Vibration of Solids and Structures under Moving Loads

Abstract

Beam subjected to a moving system with t\\;O degrees of freedom 103 8.1 Formulation of the problem 104 8.2 Solution of the problem 108 8.2.1 Dimensionless parameters 108 8.2.2 Reduction of the equations to the dimensionless form 112 8.2.3 Numerical solution 114 8.3 The effect of various parameters 115 8.3.1 The effect of speed 115 8.3.2 The effect of the frequency parameter of unsprung mass 117 8.3.3 The effect of the frequency parameter of sprung mass 118 8.3.4 The effect of variable stiffness of the elastic layer 118 8.3.5 The effect of the ratio between the weights of vehicle and beam 119 8.3.6 The effect of the ratio between the weights of unsprung and sprung parts of vehicle 119 8.3.7 The effect of beam damping 121 8.3.8 The effect of vehicle spring damping III 8.3.9 The effect of initial conditions 121 8.3.10 The effect of other parameters 123 8.4 Application of the theory 125 8.4.1 Comparison of theory with experiments 125 8.4.2 Dynamic stresses in large-span railway bridges 128 8.5 Additional bibliography 128 9 Beam subjected to a moving two-axle system 129 9.1 Formulation of the problem 129 9.2 Solution of the problem 134 9.2.1 Dimensionless parameters 134 9.2.2 Reduction of the equations to the dimensionless form 137 9.2.3 Reduction of the equations to a form suitable for numerical calculations 140 9.2.4 Numerical solution 142 9.3 The effect of various parameters 145 9.3.1 The effect of speed 145 9.3.2 The effect of the frequency parameter of unsprung mass 148 9.3.3 The effect of the frequency parameter of sprung mass 148 9.3.4 The effect of the ratio between the weights of vehicle and beam 150 9.3.5 The effect of the ratio between the weights of unsprung parts and whole vehicle 150 9.3.6 The effect of the depth of irregularities 150 9.3.7 The effect of the length of irregularities 151 IX 13 Infinite beam on elastic foundation 13.1 Formulation of the problem 206 13.2 Poles of the function of a complex variable 209 13.2.1 Static case 211 13.3

Reduction of bridge dynamic amplification through adjustment of vehicle suspension damping

“…The solution for the displacement of a beam of length L [24] at location x and time t, may be expressed as an expansion in terms of the generalised coordinates, q (j) (t).…”

Analytical Model of the Dynamics of Railway Sleeper

“…In addition, the sleeper dynamic response is important because it affects the stability of the railway track and the maximum speed of the train. Substantial researches using analytic methods for rail track have been carried out, for example : the effect of wheel-rail contact forces [17,18] or the vibration of the railway track (by considering the model of a ballasted track with discrete supports [8,9,13,14,1] or the model of the infinite beam placed on a continuous foundation [10,7,6,11]). The studies of each component of the rail track were performed on the rail [19,16,15], or on the ballast [20,22].…”

Dynamic Computation and Design of a World's Record Death-Ride

“…The dynamic loading of structures under moving loads is extensively studied in [6]. In particular, the vibrations of a string subject to a moving force is a well-established theory.…”