Stability and dynamic response of Rayleigh beam–columns on an elastic foundation under moving loads of constant amplitude and harmonic variation

2005 ◽  
Vol 27 (6) ◽  
pp. 869-880 ◽  
Author(s):  
Seong-Min Kim
Keyword(s):  
Dynamic Response ◽  
Elastic Foundation ◽  
Moving Loads ◽  
Constant Amplitude ◽  
Beam Columns ◽  
Rayleigh Beam ◽  
Harmonic Variation

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.

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.

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 beam on a frequency-independent damped elastic foundation to moving load

2003 ◽  
Vol 30 (2) ◽  
pp. 460-467 ◽  
Author(s):  
Seong-Min Kim ◽  
Jose M Roesset
Keyword(s):  
Fourier Transform ◽  
Elastic Foundation ◽  
Moving Load ◽  
Harmonic Load ◽  
Moving Loads ◽  
Constant Amplitude ◽  
Maximum Displacement ◽  
Initial Application ◽  
Frequency Independent ◽  
Double Fourier Transform

The dynamic displacement response of an infinitely long beam on an elastic foundation with frequency-independent linear hysteretic damping subjected to a constant amplitude or a harmonic moving load was investigated. The advance velocity was assumed to be constant. Formulations were developed in the transformed field domain using (i) a Fourier transform in moving space for moving loads of constant amplitude, (ii) a double Fourier transform in time and moving space for moving loads of arbitrary amplitude variation or to include the transient due to the initial application of the load for moving harmonic loads, and (iii) a Fourier transform in moving space for the steady-state response to moving harmonic loads. The effects of velocity, damping, loaded length, and load frequency on the deflected shape and the maximum displacement were investigated. The critical (resonant) velocities and frequencies were obtained by analyses, and expressions to find them were suggested.Key words: beam on elastic foundation, damping, Fourier transform, frequency, harmonic load, moving load, transformed field, velocity.

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