scholarly journals An Investigation on the Nonlinear Free Vibration Analysis of Beams with Simply Supported Boundary Conditions Using Four Engineering Theories

2011 ◽  
Vol 2011 ◽  
pp. 1-17 ◽  
Author(s):  
R. A. Jafari-Talookolaei ◽  
M. H. Kargarnovin ◽  
M. T. Ahmadian ◽  
M. Abedi
Keyword(s):  
Natural Frequencies ◽  
Free Vibration Analysis ◽  
Free Vibrations ◽  
Geometrically Nonlinear ◽  
Timoshenko Beams ◽  
Analysis Method ◽  
Nonlinear Free Vibration ◽  
End Conditions ◽  
Homotopy Analysis ◽  
Transverse Deflection

The objective of this study is to present a brief survey on the geometrically nonlinear free vibrations of the Bernoulli-Euler, the Rayleigh, shear, and the Timoshenko beams with simple end conditions using the Homotopy Analysis Method (HAM). Expressions for the natural frequencies, the transverse deflection, postbuckling load-deflection relation to, and critical buckling load are presented. The results of nonlinear analysis are validated with the published results, and excellent agreement is observed. The effects of some parameters, such as slender ratio, the rotary inertia, and the shear deformation, are examined as other parameters are fixed.

Free Vibrations of Beams on Viscoelastic Pasternak Foundations

2015 ◽  
Vol 744-746 ◽  
pp. 1624-1627
Author(s):  
Li Peng ◽  
Ying Wang
Keyword(s):  
Natural Frequencies ◽  
Free Vibrations ◽  
Mode Analysis ◽  
Analysis Method ◽  
Governing Equations ◽  
Complex Mode ◽  
Transverse Vibrations ◽  
Quadrature Methods ◽  
Foundation Parameters ◽  
Good Agreement

This paper investigates free transverse vibrations of finite Euler–Bernoulli beams resting on viscoelastic Pasternak foundations. The differential quadrature methods (DQ) are applied directly to the governing equations of the free vibrations. Under the simple supported boundary condition, the natural frequencies of the transverse vibrations are calculated, and compared with the results of the complex mode analysis method. The numerical results obtained by using the DQ and the complex mode methods are in good agreement for the first seven order natural frequencies, but with the growth of the orders, the small quantitative differences between them increase. The effects of the foundation parameters on the natural frequencies are also studied in numerical examples.

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.

Formulation of Problem of Free Vibration Analysis of Isotropic Homogeneous Rectangular Mindlin Plates Having Variable Thickness With General Elastic Boundary Conditions

2017 ◽  
Author(s):  
Sangle Sourabh ◽  
Verma Shesha ◽  
Mali Kiran
Keyword(s):  
Shear Stress ◽  
Boundary Conditions ◽  
Variable Thickness ◽  
Ritz Method ◽  
Free Vibration Analysis ◽  
Free Vibrations ◽  
Element Analysis ◽  
Elastic Boundary ◽  
Constant Shear Stress ◽  
Transverse Deflection

This work presents a formulation for the free vibrations of isotropic homogeneous rectangular Mindlin plates with variable thickness. These plates are subjected to general boundary supports in present study. To obtain arbitrarily supported boundary conditions, new form of trigonometric series expansion functions is used as the admissible functions for transverse deflection and rotation due to bending. In order to account the constant shear stress assumption, a shear stress correction factor is taken into consideration. The Rayleigh-Ritz Method is employed in this formulation. The boundaries are assumed to have three set of springs to achieve required boundary condition. Thus the changes in boundary conditions can be easily obtained by varying the stiffness of these springs, without actually making any changes in the shape functions. In this study, FEA (Finite Element Analysis) has been carried out for the Mindlin plates, for simply supported and constrained on two opposite sides.

Nonlinear free vibration analysis of functionally graded rotating composite Timoshenko beams reinforced by carbon nanotubes

2019 ◽  
Vol 25 (14) ◽  
pp. 2063-2078 ◽  
Author(s):  
Mahsa Heidari ◽  
Hadi Arvin
Keyword(s):  
Carbon Nanotubes ◽  
Carbon Nanotube ◽  
Free Vibration ◽  
Direct Method ◽  
Free Vibration Analysis ◽  
Functionally Graded ◽  
Timoshenko Beams ◽  
Nonlinear Free Vibration ◽  
Reinforced Composite ◽  
Linear And Nonlinear

In this paper, the linear and nonlinear free vibrations of functionally graded rotating composite Timoshenko beams reinforced by carbon nanotubes are presented. The formulation is based on the assumptions of Timoshenko beam theory in addition to consideration of the nonlinear von Karman strain–displacement relationship. The effective material properties of carbon nanotube reinforced composites are determined employing the Mori–Tanaka micromechanics model and the extended mixture rule. For the carbon nanotube reinforced composite beams, uniform distribution and four types of functionally graded distribution patterns of single-walled carbon nanotube reinforcements are considered. A differential transform method is applied on the nondimensionalized equations of motion to release the flapping modeshapes and the associated natural frequencies. The direct method of multiple scales is implemented to derive the effective nonlinearity and the corresponding nonlinear natural frequency. The accuracy of the present outcomes is validated by the comparison with the results given in the literature. The numerical results are presented in both tabular and graphical forms to investigate the effects of nanotube volume fractions, distribution types of the carbon nanotubes, and rotation speed on linear and nonlinear free vibration characteristics of carbon nanotube reinforced composite beam. The results demonstrate the important role of carbon nanotube distribution profile on linear and nonlinear free vibration features.

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.

Free Vibration Analysis of Angle-ply Laminated Shallow Cylindrical Shell with Clamped Edges

2000 ◽  
Vol 123 (2) ◽  
pp. 188-197 ◽  
Author(s):  
Kenji Hosokawa ◽  
Minehiro Murayama ◽  
Toshiyuki Sakata
Keyword(s):  
Cylindrical Shell ◽  
Natural Frequencies ◽  
Free Vibration Analysis ◽  
Numerical Approach ◽  
Free Vibrations ◽  
Numerical Results ◽  
Mode Shapes ◽  
Shallow Cylindrical Shell ◽  
Plastic Composite ◽  
Vibration Tests

In a previous paper, the authors proposed a numerical approach for analyzing the free vibrations of a laminated FRP (fiber reinforced plastic) composite plate. In the present paper, this approach is modified for application to a symmetrically laminated shallow cylindrical shell having a rectangular planform. First, the natural frequencies of the shell are calculated for discussion of the convergence and accuracy of the solution. Next, the effects of the curvature ratio and stacking sequence on the natural frequencies and mode shapes of the shell are studied. Furthermore, to justify the numerical results, vibration tests of the clamped symmetrically laminated shallow cylindrical shell having a square planform are carried out. These experimental results are found to agree well with the numerical results computed using the measured material properties of the lamina.

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