Timoshenko Beam System Research Articles

Timoshenko Beam with Tuned Mass Dampers to Moving Loads

The structural analysis of a Timoshenko beam system with tuned mass dampers (TMDs) under moving-load excitation is presented. A proposed simplified two-degrees-of freedom system based on the first mode of the Timoshenko beam is employed for the design of TMDs. The dynamic characteristics of a Timoshenko beam, such as the structural-resonant and phase-resonant velocities, and the effectiveness of a TMD for vibrational control are especially emphasized. A practical example of an elevated railway subjected to the Japanese Shinkansen (SKS) high-speed bullet train is included.

Exact frequency and mode shape formulae for studying vibration and stability of Timoshenko beam system

Two sets of exact natural frequency and mode shape formulae for an axially loaded Timoshenko uniform single-span beam carrying elastically supported end masses are derived. The end masses are restrained against rotation and translation with linear springs. The two equations of motion of references [1,2] are used in the problem formulation. Comparisons between the derived frequency equations for a typical example of a clamped-free beam are made. The difference between natural frequencies is significant for beams subjected to high loads and for high modes of vibration. Most of the well known published exact expressions for determining the natural frequencies and the mode shapes can be obtained from the present equations as special cases. The influence of beam rotary inertia, and end mass(es) geometrical parameters on the natural frequency and critical buckling load coefficients has been studied. When an axial compressive load is acting at the centre of gravity of the end mass(es), the same critical buckling load coefficients are found for free-free, pinned-free and pinned-pinned beams, and similarly for clamped-sliding and sliding-sliding beams. In addition, if the slope due to bending is allowed at one end of the beam, the same critical buckling loads are found for, clamped-free, sliding-free and sliding-pinned beam configurations. The present work includes graphs and numerical tables describing the variation of the natural frequencies and the critical buckling load coefficients from the design point of view.

Transverse Vibrations of a Ship Hull in Ideal Fluid, Determined Through Variational Methods

A direct formulation for analyzing the vibration characteristics of an arbitrary body and predicting the three-dimensional velocity potential is presented. It consists of forming the Lagrangian for a Timoshenko-beam fluid system and minimizing Hamilton's principal function by the Rayleigh-Ritz method. Due to the boundary condition, the minimizing sequence for vibration amplitude transforms the velocity potential into an associated sequence of Neumann boundary-value functions. These are expressed further in terms of another minimizing sequence and evaluated after minimizing the corresponding energy functionals according to the method of minimal surface integrals. The theory is applied to a simple body and the resulting vibration characteristics are found to be more accurate than previous theoretical estimates and closer to published experimental data. Finally, the feasibility of the procedure is outlined for a submerged ship hull, employing approximate methods of numerical quadrature.