Suppression of random vibration in flexible structures using a hybrid vibration absorber

A design method is proposed to suppress stationary random vibration in flexible structures using a hybrid vibration absorber (HVA). While the traditional vibration absorber can damp down the vibration mainly at the pre-tuned mode of the primary structure, active damping is generated by the proposed HVA to damp down all resonant modes of interest of the vibrating structure and the spatial average mean square motion of the vibrating structure can be minimized. Only one absorber and one feedback signal are required to achieve global vibration suppression of a flexible structure under stationary random excitation. A special pole-placement controller is designed such that all vibration modes of the flexible structures become critically damped. It is proved analytically that the proposed HVA damps the vibration of the entire structure instead of just the attachment point of the absorber. The proposed optimized HVA is tested on a beam structure and it shows a superior performance on global suppression of broadband vibration in comparison to other published designs of passive and hybrid vibration absorbers.     

Modal properties and stability of centrifugal pendulum vibration absorber systems with equally spaced,identical absorbers

This work develops an analytical model of centrifugal pendulum vibration absorber systems with equally spaced, identical absorbers and uses it to investigate the structure of the modal vibration properties. The planar model admits two translational and one rotational degrees-of-freedom for the rotor and a single arclength degree-of-freedom for each absorber. The gyroscopic effects from rotor rotation are taken into account. Examination of the associated eigenvalue problem reveals well-defined structure of the vibration modes resulting from the cyclic symmetry of the absorbers. The vibration modes are classified into rotational, translational, and absorber modes. Characteristics of each mode type are analytically proved. The effects of the absorber tuning order on the modes are derived. The critical speeds and flutter instability of the system are studied numerically and analytically.     

Dynamic analysis and optimal design of a passive and an active piezo-electrical dynamic vibration absorber

This paper is concerned with the dynamic analysis and parameter optimization of both passive and active piezo-electrical dynamic vibration absorbers that are strongly coupled with a single degree of freedom vibrating structure. The passive absorber is implemented by using an R_s∥L_s parallel shunt circuit while the active absorber is implemented by feeding back the acceleration of the structure through a second-order lowpass filter. An impedance-mobility approach is used for the electromechanical coupling analysis of both types of absorbers coupled with the structure. Using this approach it is demonstrated that the passive and active absorbers can be made exactly equivalent. A maximally flat frequency response strategy is used to find the optimal damping ratio of the passive absorber while a robust, optimal control theory is used to find that for the active absorber. It is found that the passive optimization strategy corresponds to an optimal, robust feedback control of 2 dB spillover. Simulations and experiments are conducted to support the theoretical findings.     

Autoparametric vibration absorber effect to reduce the first symmetric mode vibration of a curved beam/panel

This paper presents the implementation of autoparametric phenomena to reduce the symmetrical vibration of a curved beam/panel under external harmonic excitation. The internal energy transfer of a first symmetric mode into first anti-symmetric mode in a curved panel is one example of autoparametric vibration absorber effect. This is similar to the vibration energy transfer from the resonance of a primary structure to the resonance of a secondary spring–mass (tuned mass damper). The nonlinear response of a curved beam is analyzed using an equation with two modes, and a shaker test. The effect of different configurations of the curve beam/panel, including damping ratios and excitation levels, on the energy transfer of the first symmetric mode to the first anti-symmetric mode was studied.The conventional tuned mass damper (TMD) can reduce the resonance response by energy transfer using damping dissipation, whereas an autoparametric vibration absorber (AVA) can reduce the resonance response by energy transfer using parametric interaction. The results indicate that there is a non-absorption region in which vibration is amplified. For the AVA, the non-absorption region can be minimized by tuning the resonance frequency of the first anti-symmetric mode to half of the first symmetric mode resonance frequency using additional mass. No additional damping material is required for achieving sufficient vibration reduction. The AVA can maintain reliable performance in hot and corrosive environments where damping material cannot perform effectively. This paper presents the first successful experimental results of an autoparametric vibration absorption mechanism in a curved beam.     

Analytical study of an active piezoelectric absorber on vibration attenuation of a plate

The attenuation of the transverse vibration of a plate, subjected to a harmonic force, is studied. This goal can be achieved by using an active dynamic absorber. The active absorber is made of a pair of piezoelectric sheets, attached to both sides of the plate, and closed electric circuits. One piece of the piezoelectric material provides a sensor for detecting the motion of the plate. Another piece serves as an active dynamic absorber. The equations of motion of the composite plate, including the plate and the piezoelectric material, and the circuit equations of the sensor and the absorber are derived. The displacements of the plate and the currents in the circuits are calculated. The active absorber can successfully attenuate the vibration. The numerical results show that the proposed active absorber can offer more reduction than that using a passive absorber while the absorber is designed to suppress the resonance of a particular vibration mode. Moreover, the active absorber can also reduce the displacements corresponding to other uncontrolled modes. The effects of altering various parameters of the active absorber are studied and discussed.     

Tuneable vibration absorber design to suppress vibrations: An application in boring manufacturing process

Dynamic vibration absorbers are used to reduce the undesirable vibrations in many applications such as electrical transmission lines, helicopters, gas turbines, engines, bridges, etc. Tuneable vibration absorbers (TVA) are also used as semi-active controllers. In this paper, the application of a TVA for suppression of chatter vibrations in the boring manufacturing process is presented. The boring bar is modeled as a cantilever Euler–Bernoulli beam and the TVA is composed of mass, spring and dashpot elements. In addition, the effect of spring mass is considered in this analysis. After formulation of the problem, the optimum specifications of the absorber such as spring stiffness, absorber mass and its position are determined using an algorithm based on the mode summation method. The analog-simulated block diagram of the system is developed and the effects of various excitations such as step, ramp, etc. on the absorbed system are simulated. In addition, chatter stability is analyzed in dominant modes of boring bar. Results show that at higher modes, larger critical widths of cut and consequently more material removal rate (MRR) can be achieved. In the case of self-excited vibration, which is associated with a delay differential equation, the optimum absorber suppresses the chatter and increases the limit of stability.     

Active control of geometrically nonlinear transient vibration of composite plates with piezoelectric actuators

In this paper, the incremental finite element equations for geometric non-linear analysis of piezoelectric smart structures are developed using a total Lagrange approach by using virtual velocity incremental variational principles. A four-node first order shear plate element model with reduced and selective integration is also developed. Geometrically non-linear transient vibration response and control of plates with piezoelectric patches subjected to pulse loads are investigated. Active damping is introduced on the plates by coupling a self-sensing and negative velocity feedback algorithm in a closed control loop. The numerical results show that piezoelectric actuators can introduce significant damping and suppress transient vibration effectively. The effects of the number and locations of the piezoelectric actuators on the control system are also discussed.     

Optimal active absorber with internal state feedback for controlling resonant and transient vibration

An active, standalone vibration absorber utilizing the state feedback taken from the absorber mass is proposed. Expressions of the optimum absorber parameters are obtained both by optimizing the Η_∞ norm of the frequency response function. For improved transient response featuring low peak response and fast attenuation, the design procedure utilizes the mode equalization followed by the maximization of the damping. An interesting feature of the proposed absorber is that the performance of the absorber does not require having its natural frequency close to the natural frequency of the primary system as is generally the case for tuned passive absorbers or other active and semi-active tuned vibration absorbers. In fact, the performance of the proposed system can be progressively enhanced by increasing the absorber frequency. Compared to the optimum passive absorber, the optimal active absorber can yield wider bandwidth of operation around the natural frequency of the primary system and lower frequency response within the suppression band. The active absorber also offers better transient response compared to the passive absorber both optimized for the best transient responses. The efficacy of the absorber is analyzed both for a single-degree-of-freedom and beam like primary structure.     

Reduction of sound transmission into a circular cylindrical shell using distributed vibration absorbers and Helmholtz resonators

A modal expansion method is used to model a cylindrical enclosure excited by an external plane wave. A set of distributed vibration absorbers (DVAs) and Helmholtz resonators (HRs) are applied to the structure to control the interior acoustic levels. Using an impedance matching method, the structure, the acoustic cavity, and the noise reduction devices are fully coupled to yield an analytical formulation of the structural kinetic energy and acoustic potential energy of a treated cylindrical cavity. Lightweight DVAs and small HRs tuned to the natural frequencies of the targeted structural and acoustic modes, respectively, result in significant acoustic and structural attenuation when the devices are optimally damped. Simulations show that significant interior noise reduction can only be achieved by adding damping to both structural and acoustic modes, which are resonant in the frequency bandwidth of interest. In order to be independent of the azimuth angle of the excitation and to avoid unwanted modal interactions, the devices are distributed evenly around the cylinder in rings. This treatment can only achieve good performance if the structure and the acoustic cavity are lightly damped.     

Active control effort of hybrid piezoelectric absorber for structural control

This paper aims at addressing the active control effort of the active-shunted hybrid piezoelectric absorber for structural vibration suppression. Both active control efforts of the integrated and separated hybrid piezoelectric absorbers are analyzed by using a simple cantilevered beam example. It is recognized that a new hybrid piezoelectric absorber based on a switching operation is capable of reducing the active control effort. A switching type of the hybrid piezoelectric absorber can be developed by the simple combination of integrated and separated hybrid piezoelectric absorbers. It is demonstrated that the switching type of the absorber has the capability of the trade-off between the active control effort and the damping performance.     

Flexural vibration of perforated plates and porous elastic materials under acoustic loading

This paper presents a method of theoretical treatment of acoustic coupling due to flexural vibration of perforated plates and plates of porous elastic materials. The analytical model is developed by introducing flow continuity at the plate surface in a spatially mean sense and air-solid interaction within the plate material. To demonstrate the method of application, some fundamental acoustic problems based on a classical thin-plate theory are analyzed and discussed in relation to the interactive effect of flexural vibration and plate permeability. For acoustic radiation from a vibrating plate excited by a harmonic point-force, the attenuation effect of power radiation appears at frequencies below the critical frequency of coincidence. In the problem of sound absorption of a perforated plate or a plate of porous elastic material backed by an air layer, as permeability decreases, the effect of plate vibration increases. For perforated absorber systems including plate vibration effects, the trend of variation from ordinary theory depends on plate thickness.     

Optimum vibration absorber (tuned mass damper) design for linear damped systems subjected to random loads

Optimum design of dynamic vibration absorbers (DVAs) installed on linear damped systems that are subjected to random loads is studied and closed-form design formulas are provided. Three cases are considered in the optimization process: Minimizing the variance of the displacement, velocity and acceleration of the main mass. Exact optimum design parameters for the velocity case, which to the best knowledge of the author do not exist in the literature, are derived for the first time. Exact solutions are found to be directly applicable for practical use with no simplification needed. For displacement and acceleration cases, a solution for the optimum absorber frequency ratio is obtained as a function of optimum absorber damping ratio. Numerical simulations indicate that optimum absorber damping ratio is not significantly related to the structural damping, especially when the displacement variance is minimized. Therefore, optimum damping ratio derived for undamped systems is proposed for damped systems for the displacement case. When acceleration variance is minimized, however, the optimum damping ratio derived for undamped systems is found not as accurate for damped systems. Therefore, a more accurate approximate expression is derived. Numerical comparisons with published approximate expressions at the same level of complexity indicated that proposed design formula yield more accurate estimates. Another important finding of the paper is that for specific applications where all of the response parameters are desired to be minimized simultaneously, DVAs designed per velocity criteria provide the best overall performance with the least complexity in the design equations.     

Damping in micro-scale generalized thermoelastic circular plate resonators

The out-of-plane vibrations of a generalized thermoelastic circular plate are studied under different environmental temperature, plate dimensions and boundary conditions. The analytical expressions for thermoelastic damping of vibration and phase velocity of circumferential surface wave modes are obtained. It is noticed that the damping of vibrations and phase velocities of circumferential surface wave modes significantly depend on thermal relaxation time in addition to thermoelastic coupling in circular plates under resonance conditions. The surface conditions also impose significant effects on the vibrations of such resonators. The expressions for displacement and temperature fields in the plate resonator are also derived and obtained. Some numerical results have also been presented for illustration purpose in case of silicon material plate.     

Semi-active on–off damping control of a dynamic vibration absorber using Coriolis force

A passive dynamic vibration absorber (DVA) moving along a pendulum can cause the nonlinear Coriolis damping to reduce the pendulum swing. This paper proposes a simple semi-active on–off damping controller to improve the passive Coriolis DVA. The aim of the on–off damping control is to amplify the DVA resonance motion to increase the energy dissipated. Moreover, the paper finds the analytical solution of the harmonic vibration of semi-active controlled system. The accuracy of the analytical formulas and the superior performance of the semi-active DVA are verified by numerical simulations.     

Vibration confinement and energy harvesting in flexible structures using collocated absorbers and piezoelectric devices

We propose an optimal design for supplementing flexible structures with a set of absorbers and piezoelectric devices for vibration confinement and energy harvesting. We assume that the original structure is sensitive to vibrations and that the absorbers are the elements where the vibration energy is confined and then harvested by means of piezoelectric devices. The design of the additional mechanical and electrical components is formulated as a dynamic optimization problem in which the objective function is the total energy of the uncontrolled structure. The locations, masses, stiffnesses, and damping coefficients of these absorbers and capacitances, load resistances, and electromechanical coupling coefficients are optimized to minimize the total energy of the structure. We use the Galerkin procedure to discretize the equations of motion that describe the coupled dynamics of the flexible structure and the added absorbers and harvesting devices. We develop a numerical code that determines the unknown parameters of a pre-specified set of absorbers and harvesting components. We input a set of initial values for these parameters, and the code updates them while minimizing the total energy in the uncontrolled structure. To illustrate the proposed design, we consider a simply supported beam with harmonic external excitations. Here, we consider two possible configurations for each of the additional piezoelectric devices, either embedded between the structure and the absorbers or between the ground and absorbers. We present simulations of the harvested power and associated voltage for each pair of collocated absorber and piezoelectric device. The simulated responses of the beam show that its energy is confined and harvested simultaneously.     

动力吸振器中库仑阻尼对吸振性能的影响

研究了动力吸振器中库仑阻尼(干摩擦)对吸振性能的影响。给出了库仑摩擦模型,在考虑了吸振器中的库仑阻尼的情况下,分析了库仑阻尼引起的主振动系统与附加质量块的2种相对运动状态(滑移和粘滞)以及它们存在和转换的条件,讨论了因库仑阻尼引起的吸振器自由度冻结现象;用Simulink仿真工具对非线性吸振器进行了数值仿真,研究了谐波和白噪声激励下库仑阻尼对吸振器吸振性能的影响以及库仑阻尼与线性阻尼的等效问题。结果显示:弱激励条件下,非线性吸振器减弱吸振效果,强激励条件下增强吸振效果。     

Vibration control of two degrees of freedom system using variable inertia vibration absorbers: Modeling and simulation

Variable inertia vibration absorbers (VIVA) are previously used for the vibration control of single degree of freedom (dof) primary systems. The performance of such absorbers is studied in many investigations. This paper presents the dynamic modeling and simulation of a proposed modified design of such VIVA’s for the vibration control of two dof primary systems. Lagrange formulation is used to obtain its dynamic model in an analytical form. This model, which is highly nonlinear, is used to develop a computational algorithm to study the absorber performance characteristics. This algorithm is programmed and simulated in Matlab. The obtained results are numerically verified using SAMS2000 software. The effect of mass and stiffness of the proposed VIVA on its performance and tuning is discussed. An optimization algorithm is developed to select the best absorber parameters for vibration suppression of a specific primary system. The obtained results show a good agreement with those obtained using similar techniques. In addition, a linearized model of VIVA dynamics is developed, tested and simulated for the same data used in its nonlinear model. The relative deviation between results of the linear and nonlinear models is less than 1%, which confirms the realistic use of this linearized model. The experimental testing and verification of the simulation results of the proposed VIVA is the subject of another paper.     

Tautochronic centrifugal pendulum vibration absorbers: General design and analysis

Since the 1930s, centrifugal pendulum vibration absorbers have been used in rotating and reciprocating machinery for the attenuation of torsional vibrations. A large variety of absorber types were suggested and the design was done by linearization theory until the introduction of the tautochronic bifilar pendulum absorbers. Since then, the performance and dynamic stability of this specific absorber type have been considered in analytical and numerical investigations. Different perturbations, e.g. nonlinear mistuning, were considered in order to optimize the system performance, but the characteristic bifilar design remained unchanged. In this paper, a general approach for the design of tautochronic pendulum vibration absorbers is proposed. As a result, it is possible to deal with a large variety of non-bifilar centrifugal vibration absorber designs which provide application-related optimal performance and resolve some of the existing design limitations.     

Design and Dynamics Investigation for a Silicone Rubber Shock Absorber

A new kind of coupling-type silicone rubber shock absorber was prepared. Vibration and static stiffness tests were carried out to investigate the characteristics of vibration control. A mechanical model of the shock absorber was established, and the working principle of the shock absorber was studied by comparing the vibration test with simulation results. The dynamic results show the shock absorber has excellent vibration control performance. The coupling characteristics originate from the contact of inner and outer silicone rubber. It is shown that the stiffness and damping coefficients in the coupling process are critical for vibration control of the shock absorber.     

Thermoelastic damping of the axisymmetric vibration of circular plate resonators

Thermoelastic damping is recognized as a significant loss mechanism at room temperature in micro-scale circular plate resonators. In this paper, the governing equations of coupled thermoelastic problems are established for axisymmetric out-of-plane vibration of circular plate. Then the analytical expression for thermoelastic damping is obtained. The effects of environmental temperature, plate dimensions and boundary conditions on the thermoelastic damping are studied.