Dynamics of Rayleigh beam on nonlinear foundation due to moving load using Adomian decomposition and coiflet expansion

2011 ◽  
Vol 31 (8) ◽  
pp. 1123-1131 ◽  
Author(s):  
Zdzislaw Hryniewicz
Keyword(s):  
Moving Load ◽  
Nonlinear Foundation ◽  
Rayleigh Beam ◽  
Adomian Decomposition

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.

Dynamics of a Rotating Shaft Subject to a Three-Directional Moving Load

2007 ◽  
Vol 129 (3) ◽  
pp. 386-389 ◽  
Author(s):  
Huajiang Ouyang ◽  
Minjie Wang
Keyword(s):  
Axial Force ◽  
Moving Load ◽  
Equations Of Motion ◽  
Bending Moment ◽  
Axial Direction ◽  
Force Component ◽  
Rotating Shaft ◽  
Assumed Mode Method ◽  
Rayleigh Beam ◽  
Mode Method

This paper presents a dynamic model for the vibration of a rotating Rayleigh beam subjected to a three-directional load acting on the surface of the beam and moving in the axial direction. The model takes into account the axial movement of the axial force component. More significantly, the bending moment produced by this force component is included in the model. Lagrange’s equations of motion for the modal coordinates are derived based on the assumed mode method and then solved by a fourth-order Runge-Kutta algorithm. It is found that the bending moment induced by the axial force component has a significant influence on the dynamic response of the shaft, even when the axial force and speed are low and, hence, must be considered in such problems as turning operations.

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.

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.

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