scholarly journals Optimal Design of a Damped Single Degree of Freedom Platform for Vibration Suppression in Harmonically Forced Undamped Systems

2013 ◽  
Vol 135 (5) ◽  
Author(s):  
Jimmy S. Issa
Keyword(s):  
Objective Function ◽  
Frequency Response Function ◽  
Damping Ratio ◽  
Optimal Solution ◽  
Vibration Absorber ◽  
Primary System ◽  
Mass Ratio ◽  
Optimal Damping ◽  
Mass Ratios ◽  
Invariant Points

Vibration reduction in harmonically forced undamped systems is considered using a new vibration absorber setup. The vibration absorber is a platform that is connected to the ground by a spring and damper. The primary system is attached to the platform, and the optimal parameters of the latter are obtained with the aim of minimizing the peaks of the primary system frequency response function. The minimax problem is solved using a method based on invariant points of the objective function. For a given mass ratio of the system, the optimal tuning and damping ratios are determined separately. First, it is shown that the objective function passes through three invariant points, which are independent of the damping ratio. Two optimal tuning ratios are determined analytically such that two of the three invariant points are equally leveled. Then, the optimal damping ratio is obtained such that the peaks of the frequency response function are equally leveled. The optimal damping ratio is determined in a closed form, except for a small range of the mass ratio, where it is calculated numerically from two nonlinear equations. For a range of mass ratios, the optimal solution obtained is exact, because the two peaks coincide with the two equally leveled invariant points. For the remaining range, the optimal solution is semiexact. Unlike the case of the classical absorber setup, where the absorber performance increases with increasing mass ratios, it is shown that an optimal mass ratio exists for this setup, for which the absorber reaches its utmost performance. The objective function is shown in its optimal shape for a range of mass ratios, including its utmost shape associated with the optimal mass ratio of the setup.

A Modified Optimal Design of a Vibration Absorber for Ground Motion Isolation

2014 ◽  
Author(s):  
Jimmy S. Issa
Keyword(s):  
Objective Function ◽  
Damping Ratio ◽  
Optimization Methods ◽  
Optimization Method ◽  
Design Guidelines ◽  
Vibration Absorber ◽  
Primary System ◽  
Optimal Parameters ◽  
Invariant Points ◽  
Downhill Simplex

Recently, a new vibration absorber setup was proposed where the absorber is placed between the dynamic system and its moving support. The problem was solved and design guidelines were proposed using the classical absorber design technique. In this work, the unique optimal absorber parameters are determined with the aim of minimizing the maximum of the primary system amplitude. For a given stiffness ratio of the system, the optimal mass and damping ratios are obtained analytically using an optimization method based on invariant points of the objective function. Similar to the case of the classical vibration absorber setup, these points are independent of the system damping ratio. It is shown that a trade-off relationship exists between these points, therefore the optimal mass ratio is determined first by a proper placement of the invariant points. Two suboptimal damping ratios are determined by forcing one of the two peaks of the objective function to coincide with one of the invariant points. Then, the optimal damping ratio is obtained from the average of the two suboptimal damping ratios. This approximate analytical solution is validated through comparison with the exact optimal parameters which were calculated numerically using two different numerical optimization methods. The first is based on the genetic algorithm technique and the second on the downhill simplex method. The optimal parameters are plotted and several examples are considered where the objective function is plotted in its approximate and exact optimal shapes.

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

2019 ◽  
Vol 23 (1) ◽  
pp. 9-16
Author(s):  
Dheepakram Laxmimala Barathwaaj ◽  
Sujay Yegateela ◽  
Vivek Vardhan ◽  
Vignesh Suresh ◽  
Devarajan Kaliyannan
Keyword(s):  
Damping Ratio ◽  
Maximum Amplitude ◽  
Vibration Absorber ◽  
Primary System ◽  
Base Excitation ◽  
Mass Ratio ◽  
Magnification Factor ◽  
Dynamic Vibration Absorber ◽  
Optimum Frequency ◽  
Dynamic Vibration

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.

The Use of the Fixed Points Method for Optimal Damping of Harmonically Forced Cantilever Beams

2011 ◽  
Author(s):  
Jimmy S. Issa
Keyword(s):  
Fixed Point ◽  
Objective Function ◽  
Frequency Response ◽  
Response Function ◽  
Frequency Response Function ◽  
Point Force ◽  
Cantilever Beams ◽  
Two Dimensional ◽  
Optimal Damping ◽  
Active Peak

The use of viscous dampers for vibration attenuation in harmonically forced cantilever beams is studied. The system considered is a cantilever beam with a point harmonic force applied at a given location and a viscous damper attached to it from one end, and grounded from the other. An assumed mode model of the system is derived using the first two transverse modes of the beam. For any given positions of the point force and damper, the optimal damping constant which minimizes the maximum of the frequency response function at the tip of the beam is determined analytically. It is shown that the objective function passes through a number of points independent of the damping constant. These inevitable points are used in the determination of the maximum allowable value of the objective function. As the locations of the point force and damper are varied separately from the fixed end of the beam to its tip, a two dimensional region plot is generated illustrating the different regions where each of these points is the highest. The optimal damping constant is determined analytically by forcing the frequency response function to pass horizontally through the highest fixed point which is referred to as the active peak. Four different damping ratios are determined and depending on the positions of the force and damper, the two dimensional map is consulted in the selection of the correct optimal damping ratio. The solution obtained is unique except when the active peak is the static fixed point. In this case, the solution is made unique by modifying the objective function to further enhance the solution at high frequencies.

Optimum Vibration Absorbers for Linear Damped Systems

1981 ◽  
Vol 103 (4) ◽  
pp. 908-913 ◽  
Author(s):  
S. E. Randall ◽  
D. M. Halsted ◽  
D. L. Taylor
Keyword(s):  
Damping Ratio ◽  
Maximum Amplitude ◽  
Vibration Absorber ◽  
Vibration Absorbers ◽  
Mass Ratio ◽  
Linear Vibration ◽  
Optimal Linear ◽  
Damped Systems ◽  
Independent Parameters ◽  
Qualitative Discussion

This paper presents computational graphs that determine the optimal linear vibration absorber for linear damped primary systems. Considered as independent parameters are the main system damping ratio and the mass ratio examined over the range 0 to 0.50 and 0.01 to 0.40, respectively. The remaining nondimensional parameters were optimized using numerical methods based on minimum-maximum amplitude criteria. With independent parameters specified the computational graphs can be used to find the response amplitudes as well as the optimal absorber characteristics. This procedure is illustrated in a design example. A qualitative discussion of the sensitivity to parameter errors is presented.

Investigation of dynamic characteristics of rolling particle dampers

2020 ◽  
pp. 107754632095745
Author(s):  
Takuya Kuriyama ◽  
Masato Saeki
Keyword(s):  
Granular Materials ◽  
Particle Diameter ◽  
Rotating Cylinder ◽  
Vibration Absorber ◽  
Harsh Environment ◽  
Primary System ◽  
Mass Ratio ◽  
Curved Track ◽  
Particle Dampers ◽  
Inside Wall

In this article, the investigation of the use of a rolling particle damper under sinusoidal excitation is described. A rolling particle damper is a type of ball vibration absorber and consists of a rotating cylinder placed on a curved track mounted on a primary system. The rotating cylinder is partially filled with granular materials. When the rotating cylinder rolls inside the curved track, the granular materials also move. The friction between the granular materials and the inside wall of the rotating cylinder results in some energy dissipation. A rolling particle damper can be adopted in a harsh environment because it can be operated in a wide temperature range. The effects of the mass ratio, the particle material, and the particle diameter on the damping performance were examined experimentally. To elucidate the behavior of the entire system in detail, a numerical solution using the discrete element method was established. The predicted damping results were compared with experimental results for various mass ratios. In addition, the effect of the frequency ratio on the highest displacement amplitude of the primary system was examined referring to the numerical results.

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

2019 ◽  
Vol 141 (5) ◽  
Author(s):  
Shaoyi Zhou ◽  
Claire Jean-Mistral ◽  
Simon Chesne
Keyword(s):  
Fixed Point ◽  
Optimal Design ◽  
Transient Response ◽  
Damping Ratio ◽  
Vibration Absorber ◽  
Practical Implementation ◽  
Primary System ◽  
Dynamic Vibration Absorber ◽  
Dynamic Vibration ◽  
The Stability

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.

Parameters optimization of dynamic vibration absorber based on grounded stiffness, inerter, and amplifying mechanism

2021 ◽  
pp. 107754632110382
Author(s):  
Peng Sui ◽  
Yongjun Shen ◽  
Shaopu Yang ◽  
Junfeng Wang
Keyword(s):  
Analytical Solution ◽  
Vibration Isolation ◽  
Damping Ratio ◽  
Vibration Absorber ◽  
Primary System ◽  
Vibration Absorbers ◽  
Stiffness Ratio ◽  
Dynamic Vibration Absorber ◽  
Dynamic Vibration ◽  
Dynamic Vibration Absorbers

In the field of dynamics and control, some typical vibration devices, including grounded stiffness, inerter and amplifying mechanism, have good vibration isolation and reduction effects, especially in dynamic vibration absorber (DVA). However, most of the current research studies only focus on the performance of a single device on the system, and those DVAs are gradually becoming difficult to meet the growth of performance demand for vibration control. On the basis of Voigt dynamic vibration absorber, a novel dynamic vibration absorber model based on the combined structure of grounded stiffness, inerter, and amplifying mechanism is presented, and the analytical solution of the optimal design formula is derived. First, the motion differential equation of the system is established, and the normalized amplitude amplification factor of the displacement is calculated. It is found that the system has three fixed points unrelated to the damping ratio. The optimal frequency ratio is obtained based on the fixed-point theory. In order to ensure the stability of the system, it is found that inappropriate inerter coefficient will cause the system instable when screening optimal grounded stiffness ratio. Accordingly, the best working range of inerter is determined. Finally, optimal grounded stiffness ratio and approximate optimal damping ratio are also obtained. The influence of inerter coefficient and magnification ratio on the response of the primary system is analyzed. The correctness of the derived analytical solution is verified by numerical simulation. Compared with other dynamic vibration absorbers, it is verified that presented model has superior vibration absorption performance and provides a theoretical basis for the design of a new type of dynamic vibration absorbers.

An Optimal Design Method for Rubber Dynamic Vibration Absorber

1995 ◽  
Author(s):  
Yoshihiro Satoh ◽  
Hiroshi Misawa
Keyword(s):  
Optimal Design ◽  
Objective Function ◽  
Design Method ◽  
Vibration Absorber ◽  
Response Functions ◽  
Mass Ratio ◽  
Dynamic Vibration Absorber ◽  
Dynamic Vibration ◽  
Optimal Values ◽  
Optimal Design Method

Abstract A dynamic vibration absorber can be used for suppression of excessive amplitude of structures at the resonance. This paper deals with an optimal design method for the dynamic vibration absorber which consists of a mass and a carbon-black filled rubber vulcanizate. First, a system which consists of a main system and the dynamic vibration absorber was analyzed, considering nonlinear dynamic properties possessed by the rubber vulcanizate. Frequency response functions of the system were derived in the form including the rubber geometry and a mass ratio as design parameters. Next, an objective function was composed of the frequency response functions. Minimizing the objective function with respect to the parameters of the rubber geometry for given mass ratio, the optimal values were determined. From the consideration of the results, a new convenient method to determine the optimal values was derived. This method was examined by the experiments. As a result, the validity of the analysis method was verified, and the availability of the present design method for the suppression of vibration was confirmed.

APPLICATION OF A TUNABLE ELECTROMAGNETIC DAMPER IN SUPPRESSION OF STRUCTURAL VIBRATION

2006 ◽  
Vol 30 (1) ◽  
pp. 41-61 ◽  
Author(s):  
Kefu Liu ◽  
Jie Liu ◽  
Liang Liao
Keyword(s):  
Damping Ratio ◽  
Step Change ◽  
Control Algorithms ◽  
Vibration Absorber ◽  
Primary System ◽  
Dynamic Vibration Absorber ◽  
Dynamic Vibration ◽  
Exciting Frequency ◽  
On Line ◽  
Electromagnetic Damper

An electromagnetic damper is developed to construct a tunable damped dynamic vibration absorber. The developed vibration absorber can suppress vibration of a structure subjected to a harmonic force with variable frequency. The damping of the vibration absorber can be adjusted on-line to cope with variation in the exciting frequency. The electromagnetic damper is composed of an electromagnet and a copper plate attached to the absorber mass. The relationship between the damping ratio and the damper current is discussed analytically. An experiment is conducted to determine the damping coefficients. A clamped-clamped beam is used as a primary system. The damper is connected between the absorber mass and the ground. This setup is referred to as skyhook dynamic vibration absorber in this study. The performance of a skyhook dynamic vibration absorber is compared with that of a groundhook dynamic vibration absorber where a damper is connected between the primary mass and the absorber mass. Two algorithms are proposed to tune the damper on-line. The first algorithm is FFT-based while the second one is rms-based. The control algorithms are tested against three frequency varying scenarios: multi-step change, linear change, and single-step change plus impact disturbance. Merits of each of the control algorithms are demonstrated.

Ground motion isolation using a newly designed vibration absorber

2011 ◽  
Vol 226 (3) ◽  
pp. 636-647 ◽  
Author(s):  
J S Issa
Keyword(s):  
Fixed Points ◽  
Structural Integrity ◽  
Damping Ratio ◽  
Optimal Shape ◽  
Vibration Absorber ◽  
Main Mass ◽  
Tuning Ratio ◽  
Optimal Damping ◽  
Mass Spring

A new vibration absorber setup for vibration attenuation in single degree of freedom systems subjected to harmonic base motion is proposed. The absorber is placed so as to separate between the vibrating ground and the main undamped system. It consists of a mas spring damper directly connected to the vibrating ground. The main system is modelled as a mass spring attached to the absorber's mass. The optimal absorber parameters are determined with the aim of reducing the steady-state amplitude of the main mass. It is shown that the amplitude of the main mass passes through three fixed points, two of which are used in the determination of the optimal shape of the transfer function. One of the fixed points is independent of the damping ratio and the second is independent of both the damping and tuning ratios. For this setup, the solution is not unique since the ultimate design is reached by a complete isolation of the main mass from the moving ground and is attained by removing the absorber's damper and stiffness. Since this solution is not physically achievable, for a given mass ratio of the system, the smallest tuning ratio which ensures structural integrity of the system is selected. The optimal damping ratio which yields the optimal shape of the objective function is determined analytically in terms of the mass and tuning ratios. A design flowchart is presented to be used for the design of such absorbers.

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