Dynamics of Plate Generated by Moving Harmonic Loads

2005 ◽  
Vol 72 (5) ◽  
pp. 772-777 ◽  
Author(s):  
Lu Sun
Keyword(s):  
Moving Load ◽  
Point Load ◽  
Harmonic Load ◽  
Maximum Displacement ◽  
Moving Vehicle ◽  
Vehicle Load ◽  
Airport Pavement ◽  
Winkler Elastic Foundation ◽  
Approximate Relationship ◽  
Moving Harmonic Load

A thin plate resting on a Winkler elastic foundation subject to a moving harmonic load can be used as the model for highway and airport pavement under moving vehicle load and many other applications. The study of dynamic response of the plate thus becomes very important. In this paper we study the dynamic displacement of a plate caused by a moving harmonic line and point load. The solution is represented by the convolution of dynamic Green’s function of plate. An approximate relationship between critical load velocity and critical frequency is established analytically. It is found that the maximum displacement response occurs at the center of the moving load and travels at the same speed with the load.

Viscoelastic response of a floating ice plate to a steadily moving load

1988 ◽  
Vol 196 ◽  
pp. 409-430 ◽  
Author(s):  
R. J. Hosking ◽  
A. D. Sneyd ◽  
D. W. Waugh
Keyword(s):  
Asymptotic Theory ◽  
Moving Load ◽  
Memory Function ◽  
Point Load ◽  
Flexural Waves ◽  
Moving Vehicle ◽  
Viscoelastic Theory ◽  
Subcritical Speed ◽  
Moving Line ◽  
Two Parameter

Viscoelastic theory is used to describe the response of a floating ice sheet to a moving vehicle. We adopt a two-parameter memory function to describe the behaviour of the ice, subjected to a steadily moving line or point load. The viscoelastic dissipation produces an asymmetric quasi-static response at subcritical speed, renders a finite response at the critical speed, and damps the shorter leading waves rather more severely than the longer trailing waves at supercritical speed. We extend earlier asymptotic theory to consider the anisotropic damping of the flexural waves. There is enhanced agreement between theory and experiment.

scholarly journals Dynamic analysis of prestressed Bernoulli beams resting on two-parameter foundation under moving harmonic load

2006 ◽  
Vol 28 (3) ◽  
pp. 176-188 ◽  
Author(s):  
Nguyen Dinh Kien ◽  
Bui Thanh Hai
Keyword(s):  
Dynamic Analysis ◽  
Moving Load ◽  
Excitation Frequency ◽  
Harmonic Load ◽  
Left Hand ◽  
Moving Harmonic Load ◽  
Load Vector ◽  
Hermitian Polynomials ◽  
Current Loading ◽  
Two Parameter

This paper describes the dynamic analysis of prestressed Bernoulli beams resting on a two-parameter elastic foundation under a moving harmonic load by the finite element method. Using the cubic Hermitian polynomials as interpolation functions for the deflection, the stiffness of the Bernoulli beam element augmented by that of the foundation support and prestress is formulated. The nodal load vector is derived using the polynomials with the abscissa measured from the left-hand node of the current loading element to the position of the moving load. Using the formulated element, the dynamic response of the beams is computed with the aid of the direct integration Newmark method. The effects of the foundation support, prestress as well as excitation frequency, velocity and acceleration on the dynamic characteristics of the beams are investigated in detail and highlighted.

scholarly journals VIBRATION OF 2D-FGSW TIMOSHENKO BEAMS UNDER A MOVING HARMONIC LOAD

2020 ◽  
Vol 58 (6) ◽  
pp. 760
Author(s):  
Kien Dinh Nguyen
Keyword(s):  
Moving Load ◽  
Excitation Frequency ◽  
Vibration Characteristics ◽  
Functionally Graded ◽  
Element Formulation ◽  
Harmonic Load ◽  
Timoshenko Beams ◽  
Power Functions ◽  
Material Inhomogeneity ◽  
Moving Harmonic Load

Vibration of two-directional functionally graded sandwich (2D-FGSW) Timoshenko beams under a moving harmonic load is investigated. The beams consist of three layers, a homogeneous core and two functionally graded skin layers with the material properties continuously varying in both the thickness and length directions by power functions. A finite element formulation is derived and employed to compute the vibration characteristics of the beams. The obtained numerical result reveals that the material inhomogeneity and the layer thickness ratio play an important role on the natural frequencies and dynamic response of the beams. A parametric study is carried out to highlight the effects of the power-law indexes, the moving load speed and excitation frequency on the vibration characteristics of the beams.  The influence of the beam aspect ratio on the vibration of the beams is also examined and discussed. 

scholarly journals Effect of friction on transverse vibration of string under moving load

2021 ◽  
Author(s):  
Kamal Kishor Prajapati ◽  
Soumyajit Roy
Keyword(s):  
Mathematical Model ◽  
Coefficient Of Friction ◽  
Transverse Vibration ◽  
Moving Load ◽  
Equation Of Motion ◽  
Harmonic Load ◽  
Axial Tension ◽  
Moving Harmonic Load ◽  
Catenary System ◽  
Basic Characteristics

Abstract Many engineering applications involve exerting moving harmonic load on a string like structure. Usually the interface between these structures and the moving load has some friction. A common example is a pantograph catenary system, which is used in locomotives for power collection. The aim of this paper is to develop a mathematical model of a simplified system consisting of infinitely long axially tensioned continuum and a moving harmonic load with friction acting at the interface. Equation of motion has been derived by resolving forces at that point. Subsequently the basic characteristics of the system are obtained by solving the model numerically. It is observed that the effect of friction obtained is negligibly low higher value of axial tension, but can significantly increase the string response at a particular range of coefficient of friction value when the axial tension is low.

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.

Analysis and identification of multiple-cracked beam subjected to moving harmonic load

2017 ◽  
Vol 24 (13) ◽  
pp. 2782-2801 ◽  
Author(s):  
NT Khiem ◽  
PT Hang
Keyword(s):  
Frequency Response ◽  
Moving Load ◽  
Exact Expression ◽  
Theoretical Development ◽  
Response Analysis ◽  
Multiple Cracks ◽  
Harmonic Load ◽  
Cracked Beam ◽  
Moving Harmonic Load ◽  
Measured Frequency Response

An exact expression is obtained in the frequency domain for the response of a multiple-cracked beam subjected to a moving harmonic load. The obtained solution is used first for response analysis of the beam in dependence on the load speed, frequency, and crack parameters. Then, based on the solution a procedure is developed for detecting multiple cracks in a beam from the measured frequency response. The most important advantage of the spectral approach is that it allows not only vibration analysis of beam with arbitrary number of cracks under harmonic moving load but also enables to detect an unknown amount of cracks by a sparse grid of measurement sensors. Moreover, the speed and frequency of moving load are useful control parameters for improving either measurements of the frequency response or detecting cracks by using the frequency response. The theoretical development has been illustrated and validated by numerical examples.

Parametric Effect on Bidirectional Moving Vehicle Load Identification

2011 ◽  
Vol 66-68 ◽  
pp. 194-198
Author(s):  
Ling Yu ◽  
Xue Gang Wang
Keyword(s):  
Moving Load ◽  
Identification Problem ◽  
Companion Paper ◽  
Identification Accuracy ◽  
Load Identification ◽  
Moving Vehicle ◽  
Vehicle Load ◽  
Parametric Effect ◽  
Bridge Responses ◽  
Moving Load Identification

Parametric effect on bidirectional moving vehicle load identification from plate bridge responses is studied in this paper. The equation of motion of a plate bridge-bidirectional vehicle system is formulated based on Hamilton principle and is rewritten in a state space form, the bidirectional moving load identification problem is considered as a damped least-squares problem and further solved with the regularization method. Finally, the effect of parameters on identification accuracy is investigated in order to evaluate the effectiveness and robustness of the bidirectional moving load identification method proposed in a companion paper. Some numerical simulations show that the proposed method is correct and effective for identifying the bidirectional moving vehicle loads from bridge responses with an acceptable accuracy, but the selection of parameters should be carefully considered in the identification process.

Bidirectional Moving Vehicle Load Identification from Bridge Responses

2010 ◽  
Vol 163-167 ◽  
pp. 2699-2703 ◽  
Author(s):  
Ling Yu ◽  
Xue Gang Wang
Keyword(s):  
Bridge Deck ◽  
Moving Load ◽  
Identification Problem ◽  
Dynamic Programming Method ◽  
Load Identification ◽  
Moving Vehicle ◽  
Vehicle Load ◽  
Vehicle Loads ◽  
Bridge Responses ◽  
Damped Least Squares

A time domain method on bidirectional moving vehicle load identification from plate bridge responses is proposed in this paper. The bridge deck is modeled as a plate based on the theory of plate and the vehicle loads are modeled as two groups of axle loads moving on top of the bridge deck in two opposite directions. The equation of motion of the bridge-vehicle system is formulated in state space and the bidirectional moving load identification problem is formulated as a damped least-squares problem and further solved using the dynamic programming method with regularization on the solution. Some numerical simulations show that the proposed method is correct and effective and can be used to identify the bidirectional moving vehicle loads from the bridge responses with an acceptable accuracy.

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