Moving Load and Beam Response: a Systematic Investigation and Analytical Solution of Timoshenko Beam Vibrations Due to Moving Gravity and Inertia Force

This book represents a valuable contribution to civil engineering, mechanical engineering, naval architecture and nanotechnology. It includes an analytical solution of Timoshenko beam response due to moving gravity and inertia force. The problem is solved by the modified Timoshenko beam theory, which deals with a 4th order partial differential equation in terms of pure bending deflection. A differential equation is transformed into modal equations by the Galerkin and the energy balance method. Gravity force excites linear vibrations which are solved in the frequency domain, while the inertia force causes a complex problem of parametric excitation which is solved by the perturbation method. The resonant phenomenon is identified and investigated in detail. The influence of moving mass on natural vibrations is recorded as a novelty. It is found that the influence of damping on response is significant in the whole frequency domain. In spite of the fact that many papers have been published on this challenging subject, this book is highly educative since it is self-contained and offers an analytical solution of the problem in a physically transparent way.