The natural frequency and the mode of vibration of a plate with multiple fixed points on edges are computed by the finite element method (FEM) and are observed experimentally. The frequency of each mode for the plate is found by the extrapolation method, and the frequency obtained by this method is highly accurate. The natural frequency of the plate depends on the number of fixed points. When the number of fixed points is small, the influence that the number of fixed points exerts on the frequency is very large. As the number of fixed points becomes large, the frequency of a plate approaches the value of a square plate with four fixed edges. The frequency of a plate with several fixed points which do not exist on the corners is always higher than that of a plate with the same number of fixed points containing the four corners, but as the number of fixed points becomes large, the difference in frequency becomes small. In the square plate in which the fixed points exist slightly inside the edges, the frequency of the square plate increases a little; however, the mode shape of vibration does not change appreciably.

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For machine structures which are exposed to hard working conditions, for example, those of construction machinery, and offroad-type vehicles, maintenance schemes that allow longer operating life are becoming more imporant in the attempt to improve productivity and reduce maintenance cost. We propose several algorithms for a nearly real-time monitoring system on operating machines, which predicts strain responses and damage at evaluation points based on strain modal analysis without measurement of strain meters. This paper introduces applications of these methods for offroad-type dump trucks. The validity of the method, which uses four measured suspension forces for driving on uneven road and transfer functions about strain on the main frame, is demonstrated through comparison with measured strain responses.

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This paper deals numerically with the inner ring motion in the radial plane of an ideal ball bearing which represents the simplest rotor system. The inner ring has a mass, rotates with a constant speed, and is subjected to a constant radial load. Effects of both damping and radial clearance are taken into account. In carrying out the computation. RKG scheme has been applied to solve the differential equation of motion and also the "cycle-shooting scheme" to periodic solutions. The results show that the system basically reveals harmonic vibrations synchronized with the ball passage motion in the almost range of the rotor speed. In addition, many kinds of subharmonic oscillation and their successive evolution, i. e., the period doubling bifurcation and chaotic vibrations with many so-called windows, have been observed. This chaotic phenomenon has been identified by means of Lyapunov exponents, invariant manifold and bifurcation diagram inspections.

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Burst random excitation is one of the most popular excitation techniques for frequency response function measurement. But in the case of very lightly damped structures, the leakage error can be a serious problem. In this paper, we propose a new excitation technique in which the system response after the random signal is turned off is actively controlled by velocity feedback such that the response quickly decays to zero within the time window. Comparing the results using this new method with the usual burst random excitation, the coherence functions are shown to be greatly improved by this new method, not only at resonant frequencies but also at antiresonant frequencies.

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Monitoring of cutting conditions is one of the most important techniques in machining process. Previously we proposed the effective technique based on cutting model for lathe cutting with flow type chip. In this paper, we apply this technique for lathe cutting with shear type or crack type chip. Finally we show the good ability of this technique for cutting with shear type or crack type chip.

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An active vibration control scheme for a one-link flexible arm is presented, where the actuator is a pair of hydraulic cylinders mounted at the root, and their forces are conducted to the tip by two wires to directly manipulate its displacement. The distance between a wire and the arm is kept constant by spacers in order to prevent buckling of the arm and to conduct the arm deflection faithfully to the cylinders. Experimental results show that the ratio of the settling time to the free vibration period is about 60%, which is less than the ratio of about 150% for the conventional scheme. A model of the arm system and the stability of the controller are given.

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This paper investigates a vibration control of a cantilever rectangular orthotropic plate by two rotating actuators. The equation of motion of this system is derived by Hamilton's principle, and the state equation, which is a first-order ordinary differential equation, is obtained by the constrained modal method. The deflection of the plate is expanded in terms of time functions and eigenfunctions for the orthotropic plate, which are derived by the Ritz method. The robust servo system is applied to control the vibration of the plate. The control simulations are performed by integrating the state equation by the Runge-Kutta method.

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The simple adaptive control (SAC) method has attracted attention for interest of the simple structure of its adaptive controller. We establish that the introduction of output derivative action to the original SAC system definitely improves the responce chracteristics of the control system. The effect of such an introduction is confirmed through experimental results, by applying the method to a servo control system using a direct drive (DD) motor.

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Simple adaptive control (SAC), one of the newly approved robust adaptive control methods, has recently been attracting increased interest for it's simplified adaptive controller structure and attractive performance characteristics, such as robustness to a class of bounded disturbances and unmodelled dynamics. To date, the design procedures of SAC have mostly been discussed with respect to the case of continuous-time systems. As to discrete-time SAC systems, less attention has been paid to the physical realizability of the control system and the nonminimum phase zeros arising from sampling rate. This paper deals with the basic stability problem and the robustness of the SAC systems described by a delta operator model. The advantages of the new digital algorithm based on a delta operator representation include the physical realizability of the adaptive controller and applicability to systems with rapid sampling. The experimental results demonstrate the stability and robustness of implementation of the proposed algorithm with the electromechanical servo system using the direct drive (DD) motor.

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This paper deals with a flexible rotor-magnetic bearing system which has three concentrated masses. A mathematical model of the flexible rotor in the case of the free-free condition is derived using the finite-element method. Then we derive the reduced order model for control system desigh by eliminating higher order modes of the mechanical and electromagnetic interaction system (full-order model) beyond the first flexible mode. With the use of the solution of H^∞ output feedback control, the H^∞ central controller is designed. Control performance based on the mixed sensitivity problem is compared with that based on the robut stability. Simulations are performed on the calculating model. The two unstable rigid modes can easily be controlled as stable and the first flexible mode is better controlled than before control by the H^∞ controller. The spillover phenomena of the higher order modes are not generated. Also, it is clear that the H^∞ control desigh is robust to the variation in the parameters of the model.

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Thermoluminescence dating has attracted the attention of geology and archaeology researchers as a new method. This method requires a heating device to raise the temperature of the sample continuously at an exact rate. This paper describes the design method of a control system which can accomplish this goal. This control system tends to be unstable because of the existence of parameter perturbation and lag time. In this paper the perturbation and the lag time are treated as perturbations of a generalized system regarded as a one-order system. Tracking characteristics in the low-frequency domain and robust stability in the high-frequency domain of the control system are achieved using the mixed sensitivity problem which is a kind of H^∞ control theory. Experiments verify the effectiveness of this method.

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The previous formulation for the eigenvalue analysis of the Helmholtz differential equation with the help of the Multiple Reciprocity Boundary Element Method is successfuly transformed into the standard eigenvalue problem, which is based on the polynomial coefficients in terms of unknown eigenvalue. The new formulation makes it possible to use the standard numerical procedure (existing subroutine) for obtaining eigenvalues, without any initial approximation and iteration conducted by users. The required preprocess for the analysis is only discretization of the boundary by boundary elements.

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This paper presents a method for analyzing the dynamic characteristics of driving systems consisting of many belts and pulleys. First, the algorithm which represents the linear equations of motion of arbitrary belt systems is derived. Second, the computer program that calculates transient responses of the belt system is presented. The fundamental idea of the algorithm is as follows. Complicated belt systems consisting of many belts and pulleys are regarded as combinations of simple belt systems consisting of a single belt and some pulleys. By expressing the relationship between two simple belt systems as a transfer matrix, the equations of motion of the belt systems can be derived by assembling the equations of motion of the simple belt systems. By means of this method, the responses of arbitrary complicated belt systems can be instantaneously and systematically obtained.

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The problem of measuring small pressure differences with high accuracy has many engineering applications. These include, for instance, measurement of low flow velocities using Pitot tubes, and measurement of flow rate using nozzles. This paper describes an automatic liquid manometer that operates on the basis of a position-detecting system under fuzzy control. The manomater operates as follows. A laser beam is directed to the bottom of a float located inside a glass tube, and the spotlight is detected by a position-sensitive detector (PSD). The application of external pressure to the manometer causes the position of the spotlight on the float to change. The manomater moves the spotlight back into position by lifting a reservoir connected to the glass tube. The vertical displacement of the reservoir required to return the spotlight to its original position is equal to the pressure head applied. The system has been tested experimentally with good results.

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In order to improve the accuracy of the measurement of cylinder diameter by means of phase delay of sound waves, the effects of echoes from a pair of rigid walls have been studied. The cylinder of interest was located midway between the walls which were parallel to the impinged sound waves. Experiments having been made using a loudspeaker, microphones and a FFT-analyzer, and the problem of the disturbance of plane waves by a cylinder having been analyzed theoretically, relation-ships between the phase delay and the diameter were obtained, respectively. The results showed that the rate of increase of the phase delay with diameter, which was considerd approximately constant before utilizing echoes, became much larger within a certain diameter range which was dependent on the frequency of sound.

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This paper proposes approaches to reduce the processing load on a vision system and to detect accidents using a force/torque sensor in real time. For the former approach, the concepts of the parts isolation factor and robot manipulability at the grasping position are introduced to formulate a parts-picking strategy for executing the task while maintaining the initial environment. The picking operation is executed in the order of the highest isolation factor and manipulability. An accident recovery method in which force and torque are monitored during operation is also presented. Successful parts-picking by robot systems implementing these approaches was confirmed by simulation and by actual robot operations.

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This paper proposes an algorithm for the classification of overlapped objects using fuzzy reasoning and maximum likelihood in visual information processing, which can decrease the amount of calculation, simplify the classification procedure and improve reliability. Fuzzy reasoning is used for estimating the contour category with incomplete contour feature information. Maximum likelihood is used for estimating the surface shape class of the surrounding contour based on the local range data acquired with the laser range finder. Each area surrounded by contours is classified under an object class by integrating the results of fuzzy reasoning and the estimation based on the maximum likelihood. Finally, verification at object level is performed by integrating the relationships between the contours of the same object and geometric relationships between the surfaces of the object. Experiments proved the effectiveness of the proposed algorithm.

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Optical analyses of stereo vision systems with a parallel or cross arrangement camera optical system have been made to clarify the existence of stereo image distortion by means of optical diagrams. This distortion can be removed by applying decenterized optical systems to a stereo camera, in which the location of the optical axis cross point is decided in accordance with the display optical system. This location must be determined as a function of the camera span, the eye span, and the observing distance, and this cross point cannot be moved to any other place. Furthermore, by analysing distortions of stereo images caused by moving the observing location, an effective method to control camera locations is also presented as that the distortions are canceled. Experiments indicated that this proposed method succeeded to improve the naturalness of stereo vision.

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The driving force of an automobile depends ultimately upon the relationship between the tire and road surface. Therefore, traction control which prevents tire slip is becoming an impotrant issue from the point of view of driving performance and the stability of automobiles. Reported here is the traction control method using fuzzy control theory. Fuzzy control is "rule governed", and is said to be suitable for strong nonlinear objects such as this. Another special feature of this traction control is the use of the acceleration signal of the automobile, and this optimizes the engine performance even under the conditions of different slip characteristics. The investigation was carried out by experiment as well as by simulation. In the experiment, an electrical motor scooter on a chassis dynamometer was used instead of an actual automobile and road. Relatively good results were obtained.

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This paper presents a new strategy for path planning of a mobile robot by using a Genetic Algorithm. When a mobile robot moves from a point to another point, it is necessary to plan a optimal path avoiding obstructions in its way and minimizing a cost. On the other hand, Genetic Algorithms are search algorithms based on the mechanics of natural selection and natural genetics.They combine survival of the fittest among string structures with a structured yet randomized information exchange to form a search algorithm with some of the innovative flair of human search. An occasional new part is tried for good measure avoiding local minima. While randomized, Genetic Algorithms are no simple random walk. They efficiently exploit historical information to speculate on new search points with expected improved performance. For optimization, we apply the Genetic Algorithm to path planning of a mobile robot. We evaluate the proposed approach comparing with other optimization algorithms, such as Random Search and Simulated Annealing.

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The control input which moves a linear discrete-time system to goal states in finite time can be calculated in advance if the dynamics of the system are well understood. However, when the identified model is different from the actual system, residual state errors at the end of the motion are unavoidable. In this paper, a control scheme which improves the accuracy of the terminal-point control of the discrete-time system by learning is proposed, and the convergence of the learning process is discussed. Moveover, in the case that there are constraints on control inputs, a learning terminal-point control in which a weighted pseudoinverse matrix is utilized is presented. These control methods are applied to a flexible robot arm, and it is shown through experiments that they are able to realize high-speed motions and suppress residual vibrations.

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This paper describes the autotuning method of fuzzy set values for a small tunnelling robot. We have already proposed a fuzzy directional control method using fuzzy rule set which inputs both deviation and angular deviation, output head angle as control input. In this paper, we use a neural network to obtain the optimum fuzzy set values. The input of the neural network is the initial deviation and initial angular deviation. The output of the neural network is fuzzy set values. This neural network learns from deviation error. Total deviation error of simulation using the optimum fuzzy set values obtained by the proposed method was smaller than that of simulation using the optimum values obtained by trial and error. A neural network which can apply to any initial deviation was formed by using plural deviations. Moreover, this method can tune the optimum fuzzy set values to any design line. These results showed the validity of this method.

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This paper is concerned with computer simulation for optimum design of a sound-insulating wall using the boundary element method. In the present simulation, the influence of the ground is taken into consideration. We can deal with the ground, which is extended infinitely, by the superposition of the fundamental solution at the imaginary source point. Thus the boundary condition of the ground, which is considered to be complete absorption or complete reflection, is exactly satisfied and no boundary element is needed on the ground. In the present model, it is assumed that a sound is radiated from a point source to the two-dimensional semi-infinite acoustic field, and it should be reduced at some evaluation points by means of an insulating wall with a control board. The acoustic field is computed by the boundary element method for pure sound with a particular frequency and the optimal set of parameters corresponding to the location, length and inclination angle of the control board is determined by the standard optimization technique.

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The characteristics of a bolted joint, in which a couple of pipe flanges made of aluminum were fastened at room temperature by nuts and bolts made of steel, were examined when the joint was subjected to heat conduction. In the experiments, temperature distributions of the joint were measured with thermocouples, and an increment in bolt axial force, the maximum stress in the bolt and stress produced at the hub of the flange due to the difference in the coefficients of linear expansion were measured by strain gauges for high temperature use when the inner circumference of the pipe flange was heated and the outer circumference was kept at room temperature. With the use of the finite difference method, the temperature distributions in the joint subjected to heat conduction were analyzed. A method by which to obtain an increment in bolt axial force and the maximum stress produced in the bolt was proposed. The analytical results were fairly consistent with the experimental results.

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To clarify the seizure resistance and the frictional characteristics of a stainless steel ball, which was thermally diffused after being Sn-plated, the four-ball test was run under dip-feed lubrication and thin film lubrication. From the seizure test, the following results were obtained. Under dip-feed lubrication, the coefficient of friction was decreased with increasing thickness of the Sn-diffused layer, and the seizure resistance of the ball was increased with increasing thickness of the diffused layer. The seizure resistance of the ball in which the diffused layer was 8 μm thick was about 2.6 times larger than that without a diffused layer. Furthermore, under thin film lubrication, the running time at the incipient stage of seizuring with balls in which the thickness of the Sn-diffused layer exceeded 4 μm was about 5 min, independent of the thickness of its layer, and this was considerably longer than that without a diffused layer.

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The internal stress in elastohydrodynamic lubrication (EHL) of rolling/sliding line contacts is calculated to discuss the possibility of pitting from the surface. Pressure distributions are calculated for three cases : 1 ) isothermal EHL (IEHL), 2 ) thermal EHL (TEHL) and 3 ) non-Newtonian EHL of a circular model by Hamrock (NEHL). For each case, the maximum shear stress τ_max is calculated and discussed. Conclusions are as follows: 1 ) The maximum value of τ_max becomes larger and appears near the surface when the pressure spike Ps or the tangential traction Q becomes larger. 2 ) In case of Newtonian oil, Q becomes larger when the slip ratio increases. Q and Ps are reduced in the order of NEHL, TEHL, and IEHL. 3 ) When τ_max appears near the surface, τ_xy also takes the maximum value at the same point. 4 ) Whichever theory we use, there are some cases where τ_max appears near the surface due to the extremely high pressure spike even if Q is zero.

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Firstly, this paper describes the lubricating ability of improved lapped surfaces which have oil grooves at regular intervals. To clarify the mechanism of lubricating ability of the lapped surfaces, floating amounts of test pieces were measured using noncontact displacement gauges and the behavior of lubrication was observed with a microscope. Secondly, three advanced surfaces with intervals of 0.6, 3 and 10 mm grooves were produced. Friction forces and the floating amounts of tables were measured using a prototype machine. Four kinds of base oil with viscosity of 0.1413.81 Pa's were used as stearate lubricants. The results are summarized as follows : oil films were formed on the master guideways by movement of lapped surfaces, and the formation characteristics of oil films depend on the viscosity of the lubricants. Viscosity of lubricants and addition of stearate affect floating amounts of the table and friction forces.

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In magetic fluid grinding for innersurface of pipe of which cross-sectional shape was hexagonal circle, a ratio of ground area to whole innersurface area of pipe and distribution of ground depth were studied experimentally and theoretically. Whole innersurface of pipe was ground under revolution speed of 125 rpm. But, over its speed, ground area decreased with the increase of revolution speed. The distribution of ground depth in innersurface of pipe wad changed by the change of revolution speed. Such both properties were explained by the change of grinding load which was the sum of magnetic buoyant force Fm of a float, a force Fs due to squeeze effect and a force Fd due to viscous damping effect. Therefore, if optimum grinding load was designed, the whole innersurface of pipe of which cross-sectional shape was hexagonal circle is ground sufficiently.

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Squeeze film phenomena are investigated numerically and experimentally when the intervening fluid is compressible and the squeezing surface is a compliant one. From the previous studies, it is known that in a sinusoidally oscillating squeeze film, positive mean load-carrying capacity is generated when the fluid is compressible. In an incompressible fluid, load-carrying capacity is generated when the squeezing surface is a compliant one or squeeze action is very rapid. In this study the effects of both compressibility of fluid and surface elasticity are investigated. In the numerical analysis, the Reynolds equation for compressible fluid and the equation of elasticity are solved by the finite difference method and Newton-Raphson method. In the experimental study, squeeze action is generated by an electric vibrator and load-carrying capacity is examined for rigid and compliant surfaces.

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The friction coefficient of gear tooth flanks is an important factor in clarifying the mechanism of surface failures such as pitting and scoring and in improving the performance of power transmission gears. This is a basic study to establish a method for evaluating the friction coefficient of a spur gear pair under uniformly distributed load along the tooth trace using the fillet strains measured by strain gauges. Experiments with a rack model were carried out with static loads. The frictional and normal forces acting on the working flank were derived by solving the system of equations concerning the fillet strains on the working and nonworking flank sides. The accuracy of the ratio of the friction force to the normal force was examined. The results demonstrate that in order to obtain a meaningful friction coefficient of spur gears it is very important to consider the independence of the relation between the fillet strain and the forces on the working flank.

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A design of a pair of straight conical involute gears used for intersecting shafts is developed. This design makes it possible for the tooth bearing to occur at the central part of the face width by selecting the values of the normal pressure angle, working depth, and generating cone angles when the shaft angle and number of teeth in a pair of gears are given. Test gears are designed and made on the basis of this design. Tooth bearing tests are performed, and it is proven that this design has the potential for applicability.

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In the design of a planetary gear system, the choice of the number of teeth for each gear in the system involves various conditions that need to be taken into consideration. Determination of the number of teeth that satisfies all the above conditions is difficult, and a great deal of trial and error is required to successfully obtain even one design plan. Formulae for these conditions have not been established for a 3K-type planetary gear system with a complex mechanism. In this study, a formula for equidistant arrangement of planetary gears and a formula for concentric arrangement of all component gears for a 3K-type planetary gear system were derived using a new method, and on the basis of these formulae, a system of automatic selection of the number of teeth was developed for 3K and 2K-H planetary gear systems. This automatic system was tested through extensive computation, and the results were checked by manual calculation. As a result, the validity of the selection data obtained by this system was verified. The system was thus confirmed to be practically applicable.

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This paper presents a study on the dynamic behavior of three types of spiral bevel gears, which have different tooth profiles and tooth bearings. The circumferential, radial and axial vibration accelerations of gear bodies, the gear noise and root stresses were measured under different running conditions by using a gear testing machine of a power absorbing type. The contact ratios of these spiral bevel gears were obtained from the measured results of root stresses. The vibration accelerations and the noise of the spiral bevel gears were found to decrease with increasing area of tooth bearing and to be almost equal irrespective of the drive side (convex side or concave side) of the gear tooth. They tended to increase with increasing gear speed but to be almost equal irrespective of the applied torque used in the range of this experiment. The maximum root stresses of these gears were found to be almost equal irrespective of the gear speed used in the range of this experiment.

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This paper presents a study on the contact stresses of WN gears. A method for calculating contact stresses of WN gear teeth in mesh was developed. The validity of the method was confirmed by comparing the calculated contact stresses of WN gear teeth in mesh with measured stresses. The contact stresses of WN gears with various dimensions were calculated, and the effects of center distance, helix angle, face width and number of teeth on the maximum contact stresses of WN gear teeth in mesh were clarified to a considerable extent. Furthermore, the contact stresses of WN gear teeth were compared with those of involute helical gear teeth. The maximum contact stress of WN gear teeth was found to increase with increasing center distance and helix angle and with decreasing number of teeth but to be much smaller than that of involute gear teeth in the case of the normal center distance.

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In this study, a new mechanical indicator of slip ratio on a wheel for an Antilock Brake System (ABS) is proposed. This indicator consists of a roller whose axis of rotation can incline and two steel balls which rotate in any direction. The roller and two balls are installed in a plate, and positioned between two disks which rotate in opposite directions. They comprise the traction drive. One disk provides the rotating speed of a wheel and the other gives the vehicle speed by the wheel which is installed especially for this purpose. This indicator has the following excellent qualities : it is possible to indicate the requested slip ratio precisely, by use of the mechanism, and the indicator moves smoothly and silently.

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It has been pointed out that it is difficult to manufacture hollow molds, free curved surfaces and large molds. Therefore, much time and high cost are involved in the production of injection molds for such plastics. In this paper, a new material, for metal resin concrete, has been developed as a material for the injection mold. This material consists of heat-proof epoxy resin and a steel aggregate. It is concluded from the results that metal resin concrete has sufficient stiffness, high compressive strength, excellent copying characteristics and heat shock resistance to be used as material for the injection mold.

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The stability criterion derived by mathematical models of the machine tool vibratory system and the dynamic cutting process predicts cutting conditions under which the machine tool working against chatter develops dynamic instability. In this study, we assume that a turning workpiece has directional vibratory properties, and derive both its unconditional and conditional stability criteria, including the effect of velocity components of dynamic cutting forces. In view of the importance of designing machine tools with high dynamic stability and eliminating chatter in the shop, it is necessary to investigate the variation of the stability limit caused by the velocity component in relation to the directional vibratory properties of the workpiece. As a result of the investigation, it is revealed that the stability limit variation caused by the velocity components depends to a considerable degree on the principal coordinate direction of the workpiece vibratory system.

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It is important for fully automated machining systems or dynamic performance tests of a machine tool, to detect chatter and decide whether the cutting condition is stable or not. In this study, a method for judging the dynamic instability of cutting process is proposed. It is based on the ratio of inner to outer modulation amplitude estimated by the Fourier transform of regenerative chatter vibrations in every revolution of the workpiece. The validity of the present method is verified from numerical simulation data of regenerative chatter. Furthermore, we obtain the experimental limits of cutting process by this method, and compare them with the predicted limits which are calculated by the authors' criterion proposed in the previous paper. The predicted limits are almost in accord with the experimental ones at the cutting speed of 40-160 m/min and feed rate of 0.07-0.19 mm/rev.

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In this paper, a new precise positioning mechanism using a surface motor is proposed, and the construction and analytical and experimental results for the characteristics of a newly developed stage mechanism are also described. The surface motor consists of 3 driving elements using a brushless-type linear DC motor, and a stage, supported on a base plate by hydrostatic gas bearings, is directly driven in 3 degrees of freedom (X Y θ_z). The motion of the stage is measured by a laser interferometer system with 5 nm resolution, and each axis is controlled by a PID controller. Thrust force characteristics are analyzed by means of the permeance concept, and the method is validated by some experimental results. Also, calculated closed-loop positioning characteristics of the system have good coincidence with experimental ones. Consequently, a translational positioning resolution of 0.01μm and rotational accuracy less than ±0.07 μrad are achieved in the travel area of 10 mm square.

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This paper presents two kinds of dimension-matching processing in a highly-functional 2-D CAD system for mechanical parts. One globally fixes the location and length of line segments of outlines so that they can be kept in conformity with given dimensions and tacit constraints. First, we discuss the degree of freedom of internal dimensions defined on the line segments, which coincides with the total number of loop constraints, constraints by given dimensions and tacit constraints. On the basis of discussion, we present a method for finding tacit angular constraints and lowering the degree of freedom. Then, we propose a method for verifying that necessary and sufficient constraints are given for the drawing and a method for deriving simultaneous linear equations corresponding to all of the above constraints. The other locally fixes the location and length of other drawing elements. This is done by tracing the tree of relationships in the relationship representation model which has been generated by the method mentioned in the previous report. Some examples are also shown.

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This paper deals with a theoretical analysis of dynamic instability of vibrations induced in a flexible weir subjected to fluid discharge over the weir top. We formulate the equation of motion for the coupling vibration of a flexible weir and sloshing liquid contained in upper and lower tanks by taking into accout the time lag generated by the fluid travel from the top of the weir to the surface of the liquid contained in the lower tank. The energy of the vibration of the weir produced by sloshing and dissipation energy are evaluated to find the instability conditions in terms of discharge height. The instability conditions are clarified with respect to important parameters of this fluid structure coupling system and are compared with experimental results.

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This Paper describes a general control system design method for vibration of a multi-degree-of -freedom system. A H^∞ controller designed on the reduced order model makes the closed loop system not only cause no spillover phenomena, but also control the Vibration on the actual model. The solution to H^∞ output feedback control problems is used to design the H^∞ controller. With the result of calculating the example of the four-degree-of-freedom model, the efficiency of the control system is verified. Also, the frequency-shaped LQG control desigh is made in comparison with the H^∞ optimal control. It has been clear that both control methods have robustness to the spillover caused by the reduced-order model in the case of the same weighting functions. The most important result is that the H^∞ optimal control has strongly robust stability to parameter variations, while the frequency-shaped LQG control does not.

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