Toshiaki Nakagawa

Forced Vibration Analysis of an Elevator Rope With Both Ends Moving

An elevator rope for a high-rise building is forcibly excited by the displacement of the building caused by wind forces. Regarding the rope, there are two boundary conditions. In the first case, one end moves with time and the other end is fixed, while in the second case, both ends move with time. A theoretical solution to the forced vibration of a rope where one end is moving has been already obtained. In this paper, a theoretical solution to the forced vibration of a rope where both ends are moving is presented, based on the assumption that rope tension and movement velocity are constant, and that the damping coefficient of the rope is zero or small. The virtual sources of waves, which can be assigned to reflecting waves, are used to obtain the theoretical solution. Finite difference analyses of rope vibration are also performed to verify the validity of the theoretical solution. The calculated results of the finite difference analyses are in fairly good agreement with that of the theoretical solution. The effects of the changing rate of rope length and the damping factor on the maximum rope displacement are quantitatively clarified.

First Order Analysis for Automotive Body Structure Design-Part 2: Joint Analysis Considering Nonlinear Behavior

We have developed new CAE tools in the concept design process based on First Order Analysis (FOA). Joints are often modeled by rotational spring elements. However, it is very difficult to obtain good accuracy. We think that one of the reasons is the influence of the nonlinear behavior due to local elastic buckling. Automotive body structures have the possibility of causing local buckling since they are constructed by thin walled cross sections. In this paper we focus on this behavior. First of all, we present the concept of joint analysis in FOA, using global-local analysis. After that, we research nonlinear behavior in order to construct an accurate joint reduced model. (1) The influence of local buckling is shown using uniform beams. (2) Stiffness decrease of joints due to a local buckling is shown. (3) The way of treating joint modeling considering nonlinear behavior is proposed.

Analysis of Two-Dimensional Problems Described by Helmholtz's Equations Using the Collocation Method. A Study on Domain Decomposition.

The collocation method using analytical solutions has an important inherent issue that causes the loss of the eigen value convergence due to singular points existing in the vicinity of a domain. In our previous study, we proposed a way to cancel it in a specific domain including a notch by adding singular terms to the general solutions. This method, however, can not easily be extended to general singular problems. To overcome this fault, we present a newly improved method that employs a domain decomposition approach in order to relax the effects of any singular points. First, the conditions for continuity between two decomposed domains are derived. Second, the eigen value equations are formulated based on these condition. Finally, using some examples, it is confirmed that the method presented here provides a high acuuracy of eigen values in any problems accompanied by singular points.

An Analysis of Two-Dimensional Problems Described by Helmholtz's Equation Using the Collocation Method. A Study on Singularity at Tips of Notched Boundaries.

If a domain of the target of analysis is convex, the solution of the two dimensional problem described by Helmholtzs equation is regular on the whole domain and the usual collocation method can be applied. On the other hand, if domains have notched boundaries, the tips of notches become singular points of the flux. For such cases, the solutions used in the convex domain problems can not be applied, because they never express any singularity. This paper shows that the analytical method for the convex domains previously proposed by the authors can be extended to the problems of notched domains. A general solution for the new method consists of two parts. One of them is the same as the solution for the convex domains and the other is a series that expresses the singularity at the notch tips. Numerical results of eigenmode obtained by this method satisfy boundary conditions and eigenvalues have excellent accuracy.