Dynamic response of the beam under moving load and axial periodic force and with the damping depending on the amplitude of vibration

Abstract eng:
Analysis of the dynamic response of the beam under moving load and axial periodic force and with constant damping result in well known solution of Mathieu equation. In fact structural damping depend on the velocity of deformation. In this paper the governing equations of damping defined are and the equation of motion of the beames derived. The solution is based on the expansion of amplitude y x, t using beam functions and on the application of Van der Pole method. The results may be formulated as follows: (a) the frequency and the related band of parametric resonance are derived, (b) the influence of moving load velocity on the width of this band is discussed. (c) the increasing velocity reduce the width, (d) in general the width depend on the ratio of axial forces (static and dynamic) and critical force of buckling.

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