Free Vibration Analysis of an Inflated Toroidal Shell

2002 ◽  
Vol 124 (3) ◽  
pp. 387-396 ◽  
Author(s):  
Akhilesh K. Jha ◽  
Daniel J. Inman ◽  
Raymond H. Plaut
Keyword(s):  
Differential Equations ◽  
Free Vibration ◽  
Vibration Analysis ◽  
Natural Frequencies ◽  
Circular Cross Section ◽  
Free Vibration Analysis ◽  
Longitudinal Direction ◽  
Variable Coefficients ◽  
Mode Shapes ◽  
Toroidal Shell

Free vibration analysis of a free inflated torus of circular cross-section is presented. The shell theory of Sanders, including the effect of pressure, is used in formulating the governing equations. These partial differential equations are reduced to ordinary differential equations with variable coefficients using complete waves in the form of trigonometric functions in the longitudinal direction. The assumed mode shapes are divided into symmetric and antisymmetric groups, each given by a Fourier series in the meridional coordinate. The solutions (natural frequencies and mode shapes) are obtained using Galerkin’s method and verified with published results. The natural frequencies are also obtained for a circular cylinder with shear diaphragm boundary condition as a special case of the toroidal shell. Finally, the effects of aspect ratio, pressure, and thickness on the natural frequencies of the inflated torus are studied.

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.

scholarly journals Free Vibrations of a Reddy-Bickford Multi-Span Beam Carrying Multiple Spring-Mass Systems

2011 ◽  
Vol 18 (5) ◽  
pp. 709-726 ◽  
Author(s):  
Yusuf Yesilce
Keyword(s):  
Free Vibration ◽  
Vibration Analysis ◽  
Natural Frequencies ◽  
Free Vibration Analysis ◽  
Beam Theory ◽  
Free Vibrations ◽  
Mode Shapes ◽  
Structural Elements ◽  
Mass System ◽  
Assembly Technique

The structural elements supporting motors or engines are frequently seen in technological applications. The operation of machine may introduce additional dynamic stresses on the beam. It is important, then, to know the natural frequencies of the coupled beam-mass system, in order to obtain a proper design of the structural elements. The literature regarding the free vibration analysis of Bernoulli-Euler and Timoshenko single-span beams carrying a number of spring-mass system and multi-span beams carrying multiple spring-mass systems are plenty, but the free vibration analysis of Reddy-Bickford multi-span beams carrying multiple spring-mass systems has not been investigated by any of the studies in open literature so far. This paper aims at determining the exact solutions for the natural frequencies and mode shapes of Reddy-Bickford beams. The model allows analyzing the influence of the shear effect and spring-mass systems on the dynamic behavior of the beams by using Reddy-Bickford Beam Theory (RBT). The effects of attached spring-mass systems on the free vibration characteristics of the 1–4 span beams are studied. The natural frequencies of Reddy-Bickford single-span and multi-span beams calculated by using the numerical assembly technique and the secant method are compared with the natural frequencies of single-span and multi-span beams calculated by using Timoshenko Beam Theory (TBT); the mode shapes are presented in graphs.

Differential Transformation Approach for Free Vibration Analysis of a Centrifugally Stiffened Timoshenko Beam

2005 ◽  
Vol 128 (2) ◽  
pp. 170-175 ◽  
Author(s):  
C. Mei
Keyword(s):  
Free Vibration ◽  
Timoshenko Beam ◽  
Natural Frequencies ◽  
Free Vibration Analysis ◽  
Variable Coefficients ◽  
Mode Shapes ◽  
Governing Equations ◽  
Transformation Technique ◽  
Differential Transformation ◽  
Transformation Approach

In this paper, the differential transformation approach is applied to analyze the free vibration of centrifugally stiffened Timoshenko beam structures. Such structures involve variable coefficients in the governing equations, which in general cannot be solved analytically in closed form. Both the natural frequencies and the mode shapes are obtained using the differential transformation technique. Numerical examples are presented and results are compared with available results in the literature.

Free vibration analysis of a single edge cracked symmetric functionally graded stepped beams

2020 ◽  
Vol 23 (16) ◽  
pp. 3415-3428
Author(s):  
Yusuf Cunedioglu ◽  
Shkelzen Shabani
Keyword(s):  
Free Vibration ◽  
Vibration Analysis ◽  
Natural Frequencies ◽  
Crack Depth ◽  
Free Vibration Analysis ◽  
Functionally Graded ◽  
Mode Shapes ◽  
Single Edge ◽  
Functionally Graded Beam ◽  
Cross Sectional

Free vibration analysis of a single edge cracked multi-layered symmetric sandwich stepped Timoshenko beams, made of functionally graded materials, is studied using finite element method and linear elastic fracture mechanic theory. The cantilever functionally graded beam consists of 50 layers, assumed that the second stage of the beam (step part) is created by machining. Thus, providing the material continuity between the two beam stages. It is assumed that material properties vary continuously, along the thickness direction according to the exponential and power laws. A developed MATLAB code is used to find the natural frequencies of three types of the stepped beam, concluding a good agreement with the known data from the literature, supported also by ANSYS software in data verification. In the study, the effects of the crack location, crack depth, power law gradient index, different material distributions, different stepped length, different cross-sectional geometries on natural frequencies and mode shapes are analysed in detail.

Multistage Coupling of Eight Mistuned Bladed Disk on a Solid Shaft: Part 1—Free Vibration Analysis

2012 ◽  
Author(s):  
Romuald Rzadkowski ◽  
Artur Maurin
Keyword(s):  
Finite Element ◽  
Free Vibration ◽  
Vibration Analysis ◽  
Natural Frequencies ◽  
Free Vibration Analysis ◽  
Free Vibrations ◽  
Rotor Blades ◽  
Mode Shapes ◽  
Bladed Disk ◽  
Centrifugal Stiffening

Considered here was the effect of multistage coupling on the dynamics of a rotor consisting of eight mistuned bladed discs on a solid shaft. Each bladed disc had a different number of rotor blades. Free vibrations were examined using finite element representations of rotating single blades, bladed discs, and the entire rotor. In this study the global rotating mode shapes of eight flexible mistuned bladed discs on shaft assemblies were calculated, taking into account rotational effects such as centrifugal stiffening. The thus obtained natural frequencies of the blade, shaft, bladed disc and entire shaft with discs were carefully examined to discover resonance conditions and coupling effects. This study found that mistuned systems cause far more intensive multistage coupling than tuned ones. The greater the mistuning, the more intense the multistage coupling.

FINITE ELEMENT ANALYSIS OF CONTROLLED LOW STRENGTH MATERIAL PAVEMENT BASES: FREE VIBRATION ANALYSIS

2017 ◽  
Vol 4 (1) ◽  
Author(s):  
Li-Jeng Huang ◽  
Her-Yung Wang ◽  
Wen-Ling Huang ◽  
Ming-Chao Lin
Keyword(s):  
Finite Element ◽  
Free Vibration ◽  
Vibration Analysis ◽  
Natural Frequencies ◽  
Free Vibration Analysis ◽  
Crushed Stone ◽  
Mode Shapes ◽  
Strength Material ◽  
Low Strength ◽  
Controlled Low Strength Material

This paper presents free vibration analysis of pavement bases constructed using sustainable material, a controlled low-strength material (CLSM), using finite element (FE) method. The CLSM concrete is introduced as pavement bases for its special features of easy compaction, high workability and relatively low cost. Rut-resistant stone matrix asphalt is placed on top of CLSM as wearing surface layer. The Young's moduli of CLSM are obtained from laboratory tests for two different binder mixtures, marked as CLSM-B80/30% and CLSM-B130/30%. Two-dimensional planar strain assumption is employed in the FE formulation of steady-state elasto-dynamic analysis of four-layered flexible pavements in which four kinds of different base materials are considered: graded crushed stone, CLSM-B80/30%, CLSM-B130/30% and AC. Comparison study on computed natural frequencies and mode shapes of the flexible pavement using different bases materials will be conducted. Results show that CLSM pavement bases depict higher natural frequencies as compared with graded crushed stone bases and can be suitable sustainable materials employed for pavement design and construction in highway engineering.

scholarly journals Analytical Solution for the Free Vibration Analysis of Delaminated Timoshenko Beams

2014 ◽  
Vol 2014 ◽  
pp. 1-10 ◽  
Author(s):  
Ramazan-Ali Jafari-Talookolaei ◽  
Maryam Abedi
Keyword(s):  
Analytical Solution ◽  
Free Vibration ◽  
Variational Problem ◽  
Lagrange Multipliers ◽  
Vibration Analysis ◽  
Natural Frequencies ◽  
Free Vibration Analysis ◽  
Mode Shapes ◽  
Timoshenko Beams ◽  
Method Of Lagrange Multipliers

This work presents a method to find the exact solutions for the free vibration analysis of a delaminated beam based on the Timoshenko type with different boundary conditions. The solutions are obtained by the method of Lagrange multipliers in which the free vibration problem is posed as a constrained variational problem. The Legendre orthogonal polynomials are used as the beam eigenfunctions. Natural frequencies and mode shapes of various Timoshenko beams are presented to demonstrate the efficiency of the methodology.

scholarly journals The Effect of Axial Force on the Free Vibration of an Euler-Bernoulli Beam Carrying a Number of Various Concentrated Elements

2013 ◽  
Vol 20 (3) ◽  
pp. 357-367 ◽  
Author(s):  
Gürkan Şcedilakar
Keyword(s):  
Free Vibration ◽  
Vibration Analysis ◽  
Axial Load ◽  
Natural Frequencies ◽  
Free Vibration Analysis ◽  
Mode Shapes ◽  
The Finite Element Method ◽  
Bernoulli Beam ◽  
Euler Beam ◽  
Euler Bernoulli Beam

In this study, free vibration analysis of beams carrying a number of various concentrated elements including point masses, rotary inertias, linear springs, rotational springs and spring-mass systems subjected to the axial load was performed. All analyses were performed using an Euler beam assumption and the Finite Element Method. The beam used in the analyses is accepted as pinned-pinned. The axial load applied to the beam from the free ends is either compressive or tensile. The effects of parameters such as the number of spring-mass systems on the beam, their locations and the axial load on the natural frequencies were investigated. The mode shapes of beams under axial load were also obtained.

scholarly journals Free Vibration Analysis of Cable Stayed-Bridge by Finite Element Method

2019 ◽  
Vol 12 (4) ◽  
pp. 67-72
Author(s):  
Haneen A. Mahmood ◽  
Zaid S. Hammoudi ◽  
Ali Laftah Abbas
Keyword(s):  
Finite Element ◽  
Free Vibration ◽  
Vibration Analysis ◽  
Natural Frequencies ◽  
Three Dimensional ◽  
Free Vibration Analysis ◽  
Element Model ◽  
Dynamic Responses ◽  
Mode Shapes ◽  
Cable Stayed Bridge

A delicate analysis of the natural frequencies and mode shapes of a cable stayed bridge is essential to the solution of its dynamic responses due to seismic, wind and traffic loads. In this paper, a bridge with geometry comparable to the Quincy Bayview Bridge was modelled in order to explore the significance of the three dimensional and free vibration analysis. This paper provides a detail of the bridge and the equivalent cross section of the three-dimensional finite element model implicating cables, the bridge deck and pylons as well as the boundary conditions and free vibration analysis by Ansys15.0. The bridge was analyzed to free vibration to obtaine the natural frequency and mode shape. result of this paper present the natural frequencies and mode shapes of the bridge. The method of modelling cables is also studied. It is found that modelling cables as multi beam elements provides better results than using the traditional (and simpler) method of modeling them as single tensile elements.

An Exact Approach For Free Vibration Analysis of Multi-Step Nonuniform Shear Plates

2001 ◽  
Vol 124 (1) ◽  
pp. 141-149 ◽  
Author(s):  
Q. S. Li
Keyword(s):  
Free Vibration ◽  
Exact Solutions ◽  
Vibration Analysis ◽  
Natural Frequencies ◽  
Free Vibration Analysis ◽  
Mode Shapes ◽  
Plate Height ◽  
Exact Approach ◽  
Shear Plate ◽  
One Step

In this paper multi-story frame buildings are treated as shear plates with variably distributed mass and stiffness for free vibration analysis. An analytical model of a shear plate is proposed and an exact approach for determining natural frequencies and mode shapes of such shear plates is presented. The function for describing the distribution of mass of a shear plate along the plate height is an arbitrary one and the distribution of shear stiffness is expressed as a functional relation with the distribution of mass and vice versa. The exact solutions of one-step shear plates are obtained first for seven cases. Then the derived exact solutions of one-step shear plates are used to establish the frequency equations of multi-step shear plates by using the transfer matrix method. The numerical example shows that the natural frequencies and mode shapes of a shear plate calculated by the proposed methods are in good agreement with the measured data and those determined by the Ritz method and the finite element method, verifying the accuracy and applicability of the proposed methods.

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