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Although bladed disks are nominally designed to be cyclically symmetric (tuned system), the vibration characteristics of all the blades on a disk are slightly different due to the manufacturing tolerance, deviations in the material properties, and wear during operation. These small variations break the cyclic symmetry. Bladed disks with small variations are referred to as a mistuned system. In the forced response of a mistuned bladed disk, the responses of all the blades become different, and the response of a certain blade may become extremely large due to splitting of the duplicated eigenvalues and distortion of the vibration modes. On the other hand, mistuning suppresses blade flutter, because the complete traveling wave mode is not formed in a disk. Although such mistuning phenomena of bladed disks have been studied since 1980s, almost all studies focused on the amplification factor of the displacement response, and few studies researched the amplification factor of the vibratory stress response. In the previous paper, authors studied the amplification factor expressed by the vibratory stress for bladed disks with the continuous ring-blade structure, using the reduced order model SNM (Subset of Nominal Modes), and pointed out that the amplification factor of the displacement and the vibratory stress is different. This work is a follow-up study on the previous paper. The amplification factor of the vibratory stress for bladed disks with the free-standing blade structure is studied, using the reduced order model SNM. Comparing the mistuning phenomena of bladed disks of the continuous ring-blade structure and the free-standing blade structure, the reason why the amplification factor of the displacement and the vibratory stress is different is clarified.

Purpose of this paper is to reduce the response of rocking vibration mode of vertically isolated equipment. The rocking vibration is the motion that the top of equipment vibrates as the fulcrum in a bottom end. According to the low vertical stiffness of vertically isolated equipment, the rocking vibration is largely excited by horizontal earthquake motion. In this paper, a dynamic absorber is developed in order to apply to the rocking vibration of the vertically isolated equipment. The proposed system is a rolling pendulum type dynamic absorber using magnetic damper, which is composed of circular rails, a rolling body including magnets and a conductor plate. The design method for the dynamic absorber and the evaluation method for vibration reduction effect are showed in this paper. The dynamic characteristics are also examined by vibration test. It is confirmed from the vibration tests using a rocking model apparatus that the proposed dynamic absorber is effective for rocking vibration reduction.

This paper analyzed the suppression method of the nonlinear vibration called subharmonic vibration of order 1/2 in the car powertrain by using a dynamic absorber. In the car powertrain, the torsional forced vibration caused by engine explosions leads to inhibition of the ride quality. Thus, in the torque converter of an automatic transmission car, a piecewise-linear spring called damper is used to reduce the transmission of the forced vibration. However, the subharmonic vibration occurred in the actual vehicle, when the spring restoring characteristics is around the switching point. The fundamental vibration frequency of the subharmonic vibration is half to the engine forced vibration frequency. Although the design of the dynamic absorber to suppress the forced vibration has been established for the linear systems, the optimum design to suppress the subharmonic vibration of order 1/2 has not yet been investigated. The powertrain is modeled by multi degree-of-freedom system as an actual vehicle, including engine, torque converter, transmission gears and wheels. Equation of motion is developed with also considering spring restoring force of piecewise-linear spring. The numerical result shows subharmonic vibration occurs when the engine excitation frequency is almost twice of the second mode of natural frequency, and the result shows a good agreement with the experimental data. Then, the dynamic absorber is introduced to suppress the occurrence of subharmonic vibration theoretically. In this paper, the optimum design of the dynamic absorber to suppress the subharmonic vibration is discussed. The numerical result shows the optimally designed dynamic absorber in the natural frequency and the damping ratio is capable of suppressing the occurrence of the subharmonic vibration.

The vibration characteristics of a bladed disk with the continuous ring type structure have been studied extensively, and the vibration response analyses considering the friction damping between adjacent shrouds have been performed in the blade design. The effect of the friction damping on the self-excited vibration also has been studied by several researchers. However, because the most of these studies have been performed using the simple macroslip model, the damping characteristics of bladed disks with the friction damping are not yet clarified sufficiently. Moreover, few studies have focused on the transient response of a blade with the friction damping. In this paper, the damping characteristics of bladed disks with the continuous ring type structure is studied using the conventional macroslip model and the sophisticated microslip model for the transient response when passing through the resonance, and the results calculated by both models are compared. From the analysis results, it is concluded that, in the transient response when passing through the resonance, the damping characteristics predicted by both models are qualitatively the same if the excitation force is extremely large or small. However, when the excitation force is medium, the damping characteristics predicted by both models are quantitatively different. Therefore, it is recommended that the microslip model with appropriate parameters is used to improve the accuracy of the prediction of the damping characteristics.

The vibration characteristics of a bladed disk with the continuous ring type structure have been studied extensively, and the vibration response analyses considering the friction damping between adjacent shrouds have been performed in the recent blade design. The effect of the friction damping on the self-excited vibration also has been studied by several researchers. However, because the most of these studies have been performed using the simple macroslip model, the damping characteristics of bladed disks with the friction damping are not yet clarified sufficiently. In this paper, the damping characteristics of the bladed disks with the continuous ring type structure is studied using the conventional macroslip model and the sophisticated microslip model for the forced and self-excited vibration and the results calculated by both models are compared. From the analysis results, it is concluded that, in the forced vibration, the damping characteristics predicted by both models are almost the same if the excitation force is extremely large or small. However, when the excitation force is medium, the damping characteristics predicted by both models are different. In the self-excited vibration, the stability predicted by both models are qualitatively the same. However, the amplitude of the limit cycle oscillation and the critical aerodynamic damping predicted by both models are quantitatively different.

When an elevator rope for a high-rise building is forcibly excited by the displacement of the building induced by wind force and/or by long-period ground motion, rope displacement becomes large even if the ground acceleration and the building acceleration is small. Vibration suppressor is used to reduce the rope vibration. The elevator rope is generally modeled using a string with viscous damping. However, the flexural rigidity and the damping property of the rope are not clear yet. In this paper, we proposed a beam model with viscous damping and structural damping. And we also proposed an estimation method of 3 parameters (equivalent flexural rigidity, viscous damping ratio, structural damping ratio). Experiments of forced vibration with/without vibration suppressor and finite difference analyses of rope vibration were performed. It is clear that the identified parameters obtained by the limited conditions of vibration suppressor are applicable to other conditions.

It is desired that the forced self-excited vibrations of structures subjected to the vortex excitation and the long-period earthquake are quenched. Therefore, this paper deals with the vibration control of self-excited system and forced self-excited system using dynamic vibration absorber. Vibration quenching is researched using characteristic roots of the system and the entrained periodic solutions obtained by the shooting method. As a result of numerical calculation using the fact that the optimum vibration control of the self-excited vibration system can be performed by the theory that omits the nonlinear term of the damping term and considers only the linear term, following was made clear: At first increase the mass ratio of the dynamic vibration absorber with the increase of the negative damping coefficient. And adopt the several percent larger natural angular frequency ratio than the optimum vibration control value of forced vibration, and adopt the several tens of percent larger damping ratio than the optimum value of forced vibration, depending on the value of the negative damping coefficient. About the vibration quenching of forced self-excited vibration, following was made clear: (1) When the non-linear damping term, which is the cause of self-excited vibration, is small and the amplitude of force is also small, optimal control is approximately performed using the optimal values of the parameters for vibration quenching of forced vibration without damping. (2) When the amplitude of the forced force is large, the vibration quenching effect is reduced if the above mentioned approximate optimal values are used. The vibration quenching effect can be improved by using the smaller angular frequency ratio. (3) As the non-linear damping term increases, the optimal angular frequency ratio and optimal damping ratio of the dynamic absorber decrease.

This paper deals with the entrainment phenomenon by forced displacement excitation in vortex induced vibration of structures. This phenomenon can occur when a long-period earthquake occurs in a super high-rise structure that may have vortex induced vibration and can occur also when an offshore floating wind turbine is affected by wind and swell simultaneously. Moreover, it is important to examine this phenomenon from the viewpoint of the multi-degree-of-freedom forced self-excited system. By the experiment using wind tunnel and the numerical analysis using shooting method and ordinally numerical integration, following was made clear: (1) Entrainment phenomenon was confirmed in the excitation frequency region including the natural frequency . (2) There is the case that the entrainment region is wider at the higher wind speed than at the wind speed with the largest amplitude by vortex excitation. (3) Regarding the resonance amplitude in entrainment region, there is the case that its amplitude is slightly larger at the higher wind speed than that at the wind speed when the amplitude by the vortex excitation is the largest. (4) The largest vibration amplitude at entrainment is a value almost close to the sum of the largest amplitude at the time of only the vortex excitation and that at the time of only the forced displacement excitation. (5) The experimental results and the numerical analysis results mentioned above were almost qualitatively consistent.

To develop turbomachinery blades with high reliability, it is indispensable to verify the natural frequency, the damping, the resonant stress, etc. under operating condition, and utilize these data in the mechanical design of a new blade. BTT (Blade Tip Timing) and the telemetry system have been widely used to measure the modal parameters of turbomachinery blades. In measurement of the modal parameters of blades in rotation, it is well known that the mistuning phenomena make the identification of modal parameters difficult. Namely, because, in a mistuned bladed disk, responses of many vibration modes are superimposed, it becomes difficult to correctly identify the natural frequency and the damping of each vibration mode. This is one of the critical issues to be overcome for developing blades with high reliability. Recently LSCF（Least-Squares Complex Frequency-Domain）method has been proposed as an effective method for identifying the modal parameters from complicated frequency responses. This method was also applied to derive the modal parameters of a bladed disk from the frequency responses expressed by travelling wave coordinates. In this paper, the validity of the LSCF method is verified by numerical simulations, where the modal parameters of mistuned bladed disks are identified from the frequency responses consisting of many vibration modes. In addition, the accuracy of the conventional half power method used in identifying the blade damping is researched.

This paper deals with the vibration quenching problem of the single-degree-of-freedom system with a limited power supply using a Hula-Hoop and displacement magnification mechanism. This system is forced by the centrifugal force of rotating unbalance. If the unbalance is small, the amplitude of vibration of the main system becomes small and Hula-Hoop does not rotate. Therefore, the vibration of main system is not quenched. To solve this problem, the two types of displacement magnification mechanisms are adopted, namely, the one is the mechanism using beams with fixed ends that move and the other is that using cantilever. The quenching effects and the quenching frequency regions are studied. Following was made clear by the numerical integration of the equation of motion and the experiment: (1) The main system is quenched well by enlarging the displacement at the rotational center of Hula-Hoop using each type of displacement magnification mechanism. (2) The optimal vibration quenching condition of the Hula-Hoop and the displacement magnification mechanism for the first mode is obtained. (3) The frequency regions suitable for vibration quenching are the regions those are higher than the natural frequencies. (4) The vibration mode and the phase relation between unbalance and Hula-Hoop are made clear in each vibration mode. (5) The characteristics of the solutions obtained by the numerical integration method coincide qualitatively with those of the results obtained by the experiment.

This paper describes a structure model construction for structural statistical energy analysis (SEA) using FEM. Identigying SEA parameter regardless of the excitation method is demanded effectively. The proposed method was based on a combination of SEA and vibration response by base excitation like large mass method, forced displacement vibration analysis and random vibration analysis. In order to evaluate the SEA parameters, it is necessary to calculate the subsystem energies and input power. However, the input power at the excitation point when the entire structure is oscilatted is unknown. So, it was assumed that the input power is proportional to the vibration energy of the excited subsystem. These method are effective on an analytical cost performance for the base excitation compared with the conventional force excitation method that is called rain-on-the-roof-exctation. In this study, firstly, the proposal method was validated through two oscillators coupled by a spring. Then it was also validated through L plate consiting of two subsystems. As a result, large mass method is valid for predicting the coupling loss factors between subsystems and in terms of analytical cost. Finally, the method was applied to two flat plates connected in 60, and 30 degrees configuration and a partial car model consisting of six subsystems, as a result, the method is shown to work quantitatively well to the internal loss factors and qualitatively well to the coupling loss factors.

Vibration suppressors are used to change the natural frequency of an elevator rope and prevent resonance. The displacement of the parts of the elevator rope at both the ends is small compared to that of the center part of the rope; therefore, it is not necessary to position the vibration suppressors in the parts on either ends. In this paper, three types of theoretical solution to the free vibration of the rope is obtained, in the case where vibration suppressors are located between x=pL/N and (p+q)L/N, where L is rope length, p, q and N(=2p+q) are integer. Obtained natural frequencies are 2N/(N+1) times, 2N/(N+p) times and 2N/(N+p/2) times of the original natural frequency. Further, finite difference analysis of the rope vibration with vibration suppressors is also performed to obtain the frequency response curves. Resonance frequencies obtained by the finite difference analyses are in good agreement with the natural frequencies for the free vibration. Vibration modes obtained by the finite difference analyses are similar to that for the free vibration.

This paper deals with the quenching problem of electromagnetic vibration of the motor stator in the wide frequency region around the natural frequency using two dynamic absorbers. The iron stator of motor is modeled by circular ring, and two dynamic absorbers are installed on the outside of iron stator to quench the forced vibration caused by the rotating distributed electromagnetic force. The solutions of forced vibration are obtained by the theoretical analysis, and those are compared with the solutions obtained by the finite element method and numerical integration. Following was made clear: (1) By installing two dynamic absorbers which have not only different natural frequencies and different damping ratios but also different masses each other, the iron stator is quenched better than by installing the same dynamic absorbers. (2) It is possible to obtain nearly optimum quenching effect with a pair of dynamic absorbers with equal masses. (3) The mechanism of the above-mentioned vibration quenching method using two different dynamic absorbers is made clear. (4) In the case using the dynamic absorbers those have small values of damping ratios, about 25 degrees is better as angle made by the two dynamic absorbers. (5) The characteristics of resonance curves obtained by the theoretical analysis using ring theory and those obtained by the finite element method and numerical integration agreed well each other.

In this paper, a parameter-free optimization method is proposed for controlling the time-dependent response of a three-dimensional linear elastic structure, where the optimal shape is determined without design parameterization. The design objective is to minimize the vibration displacements or to control the vibration displacement at arbitrary domains and times for an arbitrary time-dependent loading under the volume constraint. The unsteady time-dependent optimum design problems are formulated as distributed-parameter optimization problems and the sensitivity functions with respect to the design velocity field are derived based on the variational method, Lagrange multiplier method and the adjoint method. The derived sensitivity function is applied to the H1 gradient method, a gradient method in the function space to determine the optimal shape variation. With the proposed method, the optimal shape for time-dependent response problems such as a forced-vibration, a free-vibration or a transient response is obtained while minimizing the objective functional and maintaining the smooth surface of a structure. Several numerical design examples including a continuous dynamic force or an impulse force as an input force are shown to confirm the effectiveness of the proposed method, and the results are discussed.

When an elevator rope for a high-rise building is forcibly excited by the displacements of the building induced by wind forces and/or by long-period ground motion, rope displacement becomes large even if the ground acceleration and the buildings acceleration is small. To prevent this problem, vibration suppressors are used to change the natural frequency of the elevator rope and prevent resonance. The elevator rope is generally modeled using a string, and linear string vibration is well researched. However, the vibration of the string equipped with vibration suppressor encounters geometric nonlinearity, and hence, its characteristics have been studied under a few conditions. In this paper, theoretical solution to the free vibration of the rope is obtained, in the case where the position of vibration suppressor is L/N and the pulled position is (N-i)L/N. Where L is rope length, N and i are integer. Further, finite difference analysis of the rope vibration with vibration suppressor is also performed to obtain the frequency response curves. Resonance frequencies obtained by the finite difference analyses are in good agreement with the natural frequencies for the free vibration, and the number of resonance frequencies near original natural frequency is N-1 when position of vibration suppressor is L/N of the rope.

This paper investigates the forced vibrations of double beams, consisting of upper and lower beams, which are discretely connected by N sets of springs and dashpots, when the upper beam is subjected to harmonic excitation. In the theoretical analysis, the orthogonality conditions of the vibrational modes of the system are derived and allow ones to obtain the modal equations of motion. Then, the solutions of the forced vibrations for the two beams can be theoretically obtained by summing up the results for the vibrational modes. In the numerical calculation, two cases, Cases A and B, are examined. In Case A, the two beams are connected by a single set of a spring and a dashpot, while in Case B they are connected by two sets of them. In Case A, when the two beams have identical materials and dimensions, the resonant peaks for the odd-order vibrational modes are independent of the connecting spring and dashpot because they are not stretched. However, the resonant peaks for the evenorder vibrational modes are influenced by the spring and dashpot. In Case A, when the two beams have different dimensions, the lower beam may vibrate at amplitudes lower than those of the upper beam due to the changes of the vibrational mode shapes. In Case B, the amplitudes of the even-order vibrational modes for the lower beam may be increased because increasing the number of connecting springs and dashpots results in the changes of the vibrational mode shapes and modal forces. The validity of the theoretical analysis was confirmed by comparing the theoretical results with the results obtained by the FEM analysis when the damping coefficients of the dashpots are comparatively small.

Even in a state that the person is resting, the person vibrates with a small amplitude. This vibration is called human tremor. For example, when performing precise work such as watch assembly or surgical operation, the tremor will have an influence on the accuracy of work. In order to suppress the tremor, frequency spectrum analysis of the tremor is necessary. However, only dominant frequency of the tremor have been calculated in previous works. In this paper, human tremor model for frequency spectrum analysis is proposed. In the model, the tremor is regarded as forced vibration. Forearm is modeled as a rigid link, which is antagonistically driven by two Hill's muscle models. The stiffness of muscle model is considered as non-linear. This makes it possible to estimate the difference of frequency spectrum of the tremor occurs due to different angle of the elbow. Moreover, the force driving the forearm is generated from muscle by using leaky Integrate-and-Fire cell model. In a previous study, it was confirmed that neural cell had a refractory period, and there was randomness in the period. Therefore, in this study, the refractory period of the cell model is set to the normal distribution. Because the force is intermittently generated by the random period, the forearm is vibrated. The vibration spectrum obtained from the simulations and that obtained from the experiments quantitatively agreed.

Although bladed disks of turbomachinery are nominally designed to be cyclically symmetric (tuned system), the vibration characteristics of all blades on a disk are slightly different due to the manufacturing tolerance, the deviation of the material property, the wear during operation, and so on. These small variations break the cyclic symmetry, and split the eigenvalue pairs. The actual bladed disks with the small variations are referred to a mistuned system. Many researchers have studied mistuning, and main conclusions are while mistuning has an undesirable effect on the forced response, it has a beneficial (stabilizing) effect on the blade flutter (the self-excited vibration). Although such mistuning phenomena of bladed disks have been studied since 1980s, almost all studies focused on the amplification factor of the displacement response, and few studies researched the amplification factor of the vibratory stress response. Therefore, in the previous paper, authors studied the amplification factor expressed by the vibratory stress for the lower modes of the bladed disk, using the simple assumption. In this study, the mistuning effect expressed by the vibratory stress for the lower and higher modes are examined, using the reduced order model without any assumptions. First, formulation for evaluating the mistuning effect expressed by the vibratory stress is derived, using the reduced order model SNM (Subset of Nominal Modes). Second, the frequency response analysis of the mistuned simple bladed disk consisting of flat plates is carried out systematically. Finally, comparing the amplification factor of the displacement response with that of the vibratory stress response including the synthesized stress (Mises stress and the principal stress), mistuning phenomena expressed by the vibratory stress are clarified.

This paper deals with the vibration quenching problem of the one-degree-of-freedom system with a limited power supply. This system is forced by centrifugal force of rotating unbalance, and the system is quenched using a Hula-Hoop and a motor to assist the rotation of Hula-Hoop. The entrainment region, the amount of vibration quenching, and the energy consumptions of the system are studied from the approximate analysis using the averaging method, the numerical integration analysis, and the experiment. Following was made clear: (1) When the unbalance is large, the entrainment region of the voltage of the assistant motor is large. On the other hand, when the unbalance is small, the entrainment region becomes narrow. (2) When the unbalance is large, by setting the voltage of the assist motor to a value smaller than the optimum value for vibration control, within the range that satisfies the allowable vibration amplitude level, the increase amount of the energy consumption becomes low. (3) The approximate solutions obtained by the averaging method are in good agreement with those obtained by the numerical integration method, and the characteristics of these results coincide with those of the results obtained by experiment.

Collision vibration systems are usually modeled as a nonlinear spring whose characteristics are described by the broken line model. These systems are called piecewise-linear systems. A piecewise-linear system is highly nonlinear, and it is usually difficult to predict the system response using any general analytical solution. If the effects of design parameters such as clearance size and dynamic nonlinearity of the systems are known, the structures can be designed to be safer and more comfortable. In a previous paper, forced collision vibration for 2nd order super harmonic resonance in a mass-spring system for two-degree-of-freedom was analyzed. The restoring force, which is generated when a mass collides elastically to another mass, was modeled as an asymmetric piecewise-linear system. In this research, the 1/2nd order sub-harmonic resonance is treated for the same system in the previous research. In order to analyze resulting vibration for the 1/2nd order sub-harmonic resonance, the Fourier series method is applied and analytical solutions for this system are derived. Next, following the analytical solutions, numerical calculations are performed, and the resonance curves are constructed by using resulting vibration. Effects of amplitude ratio of excitation, nonlinearity of the system and mass ratio on the resonance curves are shown numerically. For verification of the analytical solutions, numerical simulations are performed by the Runge-Kutta method, and numerical results based on analytical solutions are compared with numerical simulation results on the resonance curves. As a result, the analytical solutions are in a fairy good agreement with the numerical simulation results.

This paper deals with the quenching problem of electromagnetic vibration of the inverter motor stator. The iron stator of the inverter motor is modeled by a perfect circular ring. Single or two Houde dampers are installed on the outside of the circular ring to quench the forced vibration caused by the rotating distributed electromagnetic force. Moreover, single mass is set also on the circular ring. The solutions of forced vibration are obtained by the theoretical analysis. The following were made clear; (1) When the angle between two Houde dampers is equal to that between loop and node of the mode to be quenched, the resonant amplitude of the stator is reduced most. (2) By setting not only two Houde dampers in the suitable positions, the setting angles are apart almost 35°～65°each other, but also setting single mass which is imperfection for perfect ring, the vibration of motor stator is quenched over wide frequency region around resonance. (3) By installing single Houde damper and single mass, the vibration of motor stator is quenched over wide frequency region around resonance also. (4) The results by the ring theory coincide with those by finite element method.

When we acquire tactile sensation, contact and relative motion are necessary between our bodies and objects. This implies that the tactile sensation is produced by friction phenomena. The present paper describes the sliding test for estimating the tactile sensation associated with cosmetic foundation. When the cosmetic foundation is rubbed with an apparatus that imitates a human finger, two types of time-evolving signals-normal and tangential-are obtained as the source of the tactile information. In the sliding test with the apparatus under the frictional condition of humans acquiring the tactile sensation, frictional vibration is observed in the tangential signals, which should be related to the tactile sensation associated with the cosmetic foundation. When a surface with a grooved pattern that imitates fingerprints is used in the sliding test, two types of frictional vibrations are observed. If an adequate sliding velocity is selected, the slight difference between the four types of commercial cosmetic foundations is discriminable by using the signals of these vibrations.

An elevator rope for high-rise building is forcibly excited by the displacement of the building caused by earthquakes and wind forces. In high-rise building, the elevator rope may resonate with the natural frequency of the building; hence, effective solution to reduce the rope displacement is demanded. In this paper, a method to suppress the transverse vibration of elevator rope using vertical vibration of counterweight is proposed. Rope lateral vibration is controlled by fluctuating rope tension using up-and-down motion of this counterweight. Finite difference analyses of rope vibration with counterweight are performed to verify the validity of this method. Experiments involving forced vibration of a rope whose length is constant are performed. In the experiments, guide bar is used to suppress the rotation motion of the rope. As a result, rope sway is reduced to about 1/2, when the cage is stopped. The optimal natural frequency of vertical vibration of counterweight is about 2 times of the natural frequency of the rope lateral vibration.

This paper deals with the gear rattle of helical gear system. Introducing the mesh stiffness and torque variation into the one pair of helical gear system, the effects of the shapes of the tooth profile errors on the rattle are studied, and the subharmonic vibrations generated in the system are also studied numerically. In the numerical analysis, shooting method with high accuracy is used. To obtain the high accurate periodic solutions, all cases of meshing are considered and the very short time integral step are adopted. As a result, the followings were made clear. (1) About the resonance amplitudes caused by tooth profile errors, those in the gears with middle concave tooth profile error are generally larger than those in the gears with middle convex tooth profile error. (2) About the resonance amplitude caused by the torque variation, there is little difference between the gears with the middle concave tooth profile error and those with the middle convex tooth profile error. (3) In the case without torque variation, there is a possibility that 1/2th-subharmonic vibration and 1/3th-subharmonic vibration occur because of tooth profile error. (4) When torque variation is increased, 1/3th-subharmonic vibration caused by tooth profile error degenerates. (5) In the near region where the 1/2th-subharmonic vibration generates, by the interaction of the vibrational force by the tooth profile error and the torque variation, many unstable branches are created, and chaos occurs.

An elevator rope for a high-rise building is forcibly excited by the displacements of the building induced by wind forces and/or by long-period ground motion. In high-rise building, the elevator rope may resonate with natural frequency of the building, and lateral vibration becomes large; hence, effective solution to reduce the rope displacement is demanded. In this paper, a method to suppress the rope displacement by using dynamic damper is proposed. Rope lateral vibration is controlled by fluctuating rope tension using up-and-down motion of this dynamic damper. Finite difference analyses of rope vibration with dynamic damper are performed to verify the validity of this method. Experiments involving forced vibration of a rope whose length is constant are also performed. The optimal natural frequency of this dynamic damper is about 2 times of the natural frequency of the rope lateral vibration. The rope sway can be reduced to about 1/2, when the cage is stopped.

This paper deals with the quenching problem of electromagnetic vibration of the motor stator with imperfections at the resonant frequency using a pair of dynamic absorbers. The iron stator of motor is modeled by a circular ring with single or two imperfect masses, and dynamic absorbers are installed on the outside of the circular ring to quench the forced vibration caused by the rotating distributed electromagnetic force. The solutions of forced vibration are obtained by the theoretical analysis. The following were made clear; (1) As imperfect mass reduces the natural frequency of the motor stator, resonant frequency becomes low. (2) In the case where the weight of two imperfect masses are heavy, the closer the angle at which two imperfect masses forms, is close to the angle between the loop and node of the mode that is to be quenched, the resonant amplitude is reduced. (3) By installing single dynamic absorber and single imperfect mass, and by setting an angle between the loop and node of the mode to be quenched, quenching is possible. (4) Even if imperfections exist, installing a pair of dynamic absorbers that make an angle equal to the one between the loop and node of the mode to be quenched, makes the motor stator quenched perfectly.

This paper deals with the quenching problem of electromagnetic vibration of the motor stator in the wide frequency region around the natural frequency using multiple dynamic absorbers. The iron stator of motor is modeled by circular ring, and a pair of dynamic absorbers or two pair of them are installed on the outside of the circular ring to quench the forced vibration caused by the rotating distributed electromagnetic force. The solutions of forced vibration are obtained by the theoretical analysis. Following was made clear: (1) By installing two dynamic absorbers those have the same appropriate natural frequency ratios and damping ratio, the iron stator is quenched well. (2) By installing the same two dynamic absorbers leaving an angle that is equals to the one between loop and node of the mode to be quenched, the iron stator is quenched best. (3) By installing the two dynamic absorbers those have different natural frequency ratios and damping ratios each other, the quenching effect become a little better than the case mentioned above. (4) By installing the multiple pair of dynamic absorbers, the quenching effect become much more better than the cases using a pair of dynamic absorbers.

For the passive vibration isolation system, a friction damper is advantageous at cost, a maintenance, etc. However, the conventional damper of constant friction force has performance limitations; the isolation characteristic declines when the friction force is large, while the resonant peak becomes large when the friction force is small. Furthermore, the displacement remains apart from the equilibrium position after the vibration diminishes. In order to overcome above drawbacks, this paper proposes a vibration isolation system equipped with a new linear friction damper where the magnitude of the frictional force increases proportionally to the relative displacement. This proportionality is achieved by combining a cylindrical block and a tilt lever supported with a leaf spring. When the cylindrical block moves and pushes the tilt lever, the normal force exerted by the leaf spring at the contact position increases. Thus, the friction force varies in proportion to the relative displacement between the tilt lever and the cylindrical block. The transient response and the displacement transmissibility are investigated by numerical simulation and experiments, confirming the effectiveness of the linear friction damper.

A vane used in a low pressure end of steam turbine is usually fixed to a shroud and a casing by welding both ends. In such a vane structure, the damping in loading operation is comprised of the material damping and the aerodynamic damping, because the structural damping is very small. Recently, in order to increase the reliability of a steam turbine vane, a hollow vane with a friction damper has been used. In this paper, for the purpose of clarifying the damping characteristics of the hollow vane with a friction damper, first, the excitation test of the model vane is carried out. Second, the analysis method for predicting the damping characteristics of the hollow vane with a friction damper is proposed. The validity of the analysis method is verified by comparing the measured damping characteristics of the vane with the calculated ones. Finally, the analysis of the actual steam turbine hollow vane with a friction damper is also carried out. From these results, the damping characteristics of the hollow vane with a friction damper are clarified.