Optimum Tuning Ratio Research Articles

Optimization of a Non-Traditional Vibration Absorber for Vibration Suppression and Energy Harvesting

This paper investigates the optimization of a non-traditional vibration absorber for simultaneous vibration suppression and energy harvesting. Unlike a traditional vibration absorber, the non-traditional vibration absorber has its damper connected between the absorber mass and the base. An electromagnetic energy harvester is used as a tunable absorber damper. This non-traditional vibration absorber is attached to a primary system that is subjected to random base excitation. An analytical study is conducted by assuming that the base excitation is white noise. In terms of vibration suppression, the objective of the optimization is to minimize the power dissipated by the primary damper and maximize the power dissipated by the absorber damper. It is found that when the primary system is undamped, the power dissipated by the absorber damper remains a constant that is related to the mass ratio. The higher the mass ratio, the higher the power dissipated. When the primary system is damped, the minimization of the power dissipated by the primary damping is equivalent to the maximization of the power dissipated by the absorber damper. The existence of the optimum solutions depends on both the mass ratio and the primary damping ratio. In terms of energy harvesting, the objective of optimization is to maximize the power harvested by the load resistor. It is found that for a given mass ratio and primary damping ratio, the optimum frequency tuning ratio required to maximize vibration suppression is slightly higher than that required to maximize the harvested power. The trade-off issue between vibration suppression and energy harvesting is investigated. An apparatus is developed to allow frequency tuning and damping tuning. Both the numerical simulation and experimental study with band-limited white noise validate the general trends revealed in the analytical study.

Design and Experimental Implementation of a Passive Dynamic Vibration Absorber to Attenuate Broadband Vibration

The challenge of designing an effective vibration absorber for any mechanical or mechatronic system is formidable. A good vibration absorber must provide broadband vibration reduction yet still keep in lightweight and size to minimize space requirements and maximize equipment accessibility. Broadband vibration is usually attenuated by using an active or semi-active vibration absorber. However, these methods are relatively costly and complicated compared with a passive vibration absorber. Moreover, passive vibration absorber often limited to narrowband frequency reduction since, in the past, it is usually tuned to the targeted frequency or optimum damping and optimum tuning ratio. This paper demonstrated that a passive vibration absorber could be implemented to reduce the broadband vibration of a system, considering the effect of the parameter of passive vibration absorber, the location attachment of the absorber, and the targeted mode shape. The result shows that a properly tuned passive vibration absorber can reduce the root mean square amplitude vibration by 60.91%, covering the first four vibration modes (0 to 300Hz).

Design of a tuned mass damper for damped structures using an orthogonal-function-based equivalent linearization method

One of the most popular strategies of dissipating vibration energy in engineering structures is to use vibration absorbers. The selection of optimum absorber parameters is extremely important, especially for tuned mass dampers (TMD). Various approximate and numerical methods have been proposed to determine the optimum tuning ratio of a TMD attached to a damped linear structure, of which the application is limited either to lightly damped structures or specific forms of external excitation. In particular, the latter constrains the implementation of these existing methods to many practical engineering problems where the external excitations are typically random. In the current study, a new approach of identifying the optimum tuning ratio of a TMD in a damped primary linear structure is proposed based on an orthogonal-function-based equivalent linearization (EL) method. The effectiveness of the proposed TMD design approach is evaluated by numerical examples and two benchmark buildings. Results show that the proposed method cannot only accurately choose the optimum parameters of a TMD, but is also applicable to a structure having a relatively high mass and/or damping ratio and is subjected to random external excitations. The proposed method is an alternative approach to tune the TMD for damped structures, in methodological terms.

Optimum Design of a New Tuned Inerter-Torsional-Mass-Damper Passive Vibration Control for Stochastically Motion-Excited Structures

Abstract The inerter is referred to as a two-terminal device that provides inertial forces proportional to the relative accelerations between its two terminals. It has been widely applied in vibration control due to its mass amplification effect. In this paper, a new inerter-based damper is proposed to take advantage of the mass amplification effect, which consists of the classic rack-pinion inerter in conjunction with a torsional tuned mass damper. Unlike any other topologies of inerter-based dampers, the torsional mass damper is connected to the pinion of the inerter via a rotational spring and viscous damper. As a result, the weight of the torsional mass damper can be significantly reduced. The proposed damper is applied to single-degree-of-freedom primary structures and a two degrees-of-freedom structure, and the H2 optimization is conducted to obtain the optimum tuning ratio and damping ratio analytically. When comparing the proposed damper with its counterpart reported in the literature, the proposed damper achieves 20–70% improvement when their weights are identical.

Optimal design of a beam-based dynamic vibration absorber using fixed-points theory

The addition of a dynamic vibration absorber (DVA) to a vibrating structure could provide an economic solution for vibration suppressions if the absorber is properly designed and located onto the structure. A common design of the DVA is a sprung mass because of its simple structure and low cost. However, the vibration suppression performance of this kind of DVA is limited by the ratio between the absorber mass and the mass of the primary structure. In this paper, a beam-based DVA (beam DVA) is proposed and optimized for minimizing the resonant vibration of a general structure. The vibration suppression performance of the proposed beam DVA depends on the mass ratio, the flexural rigidity and length of the beam. In comparison with the traditional sprung mass DVA, the proposed beam DVA shows more flexibility in vibration control design because it has more design parameters. With proper design, the beam DVA's vibration suppression capability can outperform that of the traditional DVA under the same mass constraint. The general approach is illustrated using a benchmark cantilever beam as an example. The receptance theory is introduced to model the compound system consisting of the host beam and the attached beam-based DVA. The model is validated through comparisons with the results from Abaqus as well as the Transfer Matrix method (TMM) method. Fixed-points theory is then employed to derive the analytical expressions for the optimum tuning ratio and damping ratio of the proposed beam absorber. A design guideline is then presented to choose the parameters of the beam absorber. Comparisons are finally presented between the beam absorber and the traditional DVA in terms of the vibration suppression effect. It is shown that the proposed beam absorber can outperform the traditional DVA by following this proposed guideline.

Optimum LCVA for suppressing harmonic vibration of damped structures

Explicit design formulae of liquid column vibration absorber (LCVA) for suppressing harmonic vibration of structures with small inherent structural damping are developed in this study. The developed design formulae are also applicable to the design of a tuned mass damper (TMD) and a tuned liquid column damper (TLCD) for damped structures under harmonic force excitation. The optimum parameters of LCVA for suppressing harmonic vibration of undamped structures are first derived. Numerical searching of the optimum parameters of tuned vibration absorber system for suppressing harmonic vibration of damped structure is conducted. Explicit formulae for these optimum parameters are then obtained by a series of curve fitting techniques. The analytical result shows that the control performance of TLCD for reducing harmonic vibration of undamped structure is always better than that of non-uniform LCVA for same mass and length ratios. As for the effects of structural damping on the optimum parameters, it is found that the optimum tuning ratio decreases and the optimum damping ratio increases as the structural damping is increased. Furthermore, the optimum head loss coefficient is inversely proportional to the amplitude of excitation force and increases as the structural damping is increased. Numerical verification of the developed explicit design expressions is also conducted and the developed expressions are demonstrated to be reasonably accurate for design purposes.

Parameters Optimization for a Kind of Dynamic Vibration Absorber with Negative Stiffness

A new type of dynamic vibration absorber (DVA) with negative stiffness is studied in detail. At first, the analytical solution of the system is obtained based on the established differential motion equation. Three fixed points are found in the amplitude-frequency curves of the primary system. The design formulae for the optimum tuning ratio and optimum stiffness ratio of DVA are obtained by adjusting the three fixed points to the same height according to the fixed-point theory. Then, the optimum damping ratio is formulated by minimizing the maximum value of the amplitude-frequency curves according toH∞optimization principle. According to the characteristics of negative stiffness element, the optimum negative stiffness ratio is also established and it could still keep the system stable. In the end, the comparison between the analytical and the numerical solutions verifies the correctness of the analytical solution. The comparisons with three other traditional DVAs under the harmonic and random excitations show that the presented DVA performs better in vibration absorption. This result could provide theoretical basis for optimum parameters design of similar DVAs.

Tuned liquid column ball damper for seismic vibration control

Summary Tuned liquid column damper (TLCD) is a passive control device for vibration control of structures. Recently, the tuned liquid column ball damper (TLCBD) has been introduced for performance enhancement over the original TLCD. In this paper, the efficiency of the TLCBD is assessed under random earthquake events. The response of a single-degree-of-freedom system with TLCBD is evaluated by stochastic analysis and compared with the TLCD. The study reveals significantly improved performance of TLCBD over TLCD in terms of reducing response of the structure as well as the liquid column. The performance largely hinges on the optimum tuning ratio and the ball-to-tube diameter ratio values, which are proposed herein. The parametric studies establish the performance robustness of the TLCBD under loading and parametric variations. Furthermore, the accuracy of the optimal stochastic responses is verified through deterministic response analysis under recorded seismic motions. Copyright © 2015 John Wiley & Sons, Ltd.

Design of TMD for damped linear structures using the dual criterion of equivalent linearization method

Abstract Design of tuned mass damper (TMD) for damped linear structures has attracted considerable attention in recent years. Some approximate expressions of optimal tuning ratio of a TMD attached to a damped linear structure have been proposed. In the paper, another closed-form expression for the optimum tuning ratio is presented for two models, excitation force and ground motion. This approximate analytical solution is obtained by using improved equivalent linearization method according to dual criterion. The values of optimum tuning ratio derived from the expression proposed in the present study have been compared with those obtained numerically and from results investigated by other authors. The comparisons have verified the accuracy of the suggested expression for both small and large structural damping.

Extension of equivalent linearization method to design of TMD for linear damped systems

SUMMARY The vibration absorber has been used in many applications since invented. In the case of vibration control by the tuned mass damper (TMD), the selection of optimum absorber parameters is extremely important. This paper presents a closed-form expression for the optimum tuning ratio of a TMD attached to a damped primary system. The result is obtained by using equivalent linearization method. The values of the optimum tuning ratio derived from the expression proposed in this paper have been compared with those obtained numerically as well as the results obtained from other authors. These values are reliable even the mass ratio of TMD to the primary structure and the structural damping ratio are quite high. A simulation study has also been carried out to illustrate the obtained results. Copyright © 2011 John Wiley & Sons, Ltd.

Alternative Approach to Optimal Tuning Parameter of Liquid Column Damper for Seismic Applications

A closed-form solution for the optimum tuning ratio of a liquid column damper (LCD) that is valid for damped structures subjected to generalized seismic loading is presented. The closed-form expression is based on the extension of the theory of “fixed-point” frequencies for a classical undamped structure-mass damper system to damped structure-nonlinear LCD system. For the specific case of white noise input, the values of optimum tuning ratio have been compared with those obtained from a standard expression.

A closed-form optimal tuning criterion for TMD in damped structures

The selection of optimum absorber parameters is of utmost importance in the case of vibration control by the tuned mass damper (TMD). This paper presents an alternative expression for the optimum tuning ratio of the TMD. It has been derived in closed-form, based on the ‘fixed-point’ theory of Den Hartog which had been proposed for the case of undamped structural systems. The present expression has the advantage of being applicable for damped structures. The values of the optimum tuning ratio have been derived from the expression proposed in this paper for different structural and damper parameters. These values of optimum tuning ratio have been compared with those obtained from existing theories as well as from those obtained numerically. A simulation study has also been carried out to examine the performance of the optimally designed TMD. Copyright © 2006 John Wiley & Sons, Ltd.

Closed-Form Solutions to the Exact Optimizations of Dynamic Vibration Absorbers (Minimizations of the Maximum Amplitude Magnification Factors)

A typical design problem for which the fixed-points method was originally developed is that of minimizing the maximum amplitude magnification factor of a primary system by using a dynamic vibration absorber. This is an example of usual cases for which their exact solutions are not obtained by the well-known heuristic approach. In this paper, more natural formulation of this problem is studied, and algebraic closed-form exact solutions to both the optimum tuning ratio and the optimum damping coefficient for this classic problem are derived under assumption of undamped primary system. It is also proven that the minimum amplitude magnification factor, resonance and anti-resonance frequencies are entirely algebraic.

Optimal Performance of the TLCD in Structural Pitching Vibration Control

A detailed optimal parametric study is performed for a tuned liquid column damper (TLCD) in suppressing the pitching vibration of structures. Due to the difficulty of finding analytical solutions for the damped structure, a numerical optimization approach is proposed and applied to the system to find the optimum TLCD parameters. The variations of the optimum control parameter with system parameters are determined and discussed. Using various numerical searching data, a set of practical design formulas for the optimum tuning ratio and optimum head loss coefficient of the TLCD are then derived through regression analysis. The comparison between practical design formula and numerical optimization shows a very close agreement between the two results. The practical design formulas provide a convenient tool for designers. In order to account for the possible effects of structural uncertainties, a parametric sensitivity study on the de-tuning of optimum damper parameters is also carried out. It is found that the detuning effect is more severe for low damped structure with lower ratios of mass moment of inertia, especially for the detuning of tuning ratio.

OPTIMUM PARAMETERS OF TUNED LIQUID COLUMN DAMPER FOR SUPPRESSING PITCHING VIBRATION OF AN UNDAMPED STRUCTURE

In order to evaluate the control performance of the tuned liquid column damper in suppressing pitching vibration of structures, an optimal parametric study of the damper is carried out for an undamped structure. The structure is assumed to be subjected to harmonic excitation in the analysis. The optimum tuning ratio (or the optimum liquid length) and the optimum head loss coefficient of the damper are determined using Den Hartog's method. Theanalytical formulas of the optimum TLCD parameters for the undamped structure are derived. The optimum peak amplitudes for the structure and the liquid are also obtained. Based on the developed analytical formulas, the practical solution procedures for finding the optimum parameters are proposed. The presented example indicates that the optimum TLCD parameters can be easily calculated from the developed formulas. With the help of this study, the understanding of TLCD behavior with respect to its optimum parameters is enhanced.

Optimization of tuned liquid column dampers

The effectiveness of a tuned liquid column damper (TLCD) in controlling structural vibration is studied. A numerical method is adopted to account for nonlinearity of the governing equation. Optimum parameters of the TLCD for maximum reduction of peak structural response to harmonic excitations in a wide frequency range are presented for a wide range of flexible structures. A variation of U-shaped TLCD with different cross-sectional areas in its vertical and horizontal sections is investigated. It is found that an increase in cross-sectional area ratio (vertical/horizontal) can greatly reduce the length requirement of a TLCD making it more attractive to flexible structures. A new type V-shaped TLCD is also investigated. This type of TLCD can suppress stronger vibrations such as those caused by strong wind. It is found that, like the tuned mass damper (TIVID), there is an optimum tuning ratio (damper frequency/structure frequency) for maximum reduction in response of a structure system which is independent of the excitation. The optimum coefficient of head loss will depend on the intensity of the excitation with smaller coefficient of head loss associated with stronger excitation.

High Flux Ion, and Odd Multi-Half Wave Length Resonant Transformer Accelerators in the Space and Time Domains

This paper carried out analytical work for identification of beam instabilities in the high flux ion collective accelerator generated by MHD effects. Density as well as beam velocity deviations are observed with the effect of incremental change in electron temperature. Also for the resonant transformer collective accelerator, dynamic model has been derived indicating the dependence of the accelerating potential with respect to various system parameters, establishing steady state stability limit and optimum tuning ratio at resonance.