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.
In this present study, the response characteristics of a flexible member carrying harmonic moving load are investigated. The beam is assumed to be of uniform cross section and has simple support at both ends. The moving concentrated force is assumed to move with constant velocity type of motion. A versatile mathematical approximation technique often used in structural mechanics called assumed mode method is in first instance used to treat the fourth order partial differential equation governing the motion of the slender member to obtain a sequence of second order ordinary differential equations. Integral transform method is further used to treat this sequence of differential equations describing the motion of the beam-load system. Various results in plotted curves show that, the presence of the vital structural parameters such as the axial force N, rotatory inertia correction factor r 0 , the foundation modulus F 0 , and the shear modulus G 0 , significantly enhances the stability of the beam when under the action of moving load. Dynamic effects of these parameters on the critical speed of the dynamical system are carefully studied. It is found that as the values of these parameters increase, the critical speed also increases. Thereby reducing the risk of resonance and thus the safety of the occupant of this structural member is guaranteed.
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