Dynamic Response of Prestressed Rayleigh Beam Resting on Elastic Foundation and Subjected to Masses Traveling at Varying Velocity

2011 ◽  
Vol 133 (4) ◽  
Author(s):  
S. T. Oni ◽  
B. Omolofe
Keyword(s):  
Dynamic Response ◽  
Elastic Foundation ◽  
Resonance Effect ◽  
Transverse Displacement ◽  
Rotatory Inertia ◽  
Perfect Agreement ◽  
Rayleigh Beam ◽  
Moving Force ◽  
Concentrated Masses ◽  
Vibrating Systems

In this study, the dynamic response of axially prestressed Rayleigh beam resting on elastic foundation and subjected to concentrated masses traveling at varying velocity has been investigated. Analytical solutions representing the transverse-displacement response of the beam under both concentrated forces and masses traveling at nonuniform velocities have been obtained. Influence of various parameters, namely, axial force, rotatory inertia correction factor, and foundation modulus on the dynamic response of the dynamical system, is investigated for both moving force and moving mass models. Effects of variable velocity on the vibrating system have been established. Furthermore, the conditions under which the vibrating systems will experience resonance effect have been established. Results arrived at in this paper are in perfect agreement with existing results.

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 Dynamic Response to Moving Distributed Masses of Pre-Stressed Uniform Rayleigh Beam Resting on Variable Elastic Pasternak Foundation

2018 ◽  
pp. 1-9
Author(s):  
AS Adeoye ◽  
TO Awodola
Keyword(s):  
Differential Equation ◽  
Dynamic Response ◽  
Moving Mass ◽  
Order Partial Differential Equation ◽  
Pasternak Foundation ◽  
Mass System ◽  
Force System ◽  
Rayleigh Beam ◽  
Moving Force ◽  
Pasternak Elastic Foundation

The dynamic response to moving distributed masses of pre-stressed uniform Rayleigh beam resting on variable elastic Pasternak foundation is examined. The equation governing this problem is a fourth order partial differential equation with variable and singular co-efficients. To solve this cumbersome equation, the method of Galerkin approach is adopted to reduce the governing differential equation to a sequence of coupled second order ordinary differential equation which is then simplified further with modified asymptotic method of Struble. The more simplified equation is solved using the Laplace transformation technique. The closed form solutions obtained are analyzed in order to show the conditions of resonance, and to show that resonance is attained earlier in moving mass system than in the moving force system. The results in plotted graphs show that as the axial force, the rotatory inertia, foundation modulus and shear modulus increase, the deflection of the elastically supported non-uniform Rayleigh beam decreases in each case. The transverse deflections of the beam on variable Pasternak elastic foundation are higher under the action of moving masses than those when only the force effects of the moving load are considered. This implies that resonance is reached faster in moving mass problem than in moving force problem.

scholarly journals Seismic Analysis of Simply Supported Damped Rayleigh Beams on Elastic Foundation

2020 ◽  
pp. 31-47
Author(s):  
Ogunbamike Oluwatoyin Kehinde
Keyword(s):  
Dynamical System ◽  
Elastic Foundation ◽  
Seismic Analysis ◽  
Integral Transformation ◽  
Structural Parameters ◽  
Moving Load ◽  
Transverse Displacement ◽  
Simply Supported ◽  
Rayleigh Beam ◽  
Beams On Elastic Foundation

In this paper, the flexural analysis of a simply supported damped Rayleigh beam subjected to distributed loads and with damping due to resistance to the transverse displacement resting on elastic foundation is obtained. The characteristics of the beam are assumed uniform over the beam length while the foundation is considered of Winkler type. In order to evaluate the vibration characteristics of the dynamical system, the Fourier sine integral transformation in conjunction with the asymptotic method of Struble is used to solve the governing equations for the transversal vibrations in the beam structure induced by moving load. The effect of prestress and other structural parameters were considered. Numerical results show that the structural parameters have significant influence on the behaviour of the dynamical system.

Dynamic response of an orthogonal cable network subjected to a moving force

1992 ◽  
Vol 156 (2) ◽  
pp. 337-347
Author(s):  
Y.K. Cheung ◽  
H.C. Chan ◽  
C.W. Cai
Keyword(s):  
Dynamic Response ◽  
Cable Network ◽  
Moving Force

scholarly journals Multi-moving Loads Induced Vibration of FG Sandwich Beams Resting on Pasternak Elastic Foundation

2021 ◽  
Vol 18 (9) ◽  
Author(s):  
Wachirawit SONGSUWAN ◽  
Monsak PIMSARN ◽  
Nuttawit WATTANASAKULPONG
Keyword(s):  
Dynamic Response ◽  
Elastic Foundation ◽  
Excitation Frequency ◽  
Beam Theory ◽  
Equation Of Motion ◽  
Functionally Graded ◽  
Sandwich Beams ◽  
Moving Loads ◽  
Layer Thickness Ratio ◽  
Pasternak Elastic Foundation

The dynamic behavior of functionally graded (FG) sandwich beams resting on the Pasternak elastic foundation under an arbitrary number of harmonic moving loads is presented by using Timoshenko beam theory, including the significant effects of shear deformation and rotary inertia. The equation of motion governing the dynamic response of the beams is derived from Lagrange’s equations. The Ritz and Newmark methods are implemented to solve the equation of motion for obtaining free and forced vibration results of the beams with different boundary conditions. The influences of several parametric studies such as layer thickness ratio, boundary condition, spring constants, length to height ratio, velocity, excitation frequency, phase angle, etc., on the dynamic response of the beams are examined and discussed in detail. According to the present investigation, it is revealed that with an increase of the velocity of the moving loads, the dynamic deflection initially increases with fluctuations and then drops considerably after reaching the peak value at the critical velocity. Moreover, the distance between the loads is also one of the important parameters that affect the beams’ deflection results under a number of moving loads.

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