Design Of Dynamic Vibration Absorber Research Articles

Enhancing the Design of Dynamic Vibration Absorbers through Harmonic Analysis and Lumped Parallel Configuration

Enhancing the Design of Dynamic Vibration Absorbers through Harmonic Analysis and Lumped Parallel Configuration

Concise analytical solutions to negative‐stiffness inerter‐based DVAs for seismic and wind hazards considering multi‐target responses

AbstractPractical engineering structures are subjected to hazardous seismic‐ and wind‐ induced vibrations during their lifetime. They should be designed based on capacity and serviceability targets. Similarly, the design of dynamic vibration absorbers (DVAs) should also meet multiple requirements. However, most current analytical approaches are based on a single‐target response and may lead to cumbersome expressions for complicated scenarios. To address these issues, concise solutions to negative‐stiffness inerter‐based DVAs are proposed in this paper. Firstly, a generic analytical optimization approach for H‐norm solutions considering different response targets of displacement, velocity, acceleration, and transmissibility, is established. Subsequently, the concise solutions are derived based on Taylor's expansion of these analytical solutions by ignoring higher‐order items of the equivalent mass ratio. Finally, the application scope and effectiveness of the proposed concise solutions are discussed. Consequently, the resulting concise solutions are proved to be located close to the pareto fronts of multi‐target optimization results. They have shown superior performances than conventional solutions in controlling the structural capacity and serviceability indicators of a practical five‐story steel frame case under dynamic wind and seismic hazards. Conclusively, the proposed concise solutions are simple in expression and reveal excellent multi‐target performances, which can provide guidance and insights for the optimal design of DVAs.

Equivalent linearization of hyperelastic rubber rings in dynamic vibration absorber boring bar and simulation of its dynamic properties

A slight perturbation in high-speed precision cutting could cause violent vibration of boring bars, resulting in unexpected wear and failure of the structures. In this paper, the dynamical characteristic of a boring bar with a dynamic vibration absorber (DVA) is investigated. Considering that the nonlinear characteristics of the rubber ring play a significant role in improving the capacity of DVA, we proposed an equivalent linearization method for modeling hyperelastic rubber rings based on the experimental data of uniaxial tensile test. The relationship between the stiffness of rubber rings and the precompression parameter δ is established for two types of rubber. The equivalent linearization model shows good accuracy and calculation efficiency while the mass of the DVA is confined to a narrow space and the assumption of small strain is inherently satisfied. Numerical results show that the time cost of the equivalent linearization model is only 5% of the full hyperelastic model. Furthermore, the effect of different spring stiffnesses and damping on the dynamic characteristics of the boring bar is compared by using the equivalent linearization model, and the vibration peak of the DVA boring bar is found to be reduced about 45%. Our findings establish a simplified modeling scheme for choosing rubber rings in design of dynamic vibration absorbers with acceptable accuracy and little time cost, which could also give some reference for modeling of metal rubber and gel-like materials.

A novel vertical elastic vibration reduction for railway vehicle carbody based on minimum generalized force principle

Aiming at the vertical elastic vibration reduction of a railway vehicle carbody, the traditional technology mainly focuses on the design of modal frequency, the method of increasing damping and the design of dynamic vibration absorber (DVA), with little attention to the design of modal shape. In this paper, a novel vertical elastic vibration reduction method based on the minimum generalized force principle (MGFP) is proposed, i.e., the vertical elastic vibration of carbody is reduced by adjusting its own parameters (weight distribution and stiffness distribution) to control the first-order vertical bending (FVB) modal shape nodes to the carbody–bogie interface positions. Firstly, to better apply MGFP, a factor called generalized force factor (GFF) that can determine the level of generalized force (GF) is proposed. By improving theoretical model of a railway vehicle carbody, the traditional uniform cross-section Euler–Bernoulli beam (UCEB) is replaced by variable cross-section Euler–Bernoulli beam (VCEB) model, and the influencing factors of modal frequency and modal shape node locations can be investigated by the VCEB model. Then, the vertical vehicle system dynamics model is established based on the VCEB carbody model, and the influence of weight distribution, stiffness distribution and carbody–bogie interface positions on the elastic vibration is analyzed under a sweep frequency signal and track irregularities. Finally, the vibration reduction method is verified by a full-scale roller rig test. The theoretical analysis and experimental results show that: by changing the weight distribution or stiffness distribution of the carbody, the FVB modal shape node locations can be effectively controlled, and then combined with the design of carbody–bogie interface positions, the vertical bending elastic vibration of the carbody can be reduced. The vibration reduction method proposed in this paper can be applied to the design of new carbodies or the layout optimization of carbody subsidiary mass.

Optimal Design of a Parallel-Type Double-Mass Dynamic Vibration Absorber Based on Stability Criterion

There are three typical criteria for design of dynamic vibration absorbers (DVAs): the H¥ optimization, H2 optimization,and stability maximization criteria. When single-mass, parallel-type double-mass, and series-type double-mass DVAs are optimized using these criteria, it has already been clarified that the effect of vibration suppression by the DVAs improves in the listed order. More specifically, if the vibration suppression performance of the parallel-type double-mass DVA is evaluated based on the H¥ and H2 optimization criteria, then it will be midway between the performances of the singlemass and series-type double-mass DVAs. However, if performance is evaluated by the stability criterion, that of the parallel-type double-mass DVA is only slightly improved relative to the single-mass DVA. Because the stability criterion for DVAs is a criterion for searching for the condition under which the characteristic equation of the vibratory system takes a repeated root, the characteristic root trajectories for the parallel-type double-mass DVA are compared with those for the series-type DVA in this paper.

Calculation of the <i>H</i><sub>∞</sub> Optimized Design of a Single-Mass Dynamic Vibration Absorber Attached to a Damped Primary System

There are three typical criteria used in the design of dynamic vibration absorbers (DVAs): H∞ optimization, H2 optimization, and stability maximization. In these criteria, in even the most basic single-mass DVA, the effect of primary system damping on the optimal solution is still not fully understood with respect to the H∞ criterion. This article presents exact algebraic equations for calculating the H∞-optimal solutions for a single-mass DVA attached to a damped primary system. In the H∞ optimization of the mobility transfer function, a highly accurate numerical solution was obtained by solving a single sixth-order algebraic equation. In the case of optimization of the compliance transfer function, it is shown that a highly accurate numerical solution can be obtained by solving a ternary system of simultaneous algebraic equations.

Weighted averaging technique for the design of dynamic vibration absorber installed in damped primary structures

The dynamic vibration absorber (DVA) has been widely applied in various technical fields. This paper presents a simple approach to determine a closed-form expression for the tuning ratio of a DVA attached to a damped primary structure. The result is obtained by using the so-called weighted averaging technique of the equivalent linearization method proposed by the first author. The values of the tuning ratio given in this paper are compared with those obtained numerically as well as the ones obtained from other authors. The comparison shows the reliability of the method given in this study.

Practical aspects of design, tuning, and application of dynamic vibration absorbers

Theory of dynamic vibration absorbers is a classic topic that has been thoroughly researched. Nevertheless, implementing the dynamic system in a structure and applying it properly still meet some challenges that have not been adequately addressed in the technical literature. Some of practical problems include achieving thermal stability, building a damped device with the desired undamped frequency, providing mechanisms for tuning or adjusting the dynamic absorber in situ, and effective tuning of multiple absorbers. The paper describes a new patented design of dynamic vibration absorber for optical tables together with the new method of tuning. The tuning procedure uses only one sensor and does not require access to the moving mass. Applications include suppressing flexural resonance vibrations of standard optical tables and the recent project on vibration control of large support bench for unique petawatt laser system at Lawrence Berkeley National Laboratory.

Fuzzy Robust Design of Dynamic Vibration Absorbers

This paper is dedicated to the development of robust optimization and decision making techniques taking into account the uncertain parameters of linear and nonlinear dynamic vibration absorbers. In this case, novel approaches are proposed regarding different fuzzy logic optimization strategies. The uncertain parameters of the considered mechanical systems are treated as fuzzy variables. Consequently, the associated optimization problem is described as a fuzzy function that maps the fuzzy inputs. The proposed techniques are applied to the design of dynamic vibration absorbers. This numerical study illustrates the versatility and convenience of the proposed fuzzy logic optimization strategies.

Improved design of dynamic vibration absorber by using the inerter and its application in vehicle suspension

Inerter is a recently proposed mechanical element with two terminals. The novelty of this paper is to present the improved design which aims to add traditional dynamic vibration absorber to the vehicle body by using the inerter. Based on this background, a new vehicle suspension structure called ISD suspension, including the inerter, spring and damper has been created. A dual-mass vibration model including the ISD suspension is considered in this study. Parameters are obtained by using the genetic optimizing algorithm. The frequency-domain simulation confirms that the ISD suspension can effectively improve the damping performance of the suspension system, especially at the offset frequency of the vehicle body, which is consistent with the feature of the dynamic vibration absorber added to the vehicle body mass. At last, a prototype ball screw inerter has been designed and the bench test of a quarter-car model has been undertaken. Under the conditions of the random road input, the vehicle ride comfort evaluation of body acceleration RMS value decreases by 4% at most, the suspension deflection RMS value decreases by 16% at most, the tire dynamic load RMS value decreases by 6% at most. Power spectral density results also indicate that the ISD suspension has superior damping performance than passive suspension which proves that the proposed ISD suspension is deemed effective.

A global-local approach to the design of dynamic vibration absorber for damped inverted pendulum structures

In practice, an inverted pendulum can be used to model many real structures as the arms of robots, soil structures, or fluid structures. However, the study on the design of dynamic vibration absorber for inverted pendulum structures is very limited in the literature. To the best knowledge of the authors, however, there has been no study on the dynamic vibration absorber when the primary inverted pendulum structure is damped. This paper deals with the optimization problem of dynamic vibration absorber for inverted pendulum structures. Two novel findings of the present study are summarized as follows. First, the optimal parameters of dynamic vibration absorber for undamped inverted pendulum structures are given by using \(H_{\infty }\) optimization. Second, the authors suggest a so-called global-local approach to determine approximate expressions for optimal parameters of a pendulum type absorber attached to a damped inverted pendulum structure. Finally, a numerical simulation is done for an example of the articulated tower in the ocean to validate the effectiveness of the results obtained in this work.

Global-local approach to the design of dynamic vibration absorber for damped structures

The dynamic vibration absorber (DVA) has attracted attention since its invention. This paper deals with the optimization problems of the standard DVA and two other models of DVA called three-element DVA and non-traditional DVA for damped primary structures. Unlike the standard configuration, the three-element DVA contains two spring elements in which one is connected to a dashpot in a series and the other is placed in parallel. Meanwhile the non-traditional DVA has a linear viscous damper connecting the absorber mass directly to the ground. There have been some studies on the design of three-element and non-traditional dynamic vibration absorbers in the case of undamped primary structures. These studies have shown that both three-element and non-traditional DVAs perform better than the standard DVA. When the primary structure is damped, there are very few studies on the three-element and non-traditional DVAs in the literature. This article proposes a global-local approach to give approximate analytical solutions of the optimization for all standard, three-element and non-traditional DVAs attached to damped primary structures. The main idea of the study is based on the global-local criterion of the equivalent linearization method in order to replace approximately the original damped structure by an equivalent undamped one. Afterwards, the already derived expressions of the optimal parameters for the undamped primary system case are used with the equivalent undamped structure that was just obtained. The numerical simulations are carried out to verify the effectiveness of the obtained results. Additionally, design aids, which show the variation of the optimal design quantities for various DVA mass ratios and inherent structural damping ratios are also provided.

Optimum design of dynamic vibration absorbers for a beam, based on H ∞ and H 2 Optimization

The solutions to H∞ and H2 optimization problems of a variant dynamic vibration absorber (DVA) applied to suppress vibration in beam structures are derived analytically. The H∞ optimum parameters such as tuning frequency and damping ratios are expressed based on fixed-point theory to minimize the resonant vibration amplitude, as well as, the H2 optimum parameters to minimize the total vibration energy or the mean square motion of a beam under random force excitation as analytical formulas. The reduction in maximum amplitude responses and mean square motion of a beam using the traditional vibration absorber is compared with the proposed dynamic absorber. Numerical results show the non-traditional DVA under optimum conditions has better vibration suppression performance on beam structures than the traditional design of DVA. Furthermore, comparing H∞ and H2 optimization procedures shows that for a beam under random force excitation, use of H2 optimum parameters resulting in smaller mean square motion than the other optimization.

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.

The Design of Dynamic Vibration Absorber on the Engine of Fire Smoke Exhausting Robot

The vibration of fire smoke exhausting robot affects a lot on running quality. The rotational speed of engine is fixed and the vibration of the robot’s engine has a certain dominant frequency, so a dynamic vibration absorber is possible to reduce the vibration. In this paper a typical structure has been designed, and the linear relationship between dominant frequency and engine speed has been surveyed. The elongation of the spring has been deduced to the only key parameter due to the linear relationship and determined speed. An evaluation standard of damping effect was set up, the maximum acceleration value and root mean square value of acceleration and relative value of acceleration were taken as the evaluation indexes. Comparison tests were made, the damping effect was taken into account. The experimental results demonstrate the practicability and effectiveness of the new simplified absorber.

A Study of the Effect of Cable Vibration on the Design of Dynamic Vivbariton Absoebers for Ropeway Carriers

This paper investigates the effect of cable vibration on the design of dynamic vibration absorbers for ropeway carriers which are suspended by cables. ln this analysis the ropeway carrier and cable were modeled with a lumped parameter method and an analytical Green's function was used to obtain the stiffness matrix of the cable system. The natural frequencies and mode shapes of the pendulum with cable system were determined in order to find a single equivalent pendulum by matching the kinetic energy of the two models. Using the equivalent pendulum, an optimum dynamic vibration absorber for the cable suspension carrier was designed. Experiments for the free vibration of the system were conducted to verify the modeling results and demonstrate the usefulness of this work.

Method for Design of Dynamic Vibration Absorbers with Viscoelastic Springs.

This paper deals with a new and simple method of optimum design of dynamic vibration absorbers which consist of viscoelastic springs and auxiliary masses. If the usual method of design of dynamic absorbers is applied to an absorber with a viscoelastic spring, the stiffness and the loss factor of the spring are determined as optimum values corresponding to the given ratio of the auxiliary mass to the principal mass. The actual value of the loss factor, however, cannot be chosen arbitrarily, because it depends on the material of the visco-elastic spring. In the proposed method, the optimum condition can be found for any combination of values of the mass ratio and the loss factor of the viscoelastic spring. Therefore, dynamic absorbers can be realized for springs of arbitrary viscoelastic materials.

Optimum design of dynamic absorbers for a system subject to random excitation.

This paper proposes an optimum method of design of dynamic vibration absorbers for a system subject to stationary random excitation with ideal white noise. The optimization criterion is to minimize a performance measure defined by the mean square acceleration response of the primary system to unit input acceleration. Optimum design parameters of the dynamic absorbers can be formulated if the primary system has no damping. If there is damping in the primary system, the optimum parameters are obtained from the solution of simultaneous equations. The optimum parameters obtained here are different from the former ones evaluated by the so-called Den Hartog's theory. This comes from the difference in the performance measure in these theories. The optimum parameters are tested on a vibratory model. The experiment makes, it clear that our theory is very useful for protecting the system from vibration induced by random excitation.