scholarly journals Influence of a Moving Mass on the Dynamic Behaviour of Viscoelastically Connected Prismatic Double-Rayleigh Beam System Having Arbitrary End Supports

2017 ◽  
Vol 2017 ◽  
pp. 1-30 ◽  
Author(s):  
Jacob Abiodun Gbadeyan ◽  
Fatai Akangbe Hammed
Keyword(s):  
Dynamic Response ◽  
Integral Transform ◽  
Moving Load ◽  
Dynamic Responses ◽  
Solution Technique ◽  
Moving Mass ◽  
Transform Method ◽  
Rayleigh Beam ◽  
Beam System ◽  
Finite Integral

This paper deals with the lateral vibration of a finite double-Rayleigh beam system having arbitrary classical end conditions and traversed by a concentrated moving mass. The system is made up of two identical parallel uniform Rayleigh beams which are continuously joined together by a viscoelastic Winkler type layer. Of particular interest, however, is the effect of the mass of the moving load on the dynamic response of the system. To this end, a solution technique based on the generalized finite integral transform, modified Struble’s method, and differential transform method (DTM) is developed. Numerical examples are given for the purpose of demonstrating the simplicity and efficiency of the technique. The dynamic responses of the system are presented graphically and found to be in good agreement with those previously obtained in the literature for the case of a moving force. The conditions under which the system reaches a state of resonance and the corresponding critical speeds were established. The effects of variations of the ratio (γ1) of the mass of the moving load to the mass of the beam on the dynamic response are presented. The effects of other parameters on the dynamic response of the system are also examined.

scholarly journals Dynamic Response of a Beam Subjected to Moving Load and Moving Mass Supported by Pasternak Foundation

2012 ◽  
Vol 19 (2) ◽  
pp. 205-220 ◽  
Author(s):  
Rajib Ul Alam Uzzal ◽  
Rama B. Bhat ◽  
Waiz Ahmed
Keyword(s):  
Differential Equation ◽  
Partial Differential Equation ◽  
Dynamic Response ◽  
Moving Load ◽  
Bending Moment ◽  
Dynamic Responses ◽  
Moving Mass ◽  
Pasternak Foundation ◽  
Partial Differential ◽  
Foundation Parameters

This paper presents the dynamic response of an Euler- Bernoulli beam supported on two-parameter Pasternak foundation subjected to moving load as well as moving mass. Modal analysis along with Fourier transform technique is employed to find the analytical solution of the governing partial differential equation. Shape functions are assumed to convert the partial differential equation into a series of ordinary differential equations. The dynamic responses of the beam in terms of normalized deflection and bending moment have been investigated for different velocity ratios under moving load and moving mass conditions. The effect of moving load velocity on dynamic deflection and bending moment responses of the beam have been investigated. The effect of foundation parameters such as, stiffness and shear modulus on dynamic deflection and bending moment responses have also been investigated for both moving load and moving mass at constant speeds. Numerical results obtained from the study are presented and discussed.

Dynamic Stability and Response of Inclined Beams Under Moving Mass and Follower Force

2020 ◽  
pp. 2043004
Author(s):  
D. S. Yang ◽  
C. M. Wang ◽  
J. D. Yau
Keyword(s):  
Dynamic Stability ◽  
Moving Load ◽  
Dynamic Responses ◽  
Follower Force ◽  
Load Force ◽  
Moving Mass ◽  
Concentrated Mass ◽  
Spatial Part ◽  
Method Of Solution ◽  
Fourier Sine Series

This paper is concerned with the dynamic stability and response of an inclined Euler–Bernoulli beam under a moving mass and a moving follower force. The extended Hamilton’s principle is used to derive the governing equation of motion and the boundary conditions for this general moving load/force problem. Considering a simply supported beam, one can solve the problem analytically by approximating the spatial part of the deflection with a Fourier sine series. Based on the formulation and method of solution, sample dynamic responses are determined for a beam that is inclined at 30[Formula: see text] with respect to the horizontal. It is shown that the dynamic response of the beam under a moving mass is rather different from an equivalent moving follower force. Also investigated herein are the dynamic stability of inclined beams under moving load/follower force which are described by four key variables, viz. the speed of the moving mass/follower force, concentrated mass to the beam distributed mass, vibration frequency and the magnitude of the moving mass/follower force. The critical axial load and the critical follower force are different when they are located at different positions in the beam; except for the special case when they are at the end of the beam.

Dynamic Response of a Cantilevered Beam Under Combined Moving Moment, Torque and Force

2020 ◽  
Vol 20 (05) ◽  
pp. 2050065
Author(s):  
Denil Chawda ◽  
Senthil Murugan
Keyword(s):  
Dynamic Response ◽  
High Speed ◽  
Moving Load ◽  
Numerical Results ◽  
Moving Loads ◽  
Element Analysis ◽  
Dirac Delta ◽  
Rayleigh Beam ◽  
Moving Force ◽  
Cantilevered Beam

This paper studies the dynamic response of a cantilevered beam subjected to a moving moment and torque, and combination of them with a moving force. The moving loads are considered to traverse along the length of the beam either from fixed-to-free end or free-to-fixed end. The beam is considered to have constant material and geometric properties. The beam is modeled using the Rayleigh beam theory considering the rotary inertia effects. The Dirac-delta function used to model the moving loads in the governing partial differential equations (PDEs) has complicated the solution of the problem. The Eigenfunction expansions coupled with the Laplace transformation method is used to find the semi-analytical solution for the resulting governing PDEs. The effects of moving loads on the dynamic response are studied. The dynamic effects are quantified based on the number of oscillations per unit travel time of the moving load and the Dynamic Amplification Factor (DAF) of the beam’s tip response. Numerical results are also analyzed for the two-speed regimes, namely high-speed and low-speed regimes, defined with respect to the critical speed of the moving loads. The accuracy of the analytical solutions are verified by the finite element analysis. The numerical results show that the loads moving with low speeds have significant impact on the dynamic response compared to high speeds. Also, the moving moment has significant impact on the amplitude of dynamic response compared with the moving force case.

scholarly journals A 3D Direct Vehicle-Pavement Coupling Dynamic Model and Its Application on Analysis of Asphalt Pavement Dynamic Response

2013 ◽  
Vol 2013 ◽  
pp. 1-8 ◽  
Author(s):  
Peng Cao ◽  
Changjun Zhou ◽  
Decheng Feng ◽  
Youxuan Zhao ◽  
Baoshan Huang
Keyword(s):  
Finite Element ◽  
Dynamic Response ◽  
Dynamic Model ◽  
Static Analysis ◽  
Moving Load ◽  
Dynamic Responses ◽  
Pavement Surface ◽  
Coupling Dynamic ◽  
Pavement Structure ◽  
Coupling Dynamic Model

Currently dynamic response of the pavement structure is widely studied in pavement engineering. A 3D direct vehicle-pavement coupling dynamic model was developed to describe the pavement dynamic responses in this paper. The moving vehicle was simplified as spring-dashpot components, and the pavement structure was simulated using three-dimension finite element model. Based on Newton iteration and central difference integration algorithm, the static and dynamic coupling reactions between the pavement structure and vehicle were considered using finite element platform ABAQUS. The numerical results fit analytic results very well in static analysis and fit experiment results in dynamic analysis well too. The simulated results indicate that the dynamic pavement surface deflection is much higher than the situation in static analysis, due to the overlapping effect. This phenomenon enhances when vehicle speed increases. A discontinuous zone of shear stress was observed on the base surface between the location under moving load and the location the moving load just passed. It was also found that the vertical fluctuation exists on the vehicle even if there is no roughness on the pavement surface. In general, the developed 3-D direct vehicle-pavement coupling dynamic model was validated to be effective on evaluating pavement dynamic responses.

scholarly journals Dynamic Responses of a Twin-Tunnel Subjected to Moving Loads in a Saturated Half-Space

2018 ◽  
Vol 2018 ◽  
pp. 1-12
Author(s):  
Hong-lei Sun ◽  
An-hua Chen ◽  
Li Shi ◽  
Xue-yu Geng ◽  
Yu Wang
Keyword(s):  
Finite Element ◽  
Dynamic Response ◽  
Saturated Porous Medium ◽  
Moving Load ◽  
Surrounding Medium ◽  
Element Model ◽  
Dynamic Responses ◽  
3D Finite Element ◽  
Twin Tunnel ◽  
Tunnel Model

With the fast development of rail transit, the environmental vibration problems caused by subways have received increasing attention. A 3D finite element model was built in this study to investigate the ground vibrations induced by the moving load operating in the parallel twin tunnels. Compared to the model consisting of a single tunnel that was commonly adopted in the past studies, a pair of tunnels is considered and the surrounding medium of the tunnels is taken as a saturated porous medium. The governing equations of the 3D finite element method modeling of the saturated poroelastic soil have been derived according to Biot’s theory. Computed results showed that the dynamic response of the twin-tunnel model is greater than that of the single tunnel model. And the spacing between two tunnels, tunnel buried depth, and load moving speed are the essential parameters to determine the dynamic response of the tunnel and soil.

Analysis of the Natural Vibration Properties of a Timoshenko Beam Supported by Springs (by Finite Integral Transform Method)

1999 ◽  
Author(s):  
Zhixiang Xu ◽  
Hideyuki Tamura ◽  
Kunisato Seto
Keyword(s):  
Timoshenko Beam ◽  
Natural Vibration ◽  
Natural Frequencies ◽  
Integral Transform ◽  
Frequency Equation ◽  
Transform Method ◽  
Vibration Problem ◽  
Vibration Properties ◽  
Finite Integral ◽  
Integral Transform Technique

Abstract This paper presents analytical results of transverse vibration of a Timoshenko beam supported by spring-spring which stiffness is variable, that is a simplified model of magnetically levitated vehicle body’s vibration problem and magnetic bearings support shaft’s vibration problem. By applying the finite integral transform technique, the analytical solution of this dynamic model is successfully obtained. Especially, by investigating the frequency equation, the effect of the stiffness of two supporting-springs to the natural frequencies is clarified. From the results, it is cleared that the natural frequencies of the beam system can be effectively controlled by changing the supporting-spring’s stiffness.

Singular Function Models of a Simply Continuous Beam Bridge under a Moving Load

2012 ◽  
Vol 204-208 ◽  
pp. 2240-2243
Author(s):  
Jun Zhang ◽  
Ming Kang Gou ◽  
Chuan Liang ◽  
Xiao Lu Ni ◽  
Zi Wen Zhou
Keyword(s):  
Present Model ◽  
Dynamic Models ◽  
Moving Load ◽  
Dynamic Responses ◽  
Singular Function ◽  
Moving Mass ◽  
Continuous Beam ◽  
Concentrated Force ◽  
Continuous Beam Bridge ◽  
Beam Bridge

The system of a simply continuous beam was looked on as one span beam with several internal elastic supports of inexhaustible stiffness. There were two types of models such as the dynamic models by a moving concentrated force and by a moving mass. A three-span beam was introduced as example solved with the present model by a moving concentrated force and FEM, which verified that the present model was correct. Two cases of the example bridge by a moving concentrated force and by a moving mass were considered. The results indicate that mass of the moving load has little influence over the dynamic responses of the simply continuous beam bridge.

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