Vibration of solids and structures under moving loads

Abstract

ContentsPreface XVI Symbols XIX 7 Massless beam subjected to a moving load 7.1 Formulation of the problem 94 VIII 7.2 Exact solution 95 7.3 Approximate solutions 98 7.3.1 The perturbation method 98 7.3.2 Method of successive approximations 100 7.3.3 Expansion in power series 101 66 83 94 CONTENTS 7.4 Application of the theory 102 7.5 Additional bibliography 102 8 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 1289 Beam subjected to a moving two-axle system

Transverse Motions of Rectangular Plates Resting on Elastic Foundation and Under Concentrated Masses Moving at Varying Velocities

“…It has also become the objective of various investigations in the field of applied Mathematics and Physics. In general, problems of this type are mathematically complex when the inertial effect of the moving load is taken into consideration [Fryba, L., (1972), Milormir et al (1969), Sadiku et al, (1981), Gbadeyan and Oni (1995) Kargarmovin and Younesian (2004), Shahin and Mbakisya (2010), Awodola and Oni (2013), Awodola and Oni (2011), Omolofe (2013)]. …”

“…When these are available, the inertia effects of the heavy mass are neglected. It is well known that in a dynamical system as this, analytical method is desirable as solutions so obtained often shed light on vital information about the vibrating system [Fryba, L., (1972), Omolofe (2013), Stanisic et al (1974), Stanisic (1968), Hossein et al (2013), Atteshamuddin (2013), Gbadeyan and Oni (1992)]. …”

Finite element analysis of the dynamic response of plates under traversing loads using adaptive meshes

“…There are many systems, such as railroads, cable railways, highways, bridges, overhead cranes and machining processes, that are subjected to traversing loads [2][3][4][5][7][8][9][10][11][12][13][14][15][16]. The investigation of these systems has been limited to scenarios where beam models provide a reasonable approximation to the system response [7][8][9][10]12,13,15,16] or to scenarios with simple geometries and boundary conditions such as simply supported rectangular plates [3][4][5]14].…”

“…Olsson [11] presents a general derivation of a FEM application to moving load problems but only reports simulations for beam models. The work by Frýba [2] is an excellent introduction to the subject of forces and masses traversing beams or plates; it presents analytical solutions for simple cases.…”

Dynamic Characteristics of a Rotating Timoshenko Beam Subjected to a Variable Magnitude Load Travelling at Varying Speed

“…Studies concerning vibrating bodies resting on an elastic foundation carrying moving loads are of considerable practical importance and have been a subject of numerous scientific investigations by different authors in past few years [1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20]. In most of the studies available in literature, such as the work of Sadiku and Leipolz [21], Oni and Awodola [22], the scope of the problem of assessing the dynamic response of a structural member under the passage of moving load has been limited to that of thin beam or thick beam.…”