The Response of a Prestressed Beam-type Structure subjected to Partially Distributed Load Moving at Non-Uniform Velocities

The transverse vibration of a prismatic Rayleigh beam resting on bi-parametric Vlasov foundation and continuously acted upon by partially distributed masses moving at varying velocities is investigated. For the solution of the fourth order partial differential equation with singular and variable coefficients, use is made of the technique based on the Generalized Finite Fourier Integral Transform, Struble’s asymptotic technique and the use of Fresnel sine and cosine identities. Numerical results in plotted curves are presented. The results show that the response amplitude of the beam traversed by a distributed load moving with variable velocity decrease with an increase in the value of foundation modulus, Other structural parameters such as axial force, rotatory inertia and shear modulus are also found to reduce the displacement response of the beam as their values are increased in the dynamical system.  The results also show that the critical speed for the system traversed by a moving distributed force is found to be greater than that traversed by moving mass. This confirms that the inertia effect of the moving distributed load must be considered for accurate and safe assessment of the response to moving distributed load of elastic structural members.