Katsuhisa Fujita

Motion and Vibration of a Moving Body on the 3D Trajectory Considering Running Resistance

The motion and vibration of a moving body running on the complicated 3 dimensional trajectory considering the running resistance are investigated in this paper. A roller coaster is treated with here as the concrete example of a moving body. The equations of motion of a roller coaster in which a trajectory and a vehicle are coupled are derived by using the differential-algebraic equation (DAE). The dynamic behavior of a roller coaster which moves forward due to the gravity acceleration neglecting the running resistance has been reported in our former papers. In this paper, we take the effect of an air resistance and a rolling resistance into consideration. The influences of these resistances on the required time from the starting point to the arriving one and the vibration response of a vehicle are investigated. Moreover, it is shown that the numerical solutions have a better coincidence with the experimental results which have been obtained by measuring an actual roller coaster.Copyright

Analysis Methods for the Motion and Vibration of a Moving Body on the Complicated 3D Trajectory

We investigate the motion and vibration of a moving body on a complicated 3 dimensional trajectory. We take a roller coaster as a model of a moving body. Equations of its motion and conditions of constraints are set up for using the differential-algebraic equation (DAE). In our previous reports, we showed the simulation method by using the s-u-z coordinate. Let us call it the s-u-z simulation method. s-axis is the direction of a length of trajectory which is tangential line for the projected trajectory on coordinate x-y. In this paper, we examine the simulation method by using the global coordinate x-y-z. Let us call it the x-y-z simulation method. In the process of the simulation, we apply the stablization method by Baumgarte to the both of simulation methods. It is found that the x-y-z simulation method is more complicated than the s-u-z simulation method so that it is more difficult to stablize the simulated trajectory in the x-y-z simulation method. Lastly, we compare these response accelerations in each simulation method with those in experiment.© 2005 ASME

Dynamic Instability of a Cylindrical Shell Structure Subjected to Horizontal and Vertical Excitations Simultaneously

Many structures such as support columns such as those for elevated expressways and towers tend to become larger and more flexible recently, thus the buckling or collapse of these structures is considered to easily occur than ever due to huge earthquakes. Actually, in the Hyogo-ken Nambu earthquake in Japan, buckling phenomena of tall support columns were observed every-where. Therefore, the evaluation technology on the dynamic stability is very important in order to ensure the seismic design reliability for these structures. The authors have ever studied the effects of the horizontal and vertical simultaneous excitations on the above-mentioned buckling phenomena of support columns experimentally. More-over, they also investigated the fundamental phenomena of the dynamic stability of the support columns subjected to the horizontal and vertical excitations simultaneously by numerical simulations using an analytical model where the support column is treated as a tall elastic cantilever beam. The purpose of this paper is on the dynamic instability, that is dynamic buckling, of a cylindrical shell structures such as those for elevated expressways, towers, containment vessels, LNG tanks and water tanks in various industrial plants so on subjected to horizontal and vertical excitations simultaneously. The coupled motion of equation with horizontal and vertical excitations simultaneously for these cylindrical shell structures is derived in this paper, and this modeling is shown to become a Mathieu type’s parametric excitation. The numerical simulation analysis is carried out for a cylindrical shell model with an attached mass on its tip. Comparing with the classical seismic analysis method, this proposed dynamic instability analysis method shows the larger deformation in horizontal direction due to the parametric excitation of the vertical seismic wave. As the results, the structures are apt to lose the structural stability more due to the coupling effects between the horizontal and vertical seismic simultaneous loadings.Copyright

Experimental Study of Coupling Vibration Characteristics Between a Thin Cylindrical Water Storage Tank and Its Contained Liquid

A large cylindrical water storage tank typically has a thin sidewall. When such a tank is under an earthquake, the vibrations of the water inside are coupled with the vibrations of the sidewall, producing a phenomenon called fluid-structure coupled vibration. The fluid-structure coupled vibration is an important issue for a tank like this to achieve reasonable seismic-proof design. Even though there have been many studies on fluid-structure coupled vibrations, only a few of them have examined the dynamic fluid pressure and oval vibrations. This paper reports on the investigations into the characteristics of oval vibrations exhibited by a cylindrical water storage tank, in which a vibration test was conducted using a shaking table, the correlation of changes in the excitation force and behaviors of dynamic fluid pressure with the appearance and growth of oval vibrations were analyzed, and the modes of oval vibrations that appeared were identified. The vibration test was conducted using a scale model tank of a large cylindrical water storage tank and a shaking table. The input vibrations were sinusoidal waves of 53 Hz, a frequency that was in the vicinity of the resonance frequency. The test took the form of a large amplitude excitation test, which increased the acceleration of the input vibrations gradually. The response acceleration of the tank and the dynamic fluid pressure were measured. Strain gages attached around the trunk of the tank were used to identify oval vibration modes. The frequency analysis of the dynamic fluid pressure revealed two major peaks, one at 53 Hz which matched the excitation frequency and the other at 106 Hz which was double the excitation frequency. It showed that the dynamic fluid pressure has nonlinear behavior like higher-harmonic resonance. The frequency analysis of the responses on the trunk of the tank arising from oval vibrations also revealed two major peaks, one at 53Hz and the other at 106Hz. The behavior of dynamic fluid pressure and the behavior of oval vibrations were coupled. It was found that a certain magnitude of the response acceleration of the tank that gave rise to oval vibrations were in proportion to the rate of increase of the response acceleration of the tank. In other words, oval vibrations appeared at a relatively low response acceleration if the response acceleration increased slowly, whereas oval vibrations appeared only at a relatively high response acceleration if the response acceleration increased quickly. An analysis of the circumferential distribution of circumferential strains around the trunk of the tank revealed the presence of two oval vibration modes with different circumferential wave numbers: 14 and 16, which have not been predicted by the FEM analysis. None of the natural frequencies determined by the FEM analysis of the two different vibration modes matched 106 Hz; however, a half of the sum of the two natural frequencies was close to 106 Hz. Thus oval vibrations were found to have a nonlinear characteristics experimentally.Copyright

Instability of an Axial Leakage Flow-Induced Vibration of Thin Cylindrical Shells Having Freely Supported End

When thin cylindrical shells having freely supported end at the downstream side such as heat-shielding shells of afterburners, labyrinth air seals, annular structures in large diameter pipings and valves are subjected to axial leakage flows, an unstable vibration and a fatigue failure are apt to be occurred. In this paper, the unstable vibration of thin cylindrical shells is analytically investigated considering the fluid structure interaction between shells and fluids flowing through a narrow passage. The coupled equation of motion between shells and fluids is derived using the Flugge’s shell theory and the Navier-Stokes equation. Especially, focusing on the higher circumferential vibrations, the unstable phenomenon of thin cylindrical shells is clarified by using root locus based on the complex eigenvalue analysis by using the mode functions obtained by the exact solution based on the Flugge’s shell theory. The influence of shell-dimensions and so forth on the threshold of the instability of the coupled vibration of shells and flowing fluids are investigated and discussed.Copyright

Free Vibration and Seismic Response Analysis of a Liquid Storage Thin Cylindrical Shell With Unaxisymmetric Attached Mass and Stiffness

In this paper, we investigate the free vibration and seismic response of a liquid storage thin cylindrical shell fixed on a rigid foundation including piping and attached structures which are considered as unaxisymmetric attached mass and stiffness. The coupled free vibration analysis method and seismic response analysis method are proposed when the thin cylindrical shell is coupled with a liquid contained in the shell, the attached mass due to the unaxisymmetric attached structures, and the attached stiffness due to the flexibility of piping. The equations of motion of the fixed-free cylindrical shell including a liquid, and with attached mass and stiffness are derived by the Flugge’s shell theory analytically for a shell and the velocity potential theory for a liquid. Taking the dimensions of a shell, liquid and attached mass, stiffness as parameters, the free vibration and seismic response are investigated. Moreover, the comparison between the analytical results and the experimental ones is performed.Copyright

Multibody Dynamics of the 2 Sections Flexible Ladder Model Extending and Retracting Each Other

A ladder of the ladder truck with lift mechanism often generates a lot of vibrations at the time of the lift operation. The lift operation includes the extending and retracting motions, the ascending and descending motions, and the turning motion. In this paper, the simulation analysis of the dynamic behavior for the 2 sections flexible ladder which can extend and retract each other is described. We make the dynamic analytical model of the 2 sections flexible ladder using multibody dynamics though we have already reported the simulation analysis of the 2 sections ladder composed of a rigid and a flexible ones. A coupled equation of motion of the 2 sections flexible ladder is derived using the differential algebraic equation (DAE). Performing the numerical simulation studies taking the dimensions of the 2 sections flexible ladder model parameters, the physical meaning of the dynamic behavior at the time of extending and retracting motions between 2 ladder sections is discussed comparing with the former reported results for the 2 sections ladder composed of a rigid and a flexible ones. Moreover, the validity of our proposed simulation method is investigated comparing with the experimental results partially.Copyright

Axial Leakage Flow-Induced Vibration of Thin Cylindrical Shell With Respect to Circumferential Vibration

In this paper, the dynamic stability of a thin cylindrical shell subjected to axial leakage flow is discussed. In this paper, the third part of a study of the axial leakage flow-induced vibration of a thin cylindrical shell, we focus on circumferential vibration, that is, the ovaling vibration of a shell. The coupled equations of motion between shell and liquid are obtained by using Donnell’s shell theory and the Navier-Stokes equation. The added mass, added damping and added stiffness in the coupled equations of motion are described by utilizing the unsteady fluid pressure acting on the shell. The relations between axial velocity and the unstable vibration phenomena are clarified concerning the circumferential vibration of a shell. Numerical parametric studies are done for various dimensions of a shell and an axial leakage flow.Copyright

Vibration Test of 1/10 Scale Model of Cylindrical Water Storage Tank

Large-scale cylindrical water storage tanks have a large ratio of radius to thickness, which means their thickness is relatively thin compared with the radius. Regarding seismic responses, the deformation of a tank frame is significantly influenced by the sloshing of the water inside the tank and by the bulging vibration of the tank structure, therefore it is important to consider such deformation theoretically and experimentally. This paper describes the results of a vibration test with a 1/10 reduced scale model of a large-scale industrial cylindrical water storage tank, conducted particularly to clarify the dynamic behavior of the tank during a seismic excitation. First a sinusoidal wave excitation experiment was performed for the scale model tank, which measured axial distributions of dynamic fluid pressures, strains and accelerations. Ovaling vibration of the scale model tank also was examined by measuring the circumferential distribution of strains. Furthermore, the dependence of dynamic fluid pressure on the acceleration magnitude of the input excitation was investigated. Secondly, a seismic excitation experiment was conducted using typical seismic waves. Finally, the measuring results were compared with the values calculated using common seismic-proof design methods based on the Housner method or velocity potential theory and the finite element method. Considering the differences between the experiment values and numerical design ones, it became obvious that there was inconsistent between the positive and the negative pressures of the dynamic fluid pressure and that the dynamic fluid pressure was dependent on the acceleration magnitude. And it was suggested that such phenomena were caused by ovaling vibration. They, however, had little effect on the seismic-proof design of the tank in the range of acceleration used in this study.© 2004 ASME

Applicability of Optimal Seismic Design Methodology for Piping Systems Subjected to Seismic Waves With Various Frequency Characteristics

In this study, the optimal seismic design methodology which can consider the structural integrity of both piping systems and elasto-plastic support devices are developed. This methodology employs genetic algorithm and can search the optimal conditions such as supporting locations, capacity and stiffness of supporting devices. A lead extrusion damper is treated here as a typical elasto-plastic damper. Numerical simulations are performed using a simple piping system model for the various kinds of seismic waves with different frequency characteristics. As a result, it is shown that the optimal seismic design methodology proposed here is applicable to the seismic design of piping systems supported by elasto-plastic dampers subjected to the seismic waves with various kinds of frequency characteristics.Copyright