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This study is concerned with the development of multi-input multi-output control algorithms for the active vibration suppression of structures using accelerometer signals and force-type actuators. The concept of the single-input single-output virtual tuned mass damper control algorithm developed in the previous study was extended to cope with multiple natural modes of structure equipped with a limited number of sensors and actuators. Two control algorithms were developed based on the assumption of collocated control. One is the decentralized virtual tuned mass damper control that produces the actuator signal using only the accelerometer signal of that actuator position. The other is the centralized virtual tuned mass damper control that is designed in modal-space, and produces the modal control force using the modal coordinate. Both the theoretical and experimental results show that the proposed control algorithms are effective in suppressing multiple natural modes with a lesser number of sensors and actuators. However, the decentralized virtual tuned mass damper control can be designed and implemented more easily than the centralized virtual tuned mass damper control.

This study is concerned with the hydroelastic vibration of the flexible bottom plate of a cylindrical tank coupled with sloshing. The cylindrical tank is assumed to be placed vertically with the rigid wall. The matrix equations of motion describing the free-surface elevation coupled with the hydroelastic vibration of the bottom plate was derived by using the Lagrangian equation. The so-called non-dimensionalized added virtual increment factors were also calculated and compared to the previous results, and showed exact agreement. The numerical results show that only when the water is shallow and the bottom plate is very flexible, strong coupling exists in the bulging modes and asymmetric modes having one nodal diameter. However, if the fundamental frequency of the plate in contact with fluid is much higher than the fundamental frequency of the sloshing, the coupling between sloshing and the hydroelastic vibration of the bottom plate can be ignored.

This study proposes a hybrid control methodology that combines tuned liquid damper (TLD) and active mass damper (AMD) to suppress vibrations of multi-story building structure effectively. To this end, a dynamic model that can predict the vibration of multi-story building structure coupled with TLD and AMD is derived using the energy approach. The TLD that is mainly designed to suppress the main natural mode is developed with a multi-degree-of-freedom model to investigate the effect of the TLD on natural modes of structure numerically. The AMD is an active vibration controller that can suppress remaining resonant peaks, including ones resulting from the application of the TLD as well as other higher modes of interest. In this way, the proposed control can utilize the advantages of TLD and AMD simultaneously. We set up an experimental apparatus to verify the performance of the hybrid control methodology. The numerical and experimental results show that the proposed hybrid control method can successfully suppress the vibrations of multi-story building structure. The dynamic model derived in this study can also accurately predict the actual behavior of the system.

In Chap. 2, we introduced the analysis of the SDOF vibration system. This chapter introduces the analysis method for the case where several SDOF systems are connected to each other to form a multi-degree-of-freedom

An accurate theoretical model is needed to investigate the validity of the control algorithm before practical application.

In active vibration control, a control algorithm that can suppress vibration while not destabilizing the target structure is important. We should have knowledge of the hardware we are going to implement. Many active vibration control theories are designed without taking into account their practical application, so hard to implement them in real system.

The vibration analysis begins with a simple spring-mass-damper system. This chapter introduces the role of the mass, spring, and damper constituting the vibration system, and the process of deriving the equation of motion.

This study is concerned with the active vibration control of a cart-pendulum system. The input-shaping control alone is not sufficient to suppress vibrations of the cart payload, especially when external disturbance is present. In order to solve this problem, a new control technique consisting of the input-shaping and the position-input position-output feedback controls is proposed. The input-shaping control minimizes vibrations during cart motion and the position-input position-output feedback control takes charge of suppressing residual vibrations after the cart reaches the desired position. The stability of the proposed position-input position-output feedback control was investigated theoretically. The testbed was built to validate the proposed method. It was proved both theoretically and experimentally that the proposed control technique can be successfully used to control vibrations of the pendulum.

This paper presents a new dynamic model for the simulation of power-transmission-line galloping. The energy approach using the assumed mode method was used to derive equations of motion for a single transmission line and double transmission lines connected by spring spacers. Equations of motion are expressed in matrix form, which simplifies numerical analysis and saves computational time. The dynamic models were verified experimentally by comparing theoretical natural frequencies with measured natural frequencies of real transmission lines installed in the test site. Accelerometers and a CCD camera were used to measure vibrations, and an image processing technique was used to trace a circular target mounted on the line. Experimental results are in good agreement with theoretical results, which validate the dynamic models derived in this study. Galloping forces were modeled by assuming quasi-steady aerodynamic lift and drag, which enabled us to predict the galloping phenomena. Numerical simulation results are presented.

A semi-active virtual tuned mass damper (SAVTMD) control algorithm is developed to suppress vibrations of a railway vehicle by using magneto-rheological (MR) damper. To this end, a virtual-tuned-mass-damper control algorithm analogous to the tuned mass damper was developed prior to the semi-active application. The proposed SAVTMD control algorithm uses the acceleration of the car body directly, so that it is more practical than the sky-hook control algorithm that uses the velocity of the car body. The application of the SAVTMD control to a real MR fluid damper is discussed, and a step-by-step procedure to calculate the command voltage to the driver of the MR fluid damper is presented. A hardwarein-the-loop simulation system developed in the previous study is used to test the SAVTMD control algorithm. The theoretical and experimental results showed that the proposed SAVTMD control algorithm is more effective than is the semi-active sky-hook control in suppressing vibrations of the car body of the railway vehicle by the MR damper.

This study presents the analytical solution and experimental investigation of the galloping energy harvesting from oscillating elastic cantilever beam with a rigid mass. A piezoelectric wafer was attached to galloping cantilever beam to harvest vibrational energy in electric charge form. Based on Euler-Bernoulli beam assumption and piezoelectric constitutive equation, kinetic energy and potential energy of system were obtained for the proposed structure. Virtual work by generated charge and galloping force applied onto the rigid mass was obtained based on Kirchhoff's law and quasistatic assumption. Nonlinear governing electro-mechanical equations were then obtained using Hamilton's principle. As the system vibrates by self-exciting force, the fundamental mode is the only one excited by galloping. Hence, multi-degreeof-freedom equation of motion is simplified to one-degree-of-freedom model. In this study, closed-form solutions for electro-mechanical equations were obtained by using multi-scale method. Using these solutions, we can predict galloping amplitude, voltage amplitude and harvested power level. Numerical and experimental results are presented and discrepancies between experimental and numerical results are fully discussed.

The objective of this study was to design multi-input and multi-output feedback control for vibration suppression of structures using multiple active mass dampers driven by linear servo motors. The linear servo motor was used to enhance control effectiveness and decrease noise. The multi-input and multi-output modal-space negative acceleration feedback control was developed to fully utilize multiple accelerometers and multiple active mass dampers. Control spillover problem due to mistuning of the negative acceleration feedback control was also investigated in detail. To determine the efficacy of the proposed multi-input and multi-output modal-space negative acceleration feedback control, a two-story building-like structure was built and tested. A dynamic model was derived by using energy approach and beam modeling. The proposed multi-input multi-output modal-space negative acceleration feedback controller was validated both theoretically and experimentally for the test structure. Both numerical and experimental results showed that the proposed controller could effectively suppress vibrations.

In this paper, the vibration characteristic of elevator rope was verified. To this end, the dynamic model of elevator rope was derived using Rayleigh-Ritz method. And the numerical simulation was carried out for theoretical predictions. To calculate the response of elevator rope, the parameters of real elevator was considered. Based on numerical simulation, the vibration experiments were carried out to validate the dynamic model of elevator rope. To measure the vibration of elevator rope, the CCD camera and the line laser was considered. And the image processing technique was applied to calculate the horizontal displacement of elevator rope. Measurement equipment was installed in elevator shaft at 3 m, 29 m, and 51 m from the base level. Shaker was equipped at the bottom of elevator rope to excite the rope. In experiments, the displacement of rope was measured when the elevator rope was subjected to each natural frequencies. Experimental results are in good agreement with theoretical predictions.

When a building sways due to strong wind or an earthquake, the elevator rope can undergo resonance, resulting in collision with the hoist-way wall. In this study, a hard stopper and a soft stopper comprised of a spring-mass-damper system installed along the hoist-way wall were considered to prevent the string from undergoing excessive vibrations. The collision of the string with multiple hard stoppers and multiple spring-mass-damper stoppers was investigated using an analytical method. The result revealed new formulas and computational algorithms that are suitable for simulating the vibration of the string against multiple stoppers. The numerical results show that the spring-mass-damper stopper is more effective in suppressing the vibrations of the string and reducing structural failure. The proposed algorithms were shown to be efficient to simulate the motion of the string against a vibration stopper.

This paper focuses on the dynamic modeling of a cylindrical shell equipped with piezoceramic sensors and actuators, as well as the design of a broad band multi-input and multi-output linear quadratic Gaussian controller for the suppression of vibrations. The optimal locations of actuators are derived by Genetic Algorithm (GA) to effectively control the specific structural modes of the cylinder. The dynamic model is derived based on the Sanders shell theory and the energy approach for both the cylinder and the piezoelectric transducers, all of which reflect the piezoelectric effect. The natural vibration characteristics of the cylindrical shell are investigated both theoretically and experimentally. The theoretical predictions are in good agreement with the experimental results. Then, the broad band multi-input and multi-output linear quadratic Gaussian controller was designed and applied to the test article. An active vibration control experiment is carried out on the cylindrical shell and the digital control system is used to implement the proposed control algorithm. The experimental results show that vibrations of the cylindrical shell can be suppressed by the piezoceramic sensors and actuators along with the proposed controller. The optimal location of the actuators makes the proposed control system more efficient than other configurations.

This study is concerned with the theoretical modelling and experimental verification of the coupled vibrations of building and elevator ropes. The elevator ropes consist of a main rope which supports the cage and the compensation rope which is connected to the compensation sheave. The elevator rope is a flexible wire with a low damping, so it is prone to vibrations. In the case of a high-rise building, the rope length also increases significantly, so that the fundamental frequency of the elevator rope approaches the fundamental frequency of the building thus increasing the possibility of resonance. In this study, the dynamic model for the analysis of coupled vibrations of building and elevator ropes was derived by using Hamilton's principle, where the cage motion was also considered. An experimental testbed was built to validate the proposed dynamic model. It was found that the experimental results are in good agreement with the theoretical predictions thus validating the proposed dynamic model. The proposed model was then used to predict the vibrations of real building and elevator ropes.

In this study, an Active Mass Damper (AMD) consisting of an AC servo motor, a movable mass connected to the AC servo motor by a ball-screw mechanism, and an accelerometer as a sensor for vibration measurement were considered. Considering the capability of the AC servo motor which can follow the desired displacement accurately, the Negative Acceleration Feedback (NAF) control algorithm which uses the acceleration signal directly and produces the desired displacement for the active mass was proposed. The effectiveness of the NAF control was proved theoretically using a single-degree-of-freedom (SDOF) system. It was found that the stability condition for the NAF control is static and it can effectively increase the damping of the target natural mode without causing instability in the low frequency region. Based on the theoretical results of the SDOF system, the Multi-Modal NAF (MMNAF) control is proposed to suppress the many natural modes of multi-degree-of-freedom (MDOF) systems using a single AMD. It was proved both theoretically and experimentally that the MMNAF control can suppress vibrations of the MDOF system.

A new approach is proposed in this paper based on radiation modes to control the radiated sound pressure of a smart cylindrical shell equipped with piezoelectric sensor and actuators. The radiation modes determine the specific distribution of normal velocity of the shell that independently radiates sound to the surrounding space. In this study, the first radiation mode is controlled since it is the most effective mode in terms of the radiated power. The results indicate that most of the sound power is attenuated by controlling only this mode. The extended Hamilton’s principle, the Sanders shell theory and the assumed mode method are used to derive the equations of motion in a state space form that is suitable to design the controller. The radiated sound pressure is calculated using the simplified Kirchhoff-Helmholtz integral along with a Kalman filter to observe the system states, and a modified higher harmonic control (MHHC) is designed to attenuate the sound power. A numerical simulation demonstrated the effectiveness of the proposed approach compared to active vibration control (AVC) in attenuating the radiated sound in the low frequency domain.

This study uses the Rayleigh–Ritz method to derive a dynamic model for the free vibration analysis of a circular cylindrical shell. In particular, explicit expressions for the mass and stiffness matrices are obtained to easily implement a computer simulation under different shell theories and boundary conditions. The dynamic model is constructed according to the Donnell–Mushtari theory, which is fully discussed herein, and then, dynamic models are constructed by using Sanders theory, Love–Timoshenko theory, Reissner theory, Flugge theory, and Vlasov theory. This paper also discusses the use of eigenfunctions of a uniform beam as admissible functions that produce compact expressions for the mass and stiffness matrices. The numerical results indicate that the Donnell–Mushtari theory is not sufficiently accurate to calculate the natural frequencies and that there is no discernible difference between the other shell theories considered in this study.

This study is concerned with the theory and application of a tuneable dynamic absorber. The dynamic characteristics of the tuneable dynamic absorber are discussed in terms of the mass ratio, natural frequency of the main structure, natural frequency of a dynamic absorber and excitation frequency. We proposed a semi-active dynamic absorber with a natural frequency that can change through the use of repulsive forces produced by permanent magnets and electromagnetic forces induced by current flowing through a coil. A simple active control algorithm is implemented in the LabView software and the experimental results showed that when the proposed semi-active dynamic absorber is used with the active control algorithm, the vibrations of a structure can be more effectively suppressed than when a passive dynamic absorber with a fixed natural frequency is used.

The active vibration control of a rectangular plate either partially or fully submerged in a fluid was investigated. Piezoelectric sensors and actuators were bonded to the plate, and the assumed mode method was used to derive a dynamic model for the submerged plate. The properties of the piezoelectric actuators and sensors, as well as their coupling to the structure, were used to derive the corresponding equations of their behaviour. The fluid effect was modelled according to the added virtual mass obtained by solving the Laplace equation. The natural vibration characteristics of the plate both in air and in water were obtained theoretically and were found to be consistent with the experimental results, and the changes in the natural frequencies resulting from submersion in fluid can be accurately predicted. A multi-input, multi-output positive position feedback controller was designed by taking the natural vibration characteristics into account and was then implemented by using a digital controller. The experimental results show that piezoelectric sensors and actuators along with the control algorithm can effectively suppress the vibration of a rectangular plate both in air and submerged in a fluid.

This study is concerned with the free vibration analysis of an inextensible uniform rope with a spring-mass system at the tip. The rope is hanged vertically in a gravitational field. This problem is related to the free vibration of an elevator rope connected to an elevator cage. The equation of motion and the corresponding boundary conditions are derived by using the Hamilton’s principle. The general solution of the governing equation of motion is expressed in terms of Bessel functions. The characteristic equation was derived by applying the boundary conditions. The characteristic values which are in fact non-dimensionalized natural frequencies were obtained numerically. The effects of mass and spring constant were investigated. The numerical results show how the tip mass and spring affect the natural frequencies of the rope.

The active lateral suspension (ALS) of a train consists of either active or semi-active technologies. However, such an active system on a real railway vehicle is not easy to test because of cost and time. In this study, a hardware-in-the-loop simulation (HILS) system is developed to test the ALS. To this end, the dynamic model of a railway vehicle is equipped with the actuator, two bogies and four-wheel sets, and the ALS is used. The proposed HILS system consists of an alternating current servo motor connected to a ball-screw mechanism and a digital control system. The digital control system implements the dynamic model and the control algorithm. The design and manufacture of the HILS system are explained in detail. Both the passive damper and the magneto-rheological (MR) fluid damper are tested using the HILS system, where the sky-hook control algorithm was applied for the MR fluid damper. Experimental results show that the proposed HILS system can be effectively used for the performance estimation of the ALS.

This paper is concerned with the suppression of vibrations and radiated sound of a ring-stiffened circular cylindrical shell in contact with unbounded external fluid by means of piezoelectric sensors and actuators. The dynamic model of a circular cylindrical shell based on the Sanders shell theory was considered together with a ring stiffener model. The mass and stiffness matrices for a ring stiffener were newly derived in this study and added to the mass and stiffness matrices of the cylindrical shell, respectively. The fluid-added mass matrix, which was derived by using the baffled shell theory, was also added to the mass matrix. Finally, the equations representing the piezoelectric sensor measurement and piezoelectric actuation complete the theoretical model for the addressed problem. The natural vibration characteristics of the ring-stiffened cylindrical shell both in air and in water were investigated both theoretically and experimentally. The theoretical predictions were in good agreement with the experimental results. An active vibration controller which can cope with a harmonic disturbance was designed by considering the modified higher harmonic control, which is, in fact, a band rejection filter. An active vibration control experiment on the submerged cylindrical shell was carried out in a water tank and the digital control system was used. The experimental results showed that both vibrations and radiation sound of the submerged cylindrical shell were suppressed by a pair of piezoelectric sensor and actuator.

The free flexural vibration of a cantilever plate partially submerged in a fluid is investigated. The fluid is assumed to be inviscid and irrotational. The virtual mass matrix is derived by solving the boundary-value problem related to the fluid motion using elliptical coordinates. The introduction of the elliptical coordinates naturally leads to the use of the Mathieu function. Hence, the virtual mass matrix which reflects the effect of the fluid on the natural vibration characteristics is expressed in analytical form in terms of the Mathieu functions. The virtual mass matrix is then combined with the dynamic model of a thin rectangular plate obtained by using the Rayleigh–Ritz method. This combination is used to analyze the natural vibration characteristics of a partially submerged cantilever plate qualitatively. Also, the non-dimensionalized added virtual mass incremental factors for a partially submerged cantilever plate are presented to facilitate the easy estimation of natural frequencies of a partially submerged cantilever plate. It is found that the numerical results are in good agreement with the previous results, thus validating the proposed approach.

In dealing with the dynamics of a flexible body, the rigid-body motions and elastic vibrations are analyzed separately. However, rigidbody motions cause vibrations, and elastic vibrations affect rigid-body motions, indicating the inherent coupling between rigid-body motions and elastic vibrations. The coupled equations of motion for a flexible body can be derived by means of Lagrange’s equations in terms of quasi-coordinates. The resulting equations of motion are hybrid and nonlinear. This paper proposes a unified approach for the equations of motion for a flexible body based on the perturbation method and the Lagrange’s equations of motion in terms of quasicoordinates and Euler parameters to analyze a more general case maneuvering. The resulting equations consist of zero-order nonlinear equations of motion which depict rigid-body motions and first-order time-varying linear equations of motion which depict perturbed rigid-body motions and elastic vibration. Hence, the input-shaped maneuvering can be applied to the zero-order equation considering the induced vibrations. Since the input-shaped maneuvering alone cannot achieve vibration suppression, the vibration suppression controller combined with the input-shaped maneuvering is proposed in this study. As a numerical example, a hub with elastic appendages is considered. Numerical results show that the unified modeling approach proposed in this paper is effective in numerical simulation and control design.

Numerical and analytical investigation of the effects of thermal radiation and viscous heating on a convective flow of a non-Newtonian, incompressible fluid in an axisymmetric stretching sheet with constant temperature wall is performed. The power law model of the blood is used for the non-Newtonian model of the fluid and the Rosseland model for the thermal radiative heat transfer in an absorbing medium and viscous heating are considered as the heat sources. The non-dimensional governing equations are transformed to similarity form and solved numerically. A parameter study on entropy generation in medium is presented based on the Second Law of Thermodynamics by considering various parameters such as the thermal radiation parameter, the Brinkman number, Prandtl number, Eckert number.

This paper is concerned with the dynamic modeling for the hardware-in-the-loop simulation of lateral vibrations of a railway vehicle. The resulting dynamic model is a nine degree-of-freedom model which can describe the lateral, roll and yaw motions of the car body and two bogies. It is assumed that the external disturbances come from wheel motions. In order to test the efficacy of the model, the linear quadratic regulator and the sky-hook control algorithm were designed and applied to the model. The simulation results show that both control algorithms are effective in suppressing the vibrations of railway vehicles.

This research is concerned with the derivation of equations of motion for a slewing beam and the application of input shaper to the bang-bang control to achieve vibration suppression. When a uniform beam with a tip mass rotates about the axis perpendicular to the undeformed beam`s longitudinal axis, it experiences inertial loading. Hence, the beam vibrates. In this paper, we used the input shaper for the maneuvering control to suppress vibrations. The maneuvering control which can achieve a minimum-time control is a bang-bang control. The input-shaped bang-bang maneuvering is used to suppress vibrations both theoretically and experimentally. The slewing beam experiment is not an easy subject because of the inherent damping existing inside the rotor. We propose the use of a negative damping to eliminate the rotor damping. Numerical and experimental results show that the input-shaper can be effectively used for the vibration suppression of a slewing beam.

This paper is concerned with the suppression of noise and vibrations of the brake system of elevator traction machine by means of a solenoid control technique. The solenoid is used to hold the brake shoe, which is then released by turning the solenoid off. Since the brake shoe hits the brake disk, vibrations and noise occur. We developed the solenoid control technique based on the dynamic behavior of the solenoid. The theoretical model for the solenoid is modeled by using linear magnetic principles. The solenoid model was then combined with the vibration model to simulate the vibrations of brake system. The simulation results show that the additional pulse input to the solenoid can decrease the vibrations. The timing of the applied pulse is determined by observing the current. The experimental results show that both the vibrations and noise can be substantially decreased, which validates the approach developed in this paper.

This paper is concerned with the development of power amplifier and controller for piezoelectric actuator and sensor used in smart structures. Even though a high-voltage power amplifier is provided in the form of an operational amplifier, a very high DC voltage is still necessary as a power supply. In this study, we propose a low-cost design for the power amplifier including the DC power supply. We also need a controller on which a control algorithm will be mounted. In general, a digital signal processing chip is popularly used because of high speed. However, only commercial product is available for smart structure applications. In this paper, a controller consisting of a DSP and electronic circuits suitable for piezoelectric sensor and actuator pair is proposed. To validate the proposed controller with power amplifier, experiment on smart structure was carried out. The experimental results show that the proposed control system can be effectively used for smart structure applications with low cost.

This paper is concerned with the natural vibration characteristics of a rectangular plate with a rectangular hole in contact with the water. The addressed problem was solved by using the Rayleigh-Ritz method combined with the Green function method. This study presents the numerical approach, numerical results and experimental results. In addition, the validity of the approximate formula which mainly depends on the so-called non-dimensionalized added virtual mass incremental factor and the natural mode shape change due to the presence of the water were investigated. Experiments were also carried out to validate theoretical results. The theoretical results are in good agreement with the experimental results. It was found that the effect of a square hole on the natural frequencies of the square plate in contact with water is different from the effect of a square hole on the natural frequencies of the square plate in air and the approximate formula can predict lower natural frequencies in water with a good accuracy.

The free flexural vibration of a hanged clamped-free cylindrical shell partially submerged in water with gap from bottom is investigated. The fluid is assumed to be inviscid and irrotational. The cylindrical shell is modeled by using the Rayleigh-Ritz method based on the Sanders shell theory. The kinetic energy of the fluid is derived by solving the boundary-value problem related to the fluid motion. The natural vibration characteristics of the partially submerged cylindrical shell are discussed with respect to the added virtual mass approach. In this study, experiments were carried out to confirm theoretical results. It was found that theoretical prediction is in good agreement with experimental results.

This paper is concerned with the active control experiments on elevator vibrations by means of the active roller guide. To this end, a roller guide was designed using a voice-coil actuator and linear guide. A simple proportional control algorithm combined with the band-pass filter was implemented using the DSP. Based on the initial experiments, a new control system which can handle lateral and front-back vibrations of elevator was built and tested using the elevator test tower. The experimental results show that the elevator vibrations are reduced by the active control technique.

This paper is concerned with the modeling and active controller design for elevator lateral vibrations. To this end, a dynamic model for the lateral vibration of the elevator consisting of a supporting frame, cage and active roller guides was derived using the energy method. Free vibration analysis was then carried out based on the equations of motion. Active vibration controller was designed based on the PID control algorithm and applied to the numerical model. Rail irregularity were considered as external disturbance in the numerical simulations. The numerical results show that the active vibration control of elevator is possible.