Transverse Free Vibration of Timoshenko Beams Resting on Viscoelastic Foundations

2014 ◽  
Vol 919-921 ◽  
pp. 275-279
Author(s):  
Li Peng ◽  
Ying Wang
Keyword(s):  
Free Vibration ◽  
Modal Analysis ◽  
Transverse Vibration ◽  
Natural Frequencies ◽  
Numerical Results ◽  
Complex Frequency ◽  
Pasternak Foundation ◽  
Timoshenko Beams ◽  
Numerical Examples ◽  
Complex Modal Analysis

The complex modal analysis is developed to study the transverse vibration of Timoshenko beams resting on viscoelastic Pasternak foundation. Complex frequency equations and modal function expressions are obtained for pinned-pinned ends. In numerical examples, the characteristics of natural frequencies and decrement coefficients of Timoshenko beams are compared with Euler-Bernoulli beams. The numerical results show that with increase in the length, the natural frequencies of Timoshenko beams are slightly less than Euler-Bernoulli beams, and the decrement coefficients of Timoshenko beams are not constant as that of Euler-Bernoulli beams.

Free Vibration of Thin-Walled Open Section Beams With Unconstrained Damping Treatment

1981 ◽  
Vol 48 (1) ◽  
pp. 169-173 ◽  
Author(s):  
S. Narayanan ◽  
J. P. Verma ◽  
A. K. Mallik
Keyword(s):  
Free Vibration ◽  
Cross Section ◽  
Transverse Vibration ◽  
Natural Frequencies ◽  
Vibration Characteristics ◽  
Numerical Results ◽  
Simply Supported ◽  
Clamped Beams ◽  
Thin Walled ◽  
Open Cross Section

Free-vibration characteristics of a thin-walled, open cross-section beam, with unconstrained damping layers at the flanges, are investigated. Both uncoupled transverse vibration and the coupled bending-torsion oscillations, of a beam of a top-hat section, are considered. Numerical results are presented for natural frequencies and modal loss factors of simply supported and clamped-clamped beams.

Large Amplitude Free Vibration of Shallow Spherical Shell on a Pasternak Foundation

1993 ◽  
Vol 115 (1) ◽  
pp. 70-74 ◽  
Author(s):  
D. N. Paliwal ◽  
V. Bhalla
Keyword(s):  
Free Vibration ◽  
Spherical Shell ◽  
Large Amplitude ◽  
Free Vibrations ◽  
Numerical Results ◽  
Shallow Spherical Shell ◽  
Pasternak Foundation ◽  
New Approach ◽  
Foundation Parameters ◽  
Clamped Edges

Large amplitude free vibrations of a clamped shallow spherical shell on a Pasternak foundation are studied using a new approach by Banerjee, Datta, and Sinharay. Numerical results are obtained for movable as well as immovable clamped edges. The effects of geometric, material, and foundation parameters on relation between nondimensional frequency and amplitude have been investigated and plotted.

Free Vibration Analysis of Cable Structures Using Isogeometric Approach

2017 ◽  
Vol 14 (03) ◽  
pp. 1750033 ◽  
Author(s):  
Son Thai ◽  
Nam-Il Kim ◽  
Jaehong Lee
Keyword(s):  
Free Vibration ◽  
Vibration Analysis ◽  
Penalty Method ◽  
Natural Frequencies ◽  
Free Vibration Analysis ◽  
Basis Functions ◽  
Displacement Fields ◽  
Numerical Examples ◽  
B Splines ◽  
Cable Structures

This paper presents a free vibration analysis of cable structures based on the isogeometric approach. The nonuniform rational B-splines (NURBS) basis functions are employed to represent both the exact geometry of cable and displacement fields. In order to enrich the basis functions, the [Formula: see text]-, [Formula: see text]- and [Formula: see text]-refinement strategies are implemented. Therefore, these refinement schemes increase the accuracy of solution fields. For determining the static configuration of slack cables as a reference configuration, the well-known penalty method is used. Three numerical examples for slack and taut cable structures are presented in which different refinement schemes are utilized to obtain the converged results. The accuracy and reliability of the present numerical method are verified by comparing the natural frequencies with the results given by other researchers.

scholarly journals Effect of Location of Delamination on Free Vibration of Cross-Ply Conical Shells

2012 ◽  
Vol 19 (4) ◽  
pp. 679-692 ◽  
Author(s):  
Sudip Dey ◽  
Amit Karmakar
Keyword(s):  
Finite Element ◽  
Free Vibration ◽  
Natural Frequencies ◽  
Dynamic Equilibrium ◽  
Twist Angle ◽  
Structural Instability ◽  
Numerical Results ◽  
Mode Shapes ◽  
Iteration Algorithm ◽  
Conical Shells

Location of delamination is a triggering parameter for structural instability of laminated composites. In this paper, a finite element method is employed to determine the effects of location of delamination on free vibration characteristics of graphite-epoxy cross-ply composite pre-twisted shallow conical shells. The generalized dynamic equilibrium equation is derived from Lagrange's equation of motion neglecting Coriolis effect for moderate rotational speeds. The formulation is exercised by using an eight noded isoparametric plate bending element based on Mindlin's theory. Multi-point constraint algorithm is utilized to ensure the compatibility of deformation and equilibrium of resultant forces and moments at the delamination crack front. The standard eigen value problem is solved by applying the QR iteration algorithm. Finite element codes are developed to obtain the numerical results concerning the effects of location of delamination, twist angle and rotational speed on the natural frequencies of cross-ply composite shallow conical shells. The mode shapes are also depicted for a typical laminate configuration. Numerical results obtained from parametric studies of both symmetric and anti-symmetric cross-ply laminates are the first known non-dimensional natural frequencies for the type of analyses carried out here.

Free vibration analysis of rotating tapered Timoshenko beams via variational iteration method

2016 ◽  
Vol 23 (2) ◽  
pp. 220-234 ◽  
Author(s):  
Yanfei Chen ◽  
Juan Zhang ◽  
Hong Zhang
Keyword(s):  
Free Vibration ◽  
Iteration Method ◽  
Natural Frequencies ◽  
Eigenvalue Problems ◽  
Accurate Determination ◽  
Variational Iteration Method ◽  
Mode Shapes ◽  
Engineering Practice ◽  
Timoshenko Beams ◽  
Variational Iteration

Accurate determination of natural frequencies and mode shapes of the rotating tapered Timoshenko beam is important in engineering practice. This paper re-examines the free vibration of rotating tapered Timoshenko beams using the technique of variational iteration, which is relatively new and is capable of providing accurate solutions for eigenvalue problems in a quite easy way. Natural frequencies and mode shapes for rotating tapered Timoshenko beams with linearly varying height as well as linearly varying height and width are investigated via two numerical examples, and solutions are compared with results published in literature where available. Since the method constitutes a numerical procedure, the convergence of solutions which is important for practical implementation is evaluated as well, where efficiency and accuracy of variational iteration method in solving high order eigenvalue problems are demonstrated.

Free Vibration Characteristics of SPR Joints

2006 ◽  
Author(s):  
Xiaocong He ◽  
Ian Pearson ◽  
Ken Young
Keyword(s):  
Aluminum Alloy ◽  
Free Vibration ◽  
Torsional Vibration ◽  
Natural Frequencies ◽  
Vibration Characteristics ◽  
Advanced Materials ◽  
Mode Shapes ◽  
Stress Distributions ◽  
Numerical Examples ◽  
Different Characteristics

Self-piercing riveting (SPR) has drawn more attention in recent years because it can join some advanced materials that are hard to weld, such as aluminum alloy sheets. In this paper, the free torsional vibration characteristics of single lap-jointed encastre SPR beam are investigated in detail. The focus of the analysis is to reveal the influence on the torsional natural frequencies and mode shapes of the single lap-jointed encastre SPR beam of different characteristics of sheets to be jointed. Numerical examples show that the torsional natural frequencies increase significantly as the Young’s modulus of the sheets increase, but almost no change corresponding to the change in Poisson’s ratio of the sheets to be joint. The mode shapes show that there are different deformations in the jointed section of SPR beam compared with the reference encastre beam without joint. These different deformations may cause different natural frequency values and different stress distributions.

Comparative perspective of various shear deformation theories with experimental verification for modal analysis of hybrid laminates

2015 ◽  
Vol 23 (8) ◽  
pp. 1321-1333 ◽  
Author(s):  
Dhiraj Biswas ◽  
Chaitali Ray
Keyword(s):  
Finite Element ◽  
Free Vibration ◽  
Modal Analysis ◽  
Shear Deformation ◽  
Deformation Theory ◽  
Natural Frequencies ◽  
Shear Deformation Theory ◽  
Mode Shapes ◽  
Glass Fibres ◽  
Hybrid Laminates

The present paper deals with the free vibration modal analysis of hybrid laminates using a finite element model based on the third order shear deformation theory (TSDT) and the first order shear deformation theory (FSDT). A computer code has been developed using MATLAB, 2013. The experimental investigation on the free vibration of hybrid laminates made of carbon and glass fibres has been conducted. The hybrid laminate is prepared by placing carbon fibres in the outermost laminae and glass fibres in the rest of the laminate. The bi-directional glass and carbon fabrics and the epoxy resin are used for the preparation of laminates in the laboratory. The experimental models of laminates have been prepared by the resin infusion process using vacuum bagging technique. The natural frequencies of hybrid laminates for different modes are determined and the mode shapes are plotted for the corresponding frequencies by experiment and numerical procedure. The finite element formulations based on TSDT and FSDT for the composite laminates predict the natural frequencies and are validated by comparing with the experimental results.

scholarly journals Free vibration of prestress Timoshenko beams resting on elastic foundation

2007 ◽  
Vol 29 (1) ◽  
pp. 1-12 ◽  
Author(s):  
Nguyen Dinh Kien
Keyword(s):  
Free Vibration ◽  
Shear Deformation ◽  
Elastic Foundation ◽  
Axial Force ◽  
Natural Frequencies ◽  
Mass Matrix ◽  
Element Formulation ◽  
Timoshenko Beams ◽  
Various Boundary Conditions ◽  
Consistent Mass Matrix

This paper presents a finite element formulation for investigating the free vibration of uniform Timoshenko beams resting on a Winkler-type elastic foundation and prestressing by axial force. Taking the effect of prestress, foundation support and shear deformation into account, a stiffness matrix for Timoshenko-type beam element is formulated using the energy method. The element consistent mass matrix is obtained from the kinetic energy using simple linear shape functions. Employing the formulated element, the natural frequencies of the beams having various boundary conditions are determined for different values of the axial force and foundation stiffness. The vibration Characteristics of the beams partially supported on the foundation are also studied and highlighted. Specially, the effects of shear deformation on the vibration frequencies of prestress beams fully and partially supported on the elastic foundation are investigated in detail.

Free Vibration of Beams With Two Sections of Distributed Mass

1998 ◽  
Vol 120 (4) ◽  
pp. 944-948 ◽  
Author(s):  
Kwok-Tung Chan ◽  
Xiao-Quan Wang ◽  
Tin-Pui Leung
Keyword(s):  
Experimental Data ◽  
Exact Solution ◽  
Free Vibration ◽  
Cantilever Beam ◽  
Transverse Vibration ◽  
Natural Frequencies ◽  
Computational Results ◽  
Free Transverse Vibration

The equation of free transverse vibration of beams with two sections of partially distributed mass is derived and its exact solution has been obtained. Experimental data for a cantilever beam are given to verify the computational results. Using a cantilever beam as an example, some interesting features of changes of natural frequencies with mass length and position are described. The method is finally generalized for the case of beams with multiple spans of distributed mass.

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