ORIGINAL ARTICLES Dynamic Behaviour of a double Rayleigh Beam-System due to uniform partially distributed Moving Load (original) (raw)
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A theory concerning the dynamic response of two identical simply supported Rayleigh beams viscoelastically connected together by a flexible core and traversed by a concentrated moving load is developed in this paper. The solution technique employed is based on finite Fourier and Laplace integral transformations. It is observed that the maximum amplitude of the deflection of the upper beam increases with an increase in the value of the rotatory inertia while the maximum amplitude of deflection of the lower beam decreases with increasing values of rotatory inertia.
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The problem being investigated in this paper is that of the dynamic behavior of non-uniform beam on a constant elastic foundation. The elastic properties of the beam, the flexural rigidity, the mass per unit length, and the elastic modulus parameter are expressed as functions of the spatial variable x. However, an assumed mode technique is employed to simplify the displacement of the non-uniform system to second order ordinary differential equation and then solved via Laplace method. The effects of damping, elastic foundation and rotatory inertia correction factors on the dynamic deflection of Rayleigh beams on distributed load are also investigated.
Vibration analysis of beams traversed by uniform partially distributed moving masses
Journal of Sound and Vibration, 1995
An investigation into the dynamic behavior of beams with simply supported boundary conditions, carrying either uniform partially distributed moving masses or forces, has been carried out. The present analysis in its general form may well be applied to beams with various boundary conditions. However, the results from the computer simulation model given in this paper are for beams with simply supported end conditions. Results from the numerical solutions of the differential equations of motion are shown graphically and their close agreement, in some extreme cases, with those published previously by the authors is demonstrated. It is shown that the inertial effect of the moving mass is of importance in the dynamic behavior of such structures. Moreover, when considering the maximum deflection for the mid-span of the beam, the critical speeds of the moving load have been evaluated. It is also verified that the length of the distributed moving mass affects the dynamic response considerably. These effects are shown to be of significant practical importance when designing beam-type structures such as long suspension and railway bridges. 7
VIBRATIONS OF NON-UNIFORM CONTINUOUS BEAMS UNDER MOVING LOADS
Journal of Sound and Vibration, 2002
The dynamic behavior of multi-span non-uniform beams transversed by a moving load at a constant and variable velocity is investigated. The continuous beam is modelled using Bernoulli}Euler beam theory. The solution is obtained by using both the modal analysis method and the direct integration method. The natural frequencies and mode shapes used in the solution of this problem are obtained exactly by deriving the exact dynamic sti!ness matrices for any polynomial variation of the cross-section along the beam using the exact element method. The mode shapes are expressed as in"nite polynomial series. Using the exact mode shapes yields the exact solution for general variation of the beam section in case of constant and variable velocity. Numerical examples are presented in order to demonstrate the accuracy and the e!ectiveness of the present study, and the results are compared to previously published results.
Applied Sciences, 2019
Dynamics of the double-beam system under moving loads have been paid much attention due to its wide applications in reality from the analytical point of view but the previous studies are limited to the simply supported boundary condition. In this study, to understand the vibration mechanism of the system with various boundary conditions, the double-beam system consisted of two general beams with a variety of symmetric boundary conditions (fixed-fixed, pinned-pinned, fixed-pinned, pinned-fixed and fixed-free) under the action of a moving force is studied analytically. The closed-form frequencies and mode shapes of the system with various symmetric boundary conditions are presented by the Bernoulli-Fourier method and validated with Finite Element results. The analytical explicit solutions are derived by the Modal Superposition method, which are verified with numerical results and previous results in the literature. As found, each wavenumber of the double-beam system is corresponding t...
Vibration of Viscoelastic Beams Subjected to Moving Harmonic Loads
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The transverse vibration of a beam with intermediate point constraints subjected to a moving harmonic load is analyzed within the framework of the Bernoulli-Euler beam theory. The Lagrange equations are used for examining the dynamic response of beams subjected to the moving harmonic load. The constraint conditions of supports are taken into account by using Lagrange multipliers. In the study, for applying the Lagrange equations, trial function denoting the deflection of the beam is expressed in the polynomial form. By using the Lagrange equations, the problem is reduced to the solution of a system of algebraic equations. The system of algebraic equations is solved by using the direct time integration method of Newmark (8). Results of numerical simulations are presented for various combinations of constant axial velocity, excitation frequency,
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Global Journal of Science Frontier Research in Mathematics and Decision Sciences, 2012
The problem being investigated in this paper is that of the response of non-uniform beam under tensile stress and resting on an elastic foundation. The fourth order partial differential equation governing the problem is solved when the beam is transverse by mobile distributed loads. The elastic properties of the beam, the flexible rigidity, and the mass per unit length are expressed as functions of the spatial variable using Struble's method. It is observed that the deflection of non-uniform beam under the action of moving masses is higher than the deflection of moving force when only the force effects of the moving load are considered. From the analysis, the response amplitudes of both moving force and moving mass problems decrease with increasing foundation constant.
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Journal of Sound and Vibration, 1995
A theory concerning the dynamic response of finite elastic structures (Rayleigh beams and plates) having arbitrary end supports and under an arbitrary number of moving masses is developed. The versatile solution technique presented is based on modified generalized finite integral transforms and the modified Struble's method. Various analytical results are presented. Numerical examples are given and the results compare favourably with existing ones. The efficiency of the solution technique is demonstrated and discussed.
Dynamic Response of Loads on ViscouslyDamped Axial Force Rayleigh Beam
Journal of Applied Sciences, 2008
This research examines the effects of moving loads on viscously damped axial force Rayleigh beam. The authors especially tried to find the effect of the moving mass and moving force in connection with the length of the span of a Rayleigh beam. The authors also examined the effect of the lengths of the beam and of the load. It was observed that as mass of the moving load increases the deflection along the length of the beam also increases. It was further observed that the deflection of the moving mass is greater than that of the moving force.
Mathematical Analysis of Rayleigh Beam with Damping Coefficient Subjected to Moving Load
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In this paper, the mathematical analysis of Rayleigh beam with damping coefficient subjected to moving load is investigated. The governing partial differential equation of order four was reduced to an ordinary differential equation using series solution. Numerical result was presented and it is found that the dynamic response of the beam increases as the length of the mass increases, the same result is also found for the length of the beam and the mass of the load but the dynamic response of the beam decreases as the length of the load. It also reduces as the speed at which the load moves increases. Also, the dynamic response of the beam is not affected by the damping coefficient.