Deflection profile analysis of beams on two-parameter elastic subgrade

a procedure involving spectral galerkin and integral transformation methods has been developed and applied to treat the problem of the dynamic deflections of beam structure resting on bi-parametric elastic subgrade and subjected to travelling loads. the case of the response to moving constant loads of this slender member is first investigated and a closed form solution in series form describing the motion of the beam while under the actions of the travelling load is obtained. the response under a variable magnitude moving load with constant velocity is finally treated and the effects of prestressed, foundation stiffness, shear modulus and damping coefficients are investigated. results in plotted curves indicate that these structural parameters produce significant effects on the dynamic stability of the load-beam system. conditions under which the beam-load system may experience resonance phenomenon are also established some of these findings are quite useful in practical applications.