionally graded simply supported rectangular plates. Then, considering Levy-type solution, natural frequencies of functionally graded plates are presented for various boundary conditions. Three mode shapes of a functionally graded rectangular plate are also presented for different boundary conditions. In addition, the effects of aspect ratio, thickness—length ratio, power law index, and boundary conditions on the vibration characteristics of functionally graded rectangular plates are discussed in details. Finally, it has been shown that the effects of in-plane displacements on natural frequencies of functionally graded plates under different boundary conditions have been studied.

An Extended Separation-of-Variable Method for Free Vibration of Rectangular Mindlin Plates

2021 ◽  
pp. 2150154
Author(s):  
Gen Li ◽  
Yufeng Xing ◽  
Zekun Wang
Keyword(s):  
Free Vibration ◽  
Boundary Conditions ◽  
Closed Form ◽  
Natural Frequencies ◽  
Mode Shapes ◽  
Arbitrary Boundary ◽  
Unknown Variable ◽  
Closed Form Solutions ◽  
Solution Methods ◽  
Separation Of Variable

For rectangular thick plates with non-Levy boundary conditions, it is important to explore analytical free vibration solutions because the classical inverse and semi-inverse exact solution methods are not applicable to this category of problems. This work is to develop an extended separation-of-variable (SOV) method to find closed-form analytical solutions for the free vibration of rectangular Mindlin plates with arbitrary homogeneous boundary conditions. In the extended SOV method, characteristic differential equations and boundary conditions in two directions are obtained by employing the Rayleigh principle and the assumption that the mode functions are in the SOV form, and two transcendental eigenvalue equations are achieved through boundary conditions. But these two eigenvalue equations cannot be solved simultaneously since there are two equations and only the natural frequency is the unknown variable. Considering this, the second assumption in this method is that the natural frequencies corresponding to two-direction mode functions are independent of each other in the mathematical sense, thus there are two unknowns in two transcendental eigenvalue equations, and the closed-form solutions for plates with arbitrary boundary conditions can be obtained non-iteratively. From the physical sense, the natural frequencies pertaining to different direction mode functions should be the same, and this conclusion is validated analytically and numerically. The present natural frequencies and mode shapes agree well with those obtained by other analytical and numerical methods. Especially, for the plates with at least two opposite sides simply supported, the present solutions are exact.

A Study on the Free Vibration of the Prestressed Joined Cylindricalspherical Shell Structures

2013 ◽  
Vol 390 ◽  
pp. 207-214 ◽  
Author(s):  
Mahdi Yusefzad ◽  
Firouz Bakhtiari Nejad
Keyword(s):  
Cylindrical Shell ◽  
Free Vibration ◽  
Shell Structure ◽  
Shell Theory ◽  
Natural Frequencies ◽  
Vibration Characteristics ◽  
Shell Structures ◽  
Mode Shapes ◽  
Free Boundary Conditions ◽  
Modal Test

The free vibration characteristics of the prestressed joined spherical–cylindrical shell with free-free boundary conditions are investigated. The Flügge shell theory and Rayleigh-Ritz energy method are applied in order to analyze the free vibration characteristics of the joined shell. In the modal test, the LMS software is used to calculate mode shapes and natural frequencies of the joined shell structure. The natural frequencies and mode shapes are calculated numerically and they are compared with those of the FEM and modal test to confirm the reliability of the analytical solution. The effects of the shallowness and length of the cylindrical shell to the free vibrational behavior of joined shell structure and the effect of internal pressure on the modal charactristics are investigated.

scholarly journals Wave-Based Method for Free Vibration Analysis of Orthotropic Cylindrical Shells with Arbitrary Boundary Conditions

2019 ◽  
Vol 2019 ◽  
pp. 1-15
Author(s):  
Fuzhen Pang ◽  
Ruidong Huo ◽  
Haichao Li ◽  
Cong Gao ◽  
Xuhong Miao ◽  
...  
Keyword(s):  
Free Vibration ◽  
Boundary Conditions ◽  
Circular Cylindrical Shell ◽  
Displacement Vector ◽  
Cylindrical Shells ◽  
Free Vibration Analysis ◽  
Vibration Characteristics ◽  
General Boundary ◽  
General Boundary Conditions ◽  
Arbitrary Boundary

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.

scholarly journals Application of Adomian Modified Decomposition Method to Free Vibration Analysis of Rotating Beams

2013 ◽  
Vol 2013 ◽  
pp. 1-10 ◽  
Author(s):  
Qibo Mao
Keyword(s):  
Free Vibration ◽  
Boundary Conditions ◽  
Vibration Analysis ◽  
Decomposition Method ◽  
Free Vibration Analysis ◽  
Mode Shapes ◽  
Rotating Beams ◽  
Arbitrary Boundary ◽  
Various Boundary Conditions ◽  
Governing Differential Equation

The Adomian modified decomposition method (AMDM) is employed in this paper for dynamic analysis of a rotating Euler-Bernoulli beam under various boundary conditions. Based on AMDM, the governing differential equation for the rotating beam becomes a recursive algebraic equation. By using the boundary condition equations, the dimensionless natural frequencies and corresponding mode shapes can be easily obtained simultaneously. The computed results for different boundary conditions as well as different offset length and rotational speeds are presented. The accuracy is assured from the convergence and comparison published results. It is shown that the AMDM offers an accurate and effective method of free vibration analysis of rotating beams with arbitrary boundary conditions.

scholarly journals Free vibration of functionally graded carbon nanotube-reinforced conical panels integrated with piezoelectric layers subjected to elastically restrained boundary conditions

2017 ◽  
Vol 9 (7) ◽  
pp. 168781401771181 ◽  
Author(s):  
Jianyu Fan ◽  
Jin Huang ◽  
Junbo Ding ◽  
Jie Zhang
Keyword(s):  
Carbon Nanotube ◽  
Free Vibration ◽  
Boundary Conditions ◽  
Natural Frequencies ◽  
Functionally Graded ◽  
Mode Shapes ◽  
Geometrical Parameters ◽  
Arbitrary Boundary ◽  
Piezoelectric Layers ◽  
Elastically Restrained

This article presents the free vibration of piezoelectric functionally graded carbon nanotube-reinforced composite conical panels with elastically restrained boundary conditions. The material properties of carbon nanotube-reinforced composites are assumed to be temperature-dependent and are obtained using the extended rule of mixture. First-order shear deformation theory is adopted to obtain the kinematics of the hybrid panels, and the boundary spring technique is used to implement arbitrary boundary conditions. Meanwhile, two types of electrical boundary conditions, closed circuit and open circuit, are considered for the free surfaces of the piezoelectric layers. The complete sets of electro-mechanically coupled governing equations are obtained using the Rayleigh–Ritz procedure with the Chebyshev polynomial basis functions. The resultant eigenvalue problem is solved to obtain natural frequencies and mode shapes of the hybrid panels. Convergence and comparison studies have been conducted to verify the stability and accuracy of the proposed method. Several numerical examples are examined to reveal the influences of the carbon nanotube volume fractions, carbon nanotube distribution types, boundary conditions, geometrical parameters, and temperatures on the natural frequencies of the hybrid panel. Moreover, the mode shapes of the hybrid panels under various boundary conditions are also presented.

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