Flexural motions of uniform beam under the actions of concentrated mass traveling with variable velocity

Abstract

This paper presents the dynamic analysis of the vibrations of a uniform beam under the action of a concentrated mass travelling with variable velocity. The solution technique discussed involves the expansion of Dirac delta function in cosine series form, a modification of the Stumble's asymptotic method and the use of the generating function of the Bessel function type. Analytical solution are obtained and the numerical results in plotted curves show that for the moving force and moving mass problems, the response amplitudes of the bean traversed by a load moving with variable velocity decrease with an increase in the foundation constant K. Similarly, the critical speed for the system traversed by a moving force is found to be smaller than that under the influence of moving mass showing that resonance is reached earlier in moving mass problem. Also, the displacement amplitude of the moving mass is greater than of the moving force. This further confirms the non-reliability of the moving force solution as safe approximation to the moving mass problem

Journal of the Nigerian Association of Mathematical Physics Vol. 8 2004: pp. 215-224