scholarly journals Nonlinear Dynamic Analysis of an Inclined Timoshenko Beam Subjected to a Moving Mass/Force with Beam’s Weight Included

2011 ◽  
Vol 18 (6) ◽  
pp. 875-891 ◽  
Author(s):  
Ahmad Mamandi ◽  
Mohammad H. Kargarnovin
Keyword(s):  
Cross Section ◽  
Timoshenko Beam ◽  
Equations Of Motion ◽  
Nonlinear Dynamic Analysis ◽  
Dynamic Responses ◽  
Motion Path ◽  
Mass Force ◽  
Linear Solution ◽  
Time Histories ◽  
Traveling Mass

In this study, the nonlinear vibrations analysis of an inclined pinned-pinned self-weight Timoshenko beam made of linear, homogenous and isotropic material with a constant cross section and finite length subjected to a traveling mass/force with constant velocity is investigated. The nonlinear coupled partial differential equations of motion for the rotation of warped cross section, longitudinal and transverse displacements are derived using the Hamilton's principle. These nonlinear coupled PDEs are solved by applying the Galerkin's method to obtain dynamic responses of the beam. The dynamic magnification factor and normalized time histories of mid-point of the beam are obtained for various load velocity ratios and the outcome results have been compared to the results with those obtained from linear solution. The influence of the large deflections caused by a stretching effect due to the beam's fixed ends is captured. It was seen that existence of quadratic-cubic nonlinear terms in the nonlinear governing coupled PDEs of motion causes stiffening (hardening) behavior of the dynamic responses of the self-weight beam under the act of a traveling mass as well as equivalent concentrated moving force. Furthermore, in a case where the object leaves the beam, its planar motion path is derived and the targeting accuracy is investigated and compared with those from the rigid solution assumption.

scholarly journals Nonlinear Dynamic Analysis of a Timoshenko Beam Resting on a Viscoelastic Foundation and Traveled by a Moving Mass

2014 ◽  
Vol 2014 ◽  
pp. 1-10 ◽  
Author(s):  
Ahmad Mamandi ◽  
Mohammad H. Kargarnovin
Keyword(s):  
Dynamic Response ◽  
Timoshenko Beam ◽  
Nonlinear Dynamic Analysis ◽  
Dynamic Responses ◽  
Moving Mass ◽  
Viscoelastic Foundation ◽  
Cross Sectional ◽  
Nonlinear Viscoelastic ◽  
Fixed End ◽  
Traveling Mass

The dynamic response of a Timoshenko beam with immovable ends resting on a nonlinear viscoelastic foundation and subjected to motion of a traveling mass moving with a constant velocity is studied. Primarily, the beam’s nonlinear governing coupled PDEs of motion for the lateral and longitudinal displacements as well as the beam’s cross-sectional rotation are derived using Hamilton’s principle. On deriving these nonlinear coupled PDEs the stretching effect of the beam’s neutral axis due to the beam’s fixed end conditions in conjunction with the von-Karman strain-displacement relations is considered. To obtain the dynamic responses of the beam under the act of a moving mass, derived nonlinear coupled PDEs of motion are solved by applying Galerkin’s method. Then the beam’s dynamic responses are obtained using mode summation technique. Furthermore, after verification of our results with other sources in the literature a parametric study on the dynamic response of the beam is conducted by changing the velocity of the moving mass, damping coefficient, and stiffnesses of the foundation including linear and cubic nonlinear parts, respectively. It is observed that the inclusion of geometrical and foundation stiffness nonlinearities into the system in presence of the foundation damping will produce significant effect in the beam’s dynamic response.

Analytical Solution for Longitudinal Dynamic Responses of Long Tunnels under Arbitrary Excitations

2021 ◽  
pp. 2150174
Author(s):  
Haitao Yu ◽  
Xizhuo Chen ◽  
Weile Chen ◽  
Pan Li
Keyword(s):  
Analytical Solution ◽  
Timoshenko Beam ◽  
Equations Of Motion ◽  
Differential Forms ◽  
Beam Theory ◽  
Dynamic Responses ◽  
Pasternak Foundation ◽  
Longitudinal Dynamic ◽  
Shear Distortion ◽  
Algebraic Forms

In this paper, an analytical solution is proposed for longitudinal dynamic responses of long tunnels under arbitrary excitations. For the derivation, the tunnel is assumed as a Timoshenko beam resting on a visco-Pasternak foundation. The Timoshenko beam theory is employed to consider both effects of the shear distortion as well as the rotary inertia of the tunnel, which are neglected by the Euler–Bernoulli beam. The visco-Pasternak foundation is applied to represent the viscoelastic compressive and shear resistance of soil. The governing equations of motion are transformed from partial differential forms into algebraic forms through integral transformations, and thus the solutions are conveniently obtained. The analytical solutions of the tunnel under several specific dynamic loads, including impulsive loads, moving line loads as well as traveling loads, are presented in detail and verified by comparing to the known degraded solution in literature and finite element results. Several examples are also conducted to investigate the influence of the relative stiffness ratio between the soil and the tunnel structure on the tunnel responses.

Comparison on General Track Spectrum for Chinese Main Railway Lines and Track Spectrum of American Railway Lines

2011 ◽  
Vol 250-253 ◽  
pp. 3822-3826 ◽  
Author(s):  
Xian Mai Chen ◽  
Xia Xin Tao ◽  
Gao Hang Cui ◽  
Fu Tong Wang
Keyword(s):  
Dynamic Performance ◽  
Dynamic Responses ◽  
Wave Band ◽  
Wheel Load ◽  
Railway Line ◽  
Acceleration Rate ◽  
Time Histories ◽  
Railway System ◽  
Dynamic Performances ◽  
Track Irregularity

The general track spectrum of Chinese main railway lines (ChinaRLS) and the track spectrum of American railway lines (AmericaRLS) are compared in terms of character of frequency domain, statistical property of time domain samples and dynamic performance. That the wavelength range of the ChinaRLS, which is characterized by the three levels according to the class of railway line, is less than AmericaRLS at common wave band of 1~50m is calculated. Simultaneously, the mean square values of two kinds of track spectra are provided at the detrimental wave bands of 5~10m, 10~20m, and so on. The time-histories of ChinaRLS and AmericaRLS are simulated according to the trigonometric method, and the digital statistical nature of simulated time samples is analyzed. With inputting the two kinds of time-histories into the vehicle-railway system, the comparative analysis of the two kinds of dynamic performances for ChinaRLS and AmericaRLS is done in terms of car body acceleration, rate of wheel load reduction, wheel/rail force, and the dynamic responses of track structure. The result shows that ChinaRLS can characterize the feature of the Chinese track irregularity better than AmericaRLS, the track irregularity with the ChinaRLS of 200km/h is superior to the AmericaRLS, and the track irregularity with the ChinaRLS of 160km/h corresponds to with the sixth of AmericaRLS.

A New Approach to the Rigid Finite Element Method in Modeling Spatial Slender Systems

2018 ◽  
Vol 18 (02) ◽  
pp. 1850017 ◽  
Author(s):  
Iwona Adamiec-Wójcik ◽  
Łukasz Drąg ◽  
Stanisław Wojciech
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
Dynamic Analysis ◽  
Equations Of Motion ◽  
Nonlinear Dynamic Analysis ◽  
New Approach ◽  
Static And Dynamic Analysis ◽  
Rigid Finite Element Method ◽  
Longitudinal Flexibility ◽  
Element Method

The static and dynamic analysis of slender systems, which in this paper comprise lines and flexible links of manipulators, requires large deformations to be taken into consideration. This paper presents a modification of the rigid finite element method which enables modeling of such systems to include bending, torsional and longitudinal flexibility. In the formulation used, the elements into which the link is divided have seven DOFs. These describe the position of a chosen point, the extension of the element, and its orientation by means of the Euler angles Z[Formula: see text]Y[Formula: see text]X[Formula: see text]. Elements are connected by means of geometrical constraint equations. A compact algorithm for formulating and integrating the equations of motion is given. Models and programs are verified by comparing the results to those obtained by analytical solution and those from the finite element method. Finally, they are used to solve a benchmark problem encountered in nonlinear dynamic analysis of multibody systems.

Vibrations of beams with a breathing crack and large amplitude displacements

2015 ◽  
Vol 230 (1) ◽  
pp. 34-54 ◽  
Author(s):  
Gonçalo Neves Carneiro ◽  
Pedro Ribeiro
Keyword(s):  
Time Domain ◽  
Equations Of Motion ◽  
Shape Functions ◽  
Breathing Crack ◽  
Dimensional Theory ◽  
One Dimensional ◽  
Time Histories ◽  
Linear Effects ◽  
Fourier Spectra ◽  
The Time Domain

The vibrations of beams with a breathing crack are investigated taking into account geometrical non-linear effects. The crack is modeled via a function that reduces the stiffness, as proposed by Christides and Barr (One-dimensional theory of cracked Bernoulli–Euler beams. Int J Mech Sci 1984). The bilinear behavior due to the crack closing and opening is considered. The equations of motion are obtained via a p-version finite element method, with shape functions recently proposed, which are adequate for problems with abrupt localised variations. To analyse the dynamics of cracked beams, the equations of motion are solved in the time domain, via Newmark's method, and the ensuing displacements, velocities and accelerations are examined. For that purpose, time histories, projections of trajectories on phase planes, and Fourier spectra are obtained. It is verified that the breathing crack introduce asymmetries in the response, and that velocities and accelerations can be more affected than displacements by the breathing crack.

scholarly journals Nonlinear Dynamic Analysis for Rectangular FGM Plates with Variable Thickness Subjected to Mechanical Load

2019 ◽  
Vol 35 (3) ◽  
Author(s):  
Khuc Van Phu ◽  
Le Xuan Doan ◽  
Nguyen Van Thanh
Keyword(s):  
Variable Thickness ◽  
Nonlinear Dynamic ◽  
Volume Fraction ◽  
Mechanical Load ◽  
Plate Theory ◽  
Geometrical Nonlinearity ◽  
Nonlinear Dynamic Analysis ◽  
Dynamic Responses ◽  
Rectangular Plates ◽  
Classical Plate Theory

 In this paper, the governing equations of rectangular plates with variable thickness subjected to mechanical load are established by using the classical plate theory, the geometrical nonlinearity in von Karman-Donnell sense. Solutions of the problem are derived according to Galerkin method. Nonlinear dynamic responses, critical dynamic loads are obtained by using Runge-Kutta method and the Budiansky–Roth criterion. Effect of volume-fraction index k and some geometric factors are considered and presented in numerical results.

scholarly journals Steady and unsteady flow of non-newtonian fluid in curved pipe with triangular

2006 ◽  
Vol 3 (3) ◽  
pp. 470-480
Author(s):  
Baghdad Science Journal
Keyword(s):  
Unsteady Flow ◽  
Pressure Gradient ◽  
Secondary Flow ◽  
Cross Section ◽  
Numerical Study ◽  
Equations Of Motion ◽  
Curved Pipe ◽  
First Case ◽  
Stable Flow ◽  
Flow Cross

This paper deals with numerical study of the flow of stable and fluid Allamstqr Aniotina in an area surrounded by a right-angled triangle has touched particularly valuable secondary flow cross section resulting from the pressure gradient In the first case was analyzed stable flow where he found that the equations of motion that describe the movement of the fluid

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