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Transverse Displacement of Clamped-Clamped Non-Uniform Rayleigh Beams Under Moving Concentrated Masses Resting on a Constant Elastic Foundation
Abstract
In this paper, the vibrational motion of a non-uniform beam clamped at both ends carrying moving concentrated loads is investigated. The governing equation of motion of our dynamical system is transformed via Mindlin-Goodman’s cum Generalised Galerking’s methods as alluded
to in [19]. The resulting coupled dynamic equation is simplified via struble’s asymptotic techniques alluded to in [3,5,8,11,19], a second order differential equation that ensued is solved using integral transform methods to obtain a closed form solution. From the closed form solution,
it is obtained that for the same natural frequency, the critical speed for the non-uniform Rayleigh beams traversed by moving force is greater than that under the influence of a moving mass. Hence, resonance is reached earlier in the moving mass problems. Furthermore, the transverse displacement for the moving force and moving mass models were calculated for various time t and presented in plotted curves and in the clamped-clamped non-uniform boundary conditions. It is found that, the moving force solution is not an upper bound for the accurate solution of the moving mass solution. Analysis further shows that an increase in the values of the structural parameters reduces the response amplitude of non-uniform Rayleigh beams of our dynamical problem.
Keywords: , Rayleigh beam, non-uniform, axial force, non-classical boundary, rotatory-inertia,Foundation-modulli. Clamped-clamped.
to in [19]. The resulting coupled dynamic equation is simplified via struble’s asymptotic techniques alluded to in [3,5,8,11,19], a second order differential equation that ensued is solved using integral transform methods to obtain a closed form solution. From the closed form solution,
it is obtained that for the same natural frequency, the critical speed for the non-uniform Rayleigh beams traversed by moving force is greater than that under the influence of a moving mass. Hence, resonance is reached earlier in the moving mass problems. Furthermore, the transverse displacement for the moving force and moving mass models were calculated for various time t and presented in plotted curves and in the clamped-clamped non-uniform boundary conditions. It is found that, the moving force solution is not an upper bound for the accurate solution of the moving mass solution. Analysis further shows that an increase in the values of the structural parameters reduces the response amplitude of non-uniform Rayleigh beams of our dynamical problem.
Keywords: , Rayleigh beam, non-uniform, axial force, non-classical boundary, rotatory-inertia,Foundation-modulli. Clamped-clamped.
