Traditional Dynamic Vibration Absorber Research Articles

Optimal grounded inerter-based dynamic vibration absorber for controlling inertial force-induced vibrations in rotating machines

ABSTRACT This paper proposes the optimal design of GIDVA for inertial force-induced vibrations reduction in rotating machinery considered as primary system. For this purpose, simple-to-use closed-form suboptimal design solutions were first derived based on the extended fixed point theory (EFPT). Then, the H ∞ optimization problem was formulated, which was reduced to solving a constrained system of multi-variable nonlinear equations. Thus, by considering the analytical solutions based on the EFPT as a starting point in order to accelerate the convergence of the system, the Newton-Raphson method was applied to numerically solve the nonlinear system equations for the range values of the mass ratio 1 % ≤ μ ≤ 10 % . For this range of values, the proposed GIDVA was compared with the traditional dynamic vibration absorber (TDVA) and the non-traditional dynamic vibration absorber (NDVA). The results of comparison shown that the proposed GIDVA is 47.76–70.66% and 44.82–70.54% superior to the optimized TDVA and NDVA, respectively, in the steady state vibrations suppression of primary system under inertial excitation, and can widen the effective frequency band 70.22–80.98% and 64.07–80.95% superior to TDVA and NDVA, respectively. These results were confirmed in the time domain simulation of the primary system response considered as a centrifuge pump. For this range of values, the proposed GIDVA was compared with the TDVA and the NDVA. The results of comparison shown that the proposed GIDVA is 47.76–70.66% and 44.82–70.54% superior to the optimized TDVA and NDVA, respectively, in the steady state vibrations suppression of primary system under inertial excitation and can widen the effective frequency band 70.22–80.98% and 64.07–80.95% superior to TDVA and NDVA, respectively. These results were confirmed in the time domain simulation of the primary system response considered as a centrifuge pump.

Theoretical and Experimental Analysis on Vibration Absorber with Particle Damping

To better suppress low-frequency vibrations of flexible manipulators induced by the rotation of motors and eccentricity, a novel type of tuned particle damper (TPD) is designed by combining the advantages of classical dynamic vibration absorber (DVA) and particle dampers (PD). Compared to traditional DVAs, this TPD can reduce additional mass and effectively broaden the frequency band of the DVA. Firstly, an equivalent theoretical model is established to describe the frequency tuning principle of the designed TPD. Based on the theory of a single particle damper, the equivalent damping and stiffness of the particles are calculated through an approximate approach. Then, a three-degree-of-freedom vibration model of the manipulator system with the TPD is built, and the dynamical characteristic of the primary resonance for the coupled system are analyzed by the perturbation method. Finally, the experimental platform is set up to verify the theoretical results. A manipulator is applied to test the low-frequency vibration absorption of the designed TPD, and the vibration suppression effect is discussed both in theoretical analysis and experiments.

H∞ Optimization of a Novel Maxwell Dynamic Vibration Absorber with Lever, Inerter, and Grounded Stiffness

In this paper, we propose a novel Maxwell dynamic vibration absorber (DVA) with lever, inerter, and grounded stiffness. Firstly, the governing equation of the coupled system is established. The analytical formula of the amplitude amplification factor of the primary system and the natural frequencies of the coupled system are derived. There are three fixed points in the amplitude–frequency response curve of the primary system, which are independent of damping. Then, based on H∞ optimization criterion, two possible optimal parameter designs of the proposed model are obtained. Considering the practical engineering application and ensuring the stability of the system, the optimal grounded stiffness ratio is selected, and six working ranges of inerter–mass ratio are calculated. Furthermore, the performance of the vibration reduction is compared for six cases. It is found that when the values of the mass ratio, lever amplification ratio, and inerter–mass ratio change in different intervals, and the optimal grounded stiffness ratio has different cases of negative, zero, and positive results. Especially when the stiffness coefficient of the viscoelastic Maxwell model and another grounded stiffness are positive at the same time, the vibration absorption effect is better theoretically. Finally, comparing with the traditional DVAs, the performance of the novel DVA is better under harmonic excitation and random excitation. The results could provide theoretical guidance for the design of inerter-based Maxwell-type DVA with a lever component.

Adaptive multiswarm particle swarm optimization for tuning the parameter optimization of a three-element dynamic vibration absorber

Abstract. A reliable optimization of dynamic vibration absorber (DVA) parameters is extremely important to analyze its dynamic damping characteristics and improve its vibration suppression performance. In this paper, we will discuss a parameter optimization method of the Voigt and three-element DVA models according to the H∞ optimization criterion. The particle swarm optimization method is an effective heuristic optimization algorithm; however, it is easy to lose diversity and fall into local extremum. To solve this problem, the adaptive multiswarm particle swarm optimization (AM-PSO) is used to search the solution of the DVA models. Particles in AM-PSO are adaptively divided into multiple swarms, and the variable substitution learning strategy is utilized to reduce their computational complexity and improve the algorithm's global search capability. In addition, the AM-PSO method is employed to optimize the parameters of DVA models and compared with the genetic algorithm and PSO. The simulation results show that the AM-PSO algorithm has superior performance. Also, the adaptive multiswarm numerical design method discussed herein will push the field towards practical applications, including traditional DVA and related complex three-element DVA.

A piecewise negative stiffness mechanism and its application in dynamic vibration absorber

AbstractA new type of piecewise negative stiffness (NS) mechanism is designed and the relationship between the force and displacement is studied. At first, the prototype of the piecewise NS mechanism is established, and the stiffness characteristic of this mechanism is analyzed. Then, the piecewise NS mechanism is applied to dynamic vibration absorber (DVA) system to establish a dynamic model with the piecewise linearity. The differential motion equations are derived according to Newton's law of mechanics. The approximate analytical solution and the amplitude frequency curve of the system with the piecewise NS are obtained by means of the averaging method. The correctness of the analytical solution is proved by comparing with the numerical solution. In the end, the comparisons with two other traditional DVAs show that the system in this paper has better vibration reduction effect under the condition of harmonic excitation and random excitation.

Research on vibration reduction performance of dynamic vibration absorber based on damping characteristic of a new material

The absorbing effect of traditional dynamic vibration absorber (TDVA) is satisfactory only when the natural frequency is close to the excitation frequency. For this defect, a semi-active vibration absorber is designed with magnetorheological elastomer (MRE) as a stiffness element, that its stiffness can be controlled by magnetic field, to widen the frequency band of the absorber. Theory and experiments show that reducing the damp of the absorber can improve the performance of the absorber at the anti-resonance point, but it will cause the vibration of the controlled system at the new resonance point, which caused by the addition of a DVA, to be more intense. For this problem, the compatibilizer: silane coupling agent KH570, is added to the preparation of MRE to reduce material damping, at the same time, the stiffness control strategy is used to eliminate the resonance of the controlled system caused by the addition of DVA. The final experimental results show that the frequency band of vibration reduction has been broadened effectively and the vibration reduction performance has been improved considerably. Moreover, the resonance has been eliminated very well.

Optimal design of inerter-based isolators minimizing the compliance and mobility transfer function versus harmonic and random ground acceleration excitation

This study is concerned with the problem of analysis and optimization of inerter-based systems. A main inerter system is generally composed of an inerter, a spring, and viscous damper. Series–parallel inerter systems and series inerter systems are two commonly used configurations of inerter-based systems. First, in this study, the H∞ optimum parameters of inerter-based isolators are derived to minimize the compliance and mobility transfer function of a single-degree-of-freedom system under a harmonic ground acceleration excitation. Under the optimum tuning condition, it is shown that the proposed inerter-based isolators when compared with the traditional dynamic vibration absorber provide larger suppression of the peak value of the magnitude of compliance and mobility transfer functions of the primary system. For the studied cases, more than 40% and 45% improvement can be attained in terms of minimizing the compliance and mobility transfer functions, respectively, as compared with the traditional dynamic vibration absorber for the series–parallel inerter system and 15% and 11% improvement can be attained respectively, for the series inerter system. Finally, further comparison between the inerter-based isolators and traditional dynamic vibration absorber under white noise excitation also shows that the series–parallel inerter system and series inerter systems are superior to the traditional dynamic vibration absorber. The results of the studied systems show that more than 23% and 16% improvement are attained in terms of minimizing the compliance and mobility transfer functions respectively, as compared with the traditional dynamic vibration absorber for the series–parallel inerter system and 26% and 13% improvement can be attained respectively, for the series inerter system. The optimal parameters for different cases are obtained. It is shown that the optimal parameters obtained using the minimized mobility transfer function are smaller than those using the compliance transfer function at all mass ratios or inertance-to-mass ratio. The results of this study can provide theoretical basis for design of the optimal inerter-based isolators in engineering practice.

Controlling the vibration and noise of a ballasted track using a dynamic vibration absorber with negative stiffness

In this study, a rail dynamic vibration absorber with negative stiffness is developed to reduce the vibration transmission and radiated noise from the rail components of a ballasted track. The compound models of the ballasted track system with and without the proposed dynamic vibration absorber and a traditional dynamic vibration absorber are constructed. A parametric study is performed to evaluate the effects of the design parameters of the proposed dynamic vibration absorber on the vibration and noise reduction of the track system in terms of the point receptance, the decay rate of rail vibration along the track, and the vibration energy level of the rail. Compared with the traditional dynamic vibration absorber, the proposed counterpart can work effectively over a broad frequency range around resonance. The efficiency of the dynamic vibration absorber can be improved by adjusting the design values of the active mass and damping coefficient. A comparison with the traditional dynamic vibration absorber shows that the vibration and noise suppression capability of the proposed one can be enhanced by increasing the value of the stiffness ratio. However, different from the traditional dynamic vibration absorber, the design parameters of the proposed one can also affect the decay rate and vibration energy at low-frequency regions. A discrete track with the proposed dynamic vibration absorber, which is arranged in continuous or discrete distribution along the rail, is illustrated to study the influences of the rail components on the decay rate and vibration energy level of rails. These calculated results could provide a theoretical basis for the design of the proposed dynamic vibration absorber in controlling the vibration and radiated noise from rails.

Eliminating the Fluid-Induced Vibration and Improving the Stability of the Rotor/Seal System Using the Inerter-Based Dynamic Vibration Absorber

A theoretical research on eliminating the instability vibration and improving the stability of the rotor/seal system using the inerter-based dynamic vibration absorber (IDVA) is presented in this paper. The modified Jeffcott rotor and Muszynska nonlinear seal force models are employed. The proposed IDVA is the damping element of the traditional dynamic vibration absorber (DVA) replaced by one of the six configurations of the inerter. The instability threshold speed of the system is obtained by applying the Routh–Hurwitz stability criterion. The quantum particle swarm optimization (QPSO) method is utilized to optimize the parameters of the IDVA. The numerical method is applied to investigate the nonlinear dynamic responses and stability. The results show that the IDVA can effectively improve the stability and reduce the instability vibration of the rotor/seal system. Furthermore, the performance of the IDVA is more effective than that of the traditional DVA.

Effect of Inerter in Traditional and Variant Dynamic Vibration Absorbers for One Degree-of-Freedom Systems Subjected to Base Excitations

Abstract In this paper, closed-form optimal parameters of inerter-based variant dynamic vibration absorber (variant IDVA) coupled to a primary system subjected to base excitation are derived based on classical fixed-points theory. The proposed variant IDVA is obtained by adding an inerter alone parallel to the absorber damper in the variant dynamic vibration absorber (variant DVA). A new set of optimum frequency and damping ratio of the absorber is derived, thereby resulting in lower maximum amplitude magnification factor than the inerter-based traditional dynamic vibration absorber (traditional IDVA). Under the optimum tuning condition of the absorbers, it is proved both analytically and numerically that the proposed variant IDVA provides a larger suppression of resonant vibration amplitude of the primary system subjected to base excitation. It is demonstrated that adding an inerter alone to the variant DVA provides 19% improvement in vibration suppression than traditional IDVA when the mass ratio is less than 0.2 and the effective frequency bandwidth of the proposed IDVA is wider than the traditional IDVA. The effect of inertance and mass ratio on the amplitude magnification factor of traditional and variant IDVA is also studied.

Investigation of the inerter-based dynamic vibration absorber for machining chatter suppression

This study proposes a novel approach to increase the chatter stability in machining operations. It shows the potential performance improvement when an inerter-based dynamic vibration absorber is employed in a machining operation. Tuned inerter based devices have been employed to decrease the magnitude of the vibrations in applications such as civil engineering structures and vehicle suspension systems but the nature of chatter in machining is different from these applications. Therefore, it requires a different tuning methodology to obtain the optimal design parameters. In this study, the machining operation is modelled as an undamped single degree of freedom system and different configurations of an inerter, a damper and two springs are used to ensure a stable region of operation. Strategies for the tuning parameters are developed both analytically and numerically. Using these techniques the performance improvement in the chatter stability provided by using inerter based devices instead of a traditional dynamic vibration absorber is demonstrated.

Optimal Design of an Inerter-Based Dynamic Vibration Absorber Connected to Ground

Abstract This paper addresses the optimal design of a novel nontraditional inerter-based dynamic vibration absorber (NTIDVA) installed on an undamped primary system of single degree-of-freedom under harmonic and transient excitations. Our NTIDVA is based on the traditional dynamic vibration absorber (TDVA) with the damper replaced by a grounded inerter-based mechanical network. Closed-form expressions of optimal parameters of NTIDVA are derived according to an extended version of fixed point theory developed in the literature and the stability maximization criterion. The transient response of the primary system is optimized when the coupled system becomes defective, namely having three pairs of coalesced conjugate poles, the proof of which is also spelt out in this paper. Moreover, the analogous relationship between NTIDVA and electromagnetic dynamic vibration absorber is highlighted, facilitating the practical implementation of the proposed absorber. Finally, numerical studies suggest that compared with TDVA, NTIDVA can decrease the peak vibration amplitude of the primary system and enlarge the frequency bandwidth of vibration suppression when optimized by the extended fixed point technique, while the stability maximization criterion shows an improved transient response in terms of larger modal damping ratio and accelerated attenuation rate.

Optimal design for high-performance passive dynamic vibration absorbers under random vibration

This work is motivated to determinate the optimal design for various types of Dynamic Vibration Absorbers (DVAs) under the effect of random loads. These devices are the following: DVAs connected in parallel or series; two degree-of-freedom traditional dynamic vibration absorber (2dof-TVA) with translational and rotational motion; and inerter-based DVAs (IDVA-C6, C4, and C3). These types of DVAs were selected by their high effectiveness for suppressing vibration however a comparative study on their dynamic performance has not yet been performed. Two different excitation sources of random loads are studied in this paper which are random ground motion and force excitation. An optimum design for majority of these devices has not yet been computed when subjected to random ground motion excitation, and therefore in this paper are computed. For random force excitation, some numerical solutions for the optimal design of these devices have not yet reported which in this paper are computed in order to compare the dynamic performance for each device with respect to that of the classic DVA. For both random excitation cases, the H2 optimization criteria is used to analytically compute the variance of squared modulus of frequency response of the undamped primary structure, and then nonlinear unconstrained optimization problems are formulated in order to obtain the optimal design. Numerical solutions revealed that the IDVA-C6, C3, and DVAs connected in series presents more than 13% and 10% improvement with respect to the classic DVA for random ground motion and force excitation cases, respectively. These devices can widen the suppression band (SB) from 30% to 40% for mass ratios values from 1% to 10%. It means that devices are more effective and robust for mitigating vibration than the classic DVA. In addition, the rotational inertial double tuned mass damper (IDVA-C6) has the same relative dynamic performance (RDP) and suppression band index (SB) than the double-mass dynamic vibration absorber arranged in series. For practical application where the mounting space of the DVA is extremely reduced, the DVAs connected in series could be more convenient to use than IDVA-C6. The concept of equivalent mass ratio is introduced in order to explain the superiority of these devices with respect to the classic DVA. Finally, in H∞ optimization criteria, the IDVA-C6 presents the same vibration amplitudes at all excitation frequency range and suppression band than DVAs connected in series.

Suppressing Random Response of a Regular Structure by an Inerter-Based Dynamic Vibration Absorber

AbstractThis paper concentrates on the random vibration suppression of a regular straight beam by using an inerter-based dynamic vibration absorber. For a wideband random point-driven straight beam with an inerter-based dynamic vibration absorber, the distribution of mean-square velocity response along the axis of the straight beam as well as the mean kinetic energy of the whole beam are first analytically derived through the classical linear random vibration theory. Two optimization objectives are established to determine the optimal design parameters: (1) minimizing the maximal mean-square velocity along the axis of the straight beam, which corresponds to the maximal mean kinetic energy density along the axis and (2) minimizing the mean kinetic energy of the whole beam. Numerical search gives the optimal location and the associated optimal parameters of the inerter-based dynamic vibration absorber. Numerical results for a simply supported straight beam illustrate the better performance of an inerter-based dynamic vibration absorber than a traditional dynamic vibration absorber. Parametric sensitivity studies for the robustness analysis of the beam response to deviations from the optimal parameters are conducted. The optimal location locates on the force-excited point, while the suboptimal location locates on its symmetry position. Furthermore, the optimal and suboptimal locations remain invariable regardless of the upper cutoff frequency of band-limited noise, which is fairly important to the location optimization of the inerter-based dynamic vibration absorber.

Optimal parameters for dynamic vibration absorber with negative stiffness in controlling force transmission to a rigid foundation

A dynamic vibration absorber (DVA) with negative stiffness is employed to control force transmission to a rigid foundation. The differential equation of motion is established. The necessary and sufficient conditions for stability are established by Routh–Hurwitz criterion and the stability boundary is obtained. The fixed-point theory is employed to obtain the optimum parameters of DVA stiffness ratio, negative stiffness ratio and damping ratio under given mass ratio. The optimal negative stiffness ratio is obtained based on the strategy to make the solution of the smaller fixed point approach zero. The comparison with the traditional DVA, the three-parameter isolator shows that the DVA with negative stiffness performs better in both force transmission control and mass response control under harmonic and random excitations. The transfer function of the system is below unity (or the normalized static deformation) in the entire frequency range. The comparison between force transmission control and mass response control of the primary system shows that the optimal parameters are not the same for the DVA with negative stiffness. The phase difference and balance between various forces is illustrated to study the mechanism of DVA with negative stiffness. This result could provide theoretical basis for design of DVA with negative stiffness.

Investigating the Optimal Damping Performance of a Composite Dynamic Vibration Absorber with Particle Damping

Damping system is a necessary ingredient of dynamic vibration absorber (DVA) for excellent vibration reduction performance. However, the supernumerary weight deriving from damping system is undesirable in engineering. Improving the damping performance of DVA is an important way to solve the question. A composite DVA with particle damper (PD) is proposed for reducing the additional mass of DVA and for improving the vibration control performance in this paper. The additional mass of particle damper as part of tuning mass fights against the vibration of primary system, and the damping effect of PD will be adequately inspired further to boost the damping ingredient of DVAs as a result of the strong resonance of tuning mass. In consideration of the strongly nonlinear of PD and damping effect relative to vibrating velocity at installed PD and the vibration reduction performance tightly relative to tuning rate and damping rate, optimal damping performances and these characteristics parameters of the composite DVA are investigated and optimized. The mathematical models of a composite DVA installed in spring mass systems are implemented using fixed-point theory and H2 optimization as opposed to viscous damping. The results indicate that vibration reduction performance of the composite DVA significantly outperforms traditional DVA and single PD, and the vibration of primary system can be effectively suppressed using the composite DVA with the optimal parameter from H2 optimization and especially adopting minimum value.

Application of a dynamic vibration absorber with negative stiffness for control of a marine shafting system

A dynamic vibration absorber (DVA) with negative stiffness is proposed to suppress the longitudinal vibration transmission along a marine shafting system. Stiffness models of the DVA with negative stiffness, which is composed of a rubber pad and a Belleville spring, are established. An analytical model of the shafting system with and without the proposed DVA is set up by employing the equivalent model of a propeller and employed to perform vibration control in the low frequency range. A stability analysis is carried out and optimal parameters of the DVA with negative stiffness are obtained. A parametric study is also carried out to investigate the influence of the parameters of the DVA and negative stiffness on the vibration suppression for a specific shaft. A design scheme to obtain the static and dynamic stiffness of Belleville springs under different operation conditions is given, which takes into consideration variation in oil stiffness of the thrust bearing and propeller static thrust. Compared with a traditional DVA, the proposed DVA with negative stiffness achieves enhanced vibration transmission suppression performance for a much broader absorber frequency range around resonance and with a much smaller size of mass, which is very favorable for a marine shafting system.

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.

Design optimization of a viscoelastic dynamic vibration absorber using a modified fixed-points theory.

A viscoelastic dynamic vibration absorber (VDVA) is proposed for suppressing infrasonic vibrations of heavy structures because the traditional dynamic vibration absorber equipped with a viscous damper is not effective in suppressing low frequency vibrations. The proposed VDVA has an elastic spring and a viscoelastic damper with frequency dependent modulus and damping properties. The standard fixed-points theory cannot be applied to derive the optimum design parameters of the VDVA because both its stiffness and damping are frequency dependent. A modified fixed-points theory is therefore proposed to solve this problem. H∞ design optimization of the proposed VDVA have been derived for the minimization of resonant vibration amplitude of a single degree-of-freedom system excited by harmonic forces or due to ground motions. The stiffness and damping of the proposed VDVA can be decoupled such that both of these two properties of the absorber can be tuned independently to their optimal values by following a specified procedure. The proposed VDVA with optimized design is tested numerically using two real commercial viscoelastic damping materials. It is found that the proposed viscoelastic absorber can provide much stronger vibration reduction effect than the conventional VDVA without the elastic spring.

Minimization of the beam response using inerter-based passive vibration control configurations

Two inerter-based passive vibration control configurations, i.e., a mass connected to a parallel combination of a spring and a damper in series with a spring and an inerter (Case I), and a traditional dynamic vibration absorber in series with an inerter (Case II), are proposed and are successfully applied to achieve the vibration suppression of beam-type structure. The frequency response functions of system displacement and acceleration are analytically derived through the classical vibration theory. The optimization problem of minimizing the maximum value of the frequency response function in the whole range or a certain range of frequency is expressed as a min-max problem and then the optimal parameters are derived numerically. Especially, for Case II the optimal system parameters can be analytically expressed by using the fixed-point theory. Numerical results show that the inerter-based passive vibration control configurations are more efficient than the traditional dynamic vibration absorber, especially for case with a small mass ratio. The inerter-based Case I is more efficient than the inerter-based Case II for a smaller mass ratio while contrary is true for a larger mass ratio. Also, the influences of the mass ratio and the inertance-to-mass ratio on the optimal system parameters are briefly discussed.