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The tire is one of the most important parts, which influence the noise, vibration, and harshness of the passenger cars. It is well known that effect of rotation influences tire vibration characteristics, and earlier studies presented formulas of tire vibration behavior. However, there are no studies of tire vibration including lateral vibration on effect of rotation. In this paper, we present new formulas of tire vibration on effect of rotation using a three-dimensional flexible ring model. The model consists of the cylindrical ring represents the tread and the springs represent the sidewall stiffness. The equation of motion of lateral, longitudinal, and radial vibration on the tread are derived based on the assumption of inextensional deformation. Many of the associated numerical parameters are identified from experimental tests.

To improve the accuracy of engine vibration analysis, the bolt model which fastens an engine head and an engine block had been developed. In the conventional method of engine vibration analysis, the bolt was modeled with a rigid bar. However, it is seen that the power plant rigidity becomes higher in proportion to the rigid bar bolt length. So, to precisely predict the vibration property of engine parts, the elastic deformation of the bolt was considered in this paper. It is known that the parameters, which are Young's modulus, the length of bolts, the distance between bolts, the area of contact plane, the tightening torque and so on, have a great influence on the performance of the engine vibration model. This paper describes a study of FE bolt model to correlate eigenvalue and mode shapes with the test result. The effects of following parameters were investigated: 1) Bolt model with elastic material 2) Rigidity of bolted-connection in tightening plane.