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.

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.

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.

On the Resolution of Existing Discontinuities in the Dynamic Responses of an Euler-Bernoulli Beam Subjected to the Moving Mass

2006 ◽  
Author(s):  
M. H. Kargarnovin ◽  
K. Saeedi
Keyword(s):  
Contact Point ◽  
Bending Moment ◽  
Dynamic Responses ◽  
Distributed Parameter ◽  
Moving Mass ◽  
Bernoulli Beam ◽  
Concentrated Mass ◽  
Uniform Cross Section ◽  
Support Conditions ◽  
Euler Bernoulli Beam

The dynamic response of a one-dimensional distributed parameter system subjected to a moving mass with constant speed is investigated. An Euler-Bernoulli beam with the uniform cross-section and finite length with specified boundary support conditions is assumed. In this paper, rather a new method based on the time dependent series expansion for calculating the bending moment and the shear force due to motion of the mass is suggested. Governing differential equations of the motion are derived and solved. The accuracy of the numerical results primarily is verified and further the rapid convergence of this new technique was illustrated over other existing methods. Finally, it is shown that a considerable improvement is obtained in capturing the incurred discontinuities at the contact point of traveling concentrated mass.

Transient responses of Timoshenko beams subject to a moving mass

2011 ◽  
Vol 17 (13) ◽  
pp. 1975-1982 ◽  
Author(s):  
Ji-Qing Jiang
Keyword(s):  
Timoshenko Beam ◽  
Integral Transform ◽  
Practical Importance ◽  
Neumann Series ◽  
Dynamic Responses ◽  
Moving Mass ◽  
Concentrated Mass ◽  
Moving Vehicle ◽  
Research Fields ◽  
Unknown Amplitude

The dynamic behavior of beam structures subject to a moving mass is a topic of practical importance in many research fields. In this study, the method of reverberation-ray matrix is presented to investigate the dynamic responses of an undamped Timoshenko beam subject to a moving mass. Based on Inglis’s assumption, the moving mass is simplified into a moving force and a concentrated mass fixed at the mid-span of the beam. Two dual local coordinates are introduced. Based on the theory of elastodynamics, the general wave solutions with two sets of unknown amplitude coefficients are derived in the transformed domain by the dual integral transform. From continuity conditions of forces and displacements at each joint and the compatibility conditions with respect to the dual coordinates, the unknown amplitude coefficients can be determined exactly. The transient dynamic motions for a Timoshenko beam under a moving mass are then determined numerically by inverse integral transform in which the Neumann series expansion is employed to avoid the integral singularities. Two simple numerical examples are presented and the results so obtained are compared with both the experimental and theoretical ones. It is shown that the present method can be a simple alternative for determining dynamic responses of bridges subject to a moving vehicle.

Research against the Effect of Inertia Loads on Dynamic Responses of a Simply Supported Beam

2013 ◽  
Vol 790 ◽  
pp. 283-286
Author(s):  
Xian Min Zhang ◽  
Ya Dong Wang
Keyword(s):  
Moving Load ◽  
Quantitative Description ◽  
Dynamic Responses ◽  
Moving Mass ◽  
Simply Supported Beam ◽  
Inertia Effects ◽  
Simply Supported ◽  
Matlab Program ◽  
Loading Modes ◽  
Fixed Section

In order to quantitative study the loads inertia on the effect of dynamic response on a simply supported beam, a simply supported beam with a fixed section forms and different span has been calculated under two different loading modes including moving load and moving mass by numerical method by MATLAB program. The calculated results shows the exact solution of beam vibration differential equation can be calculated and a quantitative description can be made about the load inertia effects on dynamic responses of the simply supported beam. These results provide guidance to the project practice.

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.

Dynamic stability of a free-free cylindrical shell under a follower force

AIAA Journal ◽  
2000 ◽  
Vol 38 ◽  
pp. 1070-1077
Author(s):  
Si-Hyoung Park ◽  
Ji-Hwan Kim
Keyword(s):  
Cylindrical Shell ◽  
Dynamic Stability ◽  
Follower Force

scholarly journals FORCED RESPONSE VIBRATION OF SIMPLY SUPPORTED BEAMS WITH AN ELASTIC PASTERNAK FOUNDATION UNDER A DISTRIBUTED MOVING LOAD

2020 ◽  
Vol 4 (2) ◽  
pp. 1-7
Author(s):  
Fatai Hammed ◽  
M. A. Usman ◽  
S. A. Onitilo ◽  
F. A. Alade ◽  
K. A. Omoteso
Keyword(s):  
Shear Modulus ◽  
Moving Load ◽  
Equations Of Motion ◽  
Beam Theory ◽  
Initial Boundary ◽  
Initial Boundary Value Problem ◽  
Forced Response ◽  
Dynamic Responses ◽  
Moving Force ◽  
Pasternak Elastic Foundation

In this study, the response of two homogeneous parallel beams with two-parameter Pasternak elastic foundation subjected to a constant uniform partially distributed moving force is considered. On the basis of Euler-Bernoulli beam theory, the fourth order partial differential equations of motion describing the behavior of the beams when subjected to a moving force were formulated. In order to solve the resulting initial-boundary value problem, finite Fourier sine integral technique and differential transform scheme were employed to obtain the analytical solution. The dynamic responses of the two beams obtained was investigated under moving force conditions using MATLAB. The effects of speed of the moving force, layer parameters such as stiffness (K_0) and shear modulus (G_0 ) have been conducted for the moving force. Various values of speed of the moving load, stiffness parameters and shear modulus were considered. The results obtained indicates that response amplitudes of both the upper and lower beams increases with increase in the speed of the moving load. Increasing the stiffness parameter is observed to cause a decrease in the response amplitudes of the beams. The response amplitudes decreases with increase in the shear modulus of the linear elastic layer.

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