Behavioral Study of Finite Beam Resting on Elastic Foundation and Subjected to Travelling Distributed Masses

Abstract

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.

Mechanistic Mathematical Modelling of Pothole Development from Loss of Roadway Subsurface-Materials

“…= ( * * ) + 0 (2e) (17) The Q = Flow rate of the eroded soil. We adapted it and the formula from the study [20], as shown in Eq.…”

“…Investigations have shown that potholes, warping, rutting, raveling, edge-break, cracks, and shear failures are common types of road deformation [1,2,4,13]. During road deformation (pothole) modeling, most research focused on the phenomena that affect the top layers of the road [7,2,[14][15][16][17]. It is because modeling the road's subsurface activities is tricky since it requires roadway subsurface data and different principles.…”

“…It is because modeling the road's subsurface activities is tricky since it requires roadway subsurface data and different principles. Studies assumed the roadway surface (asphalt layers) to be plates, beams, or slabs resting on foundations [2,7,[14][15][16][17]. Using those assumptions may not describe what happens below the surface layers.…”

"On the Moving Distributed Force Problem of a Non-Uniform Prestressed Simply Supported Rayleigh Beam"

“…In the latter, under tensile loads and in the former, under compressive axial loads. Later, [3] investigated the forced vibration of an elastic uniform Bernoulli-Euler beam having simple supports with a constant axial force resting on variable elastic foundation and traversed by uniformly distributed loads. [4] studied the transverse vibration of a Rayleigh cantilever beam with arbitrarily distributed axial loading and carrying a concentrated mass at the free end.…”

Damping influence on the critical velocity and response characteristics of structurally pre-stressed beam subjected to traveling harmonic load

“…The theoretical and experimental studies of the moving load problems have shown that moving loads may be divided into three categories namely: moving oscillator, moving mass, and moving force. Vibrations of beams due to moving oscillators are studied in [14,17,23,33,39], vibrations of beams due to a moving mass are investigated in [3,4,13,16,25,36,41], and vibration of beams due to moving force have been considered in [1,8,15,18,27,40]. Moving load problem with or without elastic foundation has been extensively studied and so many other aspects of the moving load problem have also been considerably explored [7,11,12,21,26,30,34].…”