Vibration of a Beam under a Random Stream of Moving Forces*

Dynamic Response of a Rotating Beam Subjected to a Random Moving Load

“…Chang [6] presented a method to perform the deterministic and random vibration analysis of a Rayleigh Timoshenko beam on an elastic foundation, he used modal analysis to compute the dynamic responses of the structure, such as the displacement and bending moment and some statistical responses such as mean square values of the dynamic displacement and bending moment. Iwankiewicz and Sniady [7] studied the problem of the dynamic response of a beam to the passage of a train of concentrated forces with random amplitudes. They obtained explicit expressions for the expected value and the variance of the beam de¯ection.…”

Random vibration of multi‐span mindlin plate due to moving load

“…(2) 0)¡j is the ijth modal frequency and the corresponding excitation g¡j(t) is The initial conditions of the plate are set at zeros. The response history of the ijth modal amplitude A ¡j(t) is (5) in which the impulse response Uy(t ) is _ I sin (py t ycDij (0<O (6) …”

Vibration of beams with general boundary conditions due to a moving random load

“…Assuming that the load sequence is a Poisson process and the inertial effect of moving loads can be neglected, the authors examined the time history, the power spectral density, and the various moments of the response. The dynamic response of a beam to the passage of a train of concentrated forces with random amplitudes was studied in [8]. Based on the introduction of two influence functions, one of which satisfies the nonhomogeneous, the other the homogeneous differential equations for beam response, the authors obtained explicit expressions for expected value and variance of the beam deflection.…”