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.
The transverse vibration of a prismatic Rayleigh beam resting on elastic foundation and continuously acted upon by concentrated masses moving with arbitrarily prescribed velocity is studied. A procedure involving generalized finite integral transform, the use of the expression of the Dirac delta function in series form, a modification of the Struble's asymptotic method and the use of the Fresnel sine and cosine functions is developed to treat this dynamical beam problem and analytical solutions for both the moving force and moving mass model which is valid for all variant of classical boundary conditions are obtained. The proposed analytical procedure is illustrated by examples of some practical engineering interest in which the effects of some important parameters such as boundary conditions, prestressed function, slenderness ratio, mass ratio and elastic foundation are investigated in depth. Resonance phenomenon of the vibrating system is carefully investigated and the condition under which this may occur is clearly scrutinized. The results presented in this paper will form basis for a further research work in this field.
A procedure involving spectral Galerkin and integral transformation methods has been developed and applied to treat the problem of the dynamic deflections of beam structure resting on biparametric elastic subgrade and subjected to travelling loads. The case of the response to moving constant loads of this slender member is first investigated and a closed form solution in series form describing the motion of the beam while under the actions of the travelling load is obtained. The response under a variable magnitude moving load with constant velocity is finally treated and the effects of prestressed, foundation stiffness, shear modulus and damping coefficients are investigated. Results in plotted curves indicate that these structural parameters produce significant effects on the dynamic stability of the load-beam system. Conditions under which the beam-load system may experience resonance phenomenon are also established some of these findings are quite useful in practical applications.
The classical problem of the response characteristics of uniform structural member resting on elastic subgrade and subjected to uniform partially distributed load is studied in this work. The closed form solutions of the governing fourth order partial differential equations with variable coefficients are presented using an elegant analytical technique for the moving force and mass models. Various results and analyses are carried out on each of the pertinent boundary conditions and phenomenon of resonance is studied for the dynamical system. It was found that in all illustrative examples considered, for the same natural frequency, the critical speed for moving distributed mass problem is smaller than that of the moving distributed force problem. Hence, resonance is reached earlier in moving mass beam-load interaction problem. Finally, this work has suggested valuable methods of analytical solution for this category of problems for all boundary conditions of practical interest.
The dynamic response to moving concentrated masses of elastically supported rectangular plates resting on Winkler elastic foundation is investigated in this work. This problem, involving non-classical boundary conditions, is solved and illustrated with two common examples often encountered in engineering practice. Analysis of the closed form solutions shows that, for the same natural frequency (i) the response amplitude for the moving mass problem is greater than that one of the moving force problem for fixed Rotatory inertia correction factor R0 and foundation modulus F0, (ii) The critical speed for the moving mass problem is smaller than that for the moving force problem and so resonance is reached earlier in the former. The numerical results in plotted curves show that, for the elastically supported plate, as the value of R0 increases, the response amplitudes of the plate decrease and that, for fixed value of R0, the displacements of the plate decrease as F0 increases. The results also show that for fixed R0 and F0, the transverse deflections of the plates under the actions of moving masses are higher than those when only the force effects of the moving load are considered. Hence, the moving force solution is not a save approximation to the moving mass problem. Also, as the mass ratio Γ approaches zero, the response amplitude of the moving mass problem approaches that one of the moving force problem of the elastically supported rectangular plate resting on constant Winkler elastic foundation.
This study concerns the dynamic characteristics of a prestressed isotropic, rectangular plate continuously supported by an elastic foundation and carrying accelerating mass M. Closed form solutions of the governing fourth order partial differential equations with variable and singular coefficients are presented. For the twodimensional plate problem, the solution techniques is based on the double Fourier Finite Sine integral transformation, the expansion of the Dirac Delta function in series form, a modification of Struble's asymptotic method and the use of Fresnel sine and Fresnel cosine integrals. Numerical analyses in plotted curves are presented. The analyses reveal interesting results on the effect of structural parameters such as foundation moduli, rotatory inertia correction factor and prestressing forces on the dynamic behaviour of isotropic rectangular plate under the actions of concentrated masses moving at variable velocity. In particular it is found that the critical velocity of the travelling load which brings about the occurrence of a resonance state increases as the values of these structural parameters increase.
Summary
In this study the problem of the dynamic characteristics of a structurally presstressed beam under compressive axial force and subjected to accelerating loads is investigated. A procedure based on Galerkin's residual method, asymptotic method of struble, and integral transformation method is developed to solve the fourth‐order partial differential equation with variable and singular coefficients governing the dynamic behavior exhibited by the beam‐mass system. The proposed solution procedure is very versatile and is suitable for handling moving mass beam problem for all pertinent boundary conditions. The theory and analysis proposed in this work are illustrated by various practical examples often encounter in engineering design and practice. Analytical solutions valid for all variants of classical boundary conditions are obtained for the beam‐load system. The effects of the traveling velocity of the moving mass, span length, and flexural rigidity on the response of the beam are investigated. A comparative analysis of the behavior of this structural member under accelerating, decelerating, and uniform velocity type of motion is performed. Various results in plotted curves are presented.
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