Takahiro Tomioka

Numerical Analysis of Three-Dimensional Flexural Vibration of Railway Vehicle Car Body

An analytical method to investigate the three-dimensional (3D) flexural vibration of railway vehicle car bodies is presented in this article. In the method, a car body is modeled as a box-type structure consisting of plates and beams. The condition to connect components is satisfied by introducing artificial springs at their joints. The detailed analytical procedure is described. Some numerical calculations are carried out employing a commuter vehicle, which has a stainless steel car body, as an example. The numerical results are compared with the measured data to evaluate the validity of the model. Although the target vehicle has complicated mode shapes, it is shown that the analytical model can express such 3D vibration mode shapes successfully. It is also demonstrated that a good agreement is observed between the calculation results by the above method and the measured data for both stationary excitation and running test.

Reduction of Bending Vibration in Railway Vehicle Carbodies using Carbody-bogie Dynamic Interaction

This paper presents a theory to utilise the longitudinal vibration in bogies as a dynamic vibration absorber (DVA) to reduce the vertical bending vibration of railway vehicle carbodies in a simple and easy way. This study focuses upon the interaction between carbody vertical bending and bogie longitudinal motion, and the condition for tuning the natural frequency of the bogie motion to the target carbody vibration is derived theoretically using a very simple formula. Numerical and experimental studies are then outlined to validate the theory and formula, and the DVA effects are observed from both of them. The effectiveness of the method is also confirmed from a running test with a Shinkansen train on a commercial line.

Vibration suppression of scale model of railway carbody with piezoelectric elements : (A study focused on designing shunt circuits)

The goal of this study is to reduce the bending vibration of railway vehicles by applying a vibration suppression technique. The technique utilizes piezoelectric elements that are electrically shunted by an external circuit. This paper presents an investigation by using a scale model of a Shinkansen vehicle with a length of about 5m, mainly focused on implementation of shunt circuits. Small pieces of piezoelectric elements are bonded to its floor structure and electrically connected to a shunt circuit. The authors propose a new method to implement shunt circuits, a part of which is virtually realized. The circuits are designed for practical use under the condition of high voltage generated by the elements. Two types of shunt circuits are tested in this study. One is equivalent to an inductor and a resistor in series, and the other consists of a negative capacitor and a resistor. In actuality, the inductor and the negative capacitor are replaced by virtually realized impedance components. Results of excitation tests show that the circuits implemented based on the proposed method function as expected and bending vibration of the carbody can be reduced successfully.

Vibration Analysis of a Railway Carbody Model as a Non-Circular Cylindrical Shell

Railway carbody is modeled as a non-circular cylindrical shell with simply-supported ends in this paper. The shell model doesn’t have end plates of the carbody and other equipments attached to actual carbody are neglected. We have applied the transfer matrix method (TMM) to the analysis of three-dimensional elastic vibration problems on the carbody. We also made a 1/12 size carbody model for experimental studies to verify the validity of the numerical simulation. The model has end plates and was placed on soft sponge at both ends of the model to emulate the freely-support. The modal analysis was applied to the experimental model, and natural frequencies and mode shapes of vibration were measured. Comparing the results by TMM and the experiment, natural frequencies and mode shapes of vibration for lower modes show good agreement each other in spite of differences of boundary conditions.Copyright

Free Vibration of a Rotating Disk–Blade Coupled System With Shrouds

The free vibration of rotating disk–blade coupled system is investigated by the Ritz method. Centrifugal effects due to rotation are taken into account for both of the disk and blades. The boundary and continuity conditions between the disk and blades are satisfied by means of artificial springs introduced at their joints, and the orthogonal polynomials generated by using the Gram–Schmidt process are employed as admissible functions for both of the disk and blades. Frequency parameters and mode shapes of vibration are obtained to investigate the vibration of the disk–blade coupled system.Copyright

Steady-State Response of Disk : Beam Coupled System Having Cyclically Symmetric Structure

The steady-state response of a disk-beam coupled system having cyclically symmetric structure subjected to a sinusoidal point force is investigated analytically. The orthogonal polynomials generated using the Gram-Schmidt process and the eigenfunction of a uniform disk are employed as admissible functions, and artificial springs are introduced between the components to satisfy their continuity condition. The equations for steady-state response are derived by means of the Lagrange equation. The response curves of the system are calculated numerically to examine the effect of damping factors, the location of the driving point, the existence of the shroud, and the stiffness ratio of the disk and beams.

Vibration Analysis of Disk-Beam Coupled System Having Cyclically Symmetric Structure.

The free vibration of a disk-beam coupled system having cyclically symmetric structure is investigated by the Ritz method in this study. The orthogonal polynomials generated using the Gram-Schmidt process and the eigenfunction of a uniform disk are employed as admissible functions. The continuity conditions between the disk and beams are satisfied by means of artificial springs at their joints. By this approach, the mass matrices derived from kinetic energies of the system become diagonal, and this will make the numerical manipulation of the matrices easy and stable. It is also described in this paper that the mode shapes of the disk-beam coupled vibration consist of specific circumferential wave components and thus the modes can be classified. Numerical calculations are carried out, and the frequency parameters and mode shapes are obtained to investigate the vibration of the disk-beam coupled system.