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 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.

The Effect of Different Optimization Methods on Robustness for Robust Optimization Design

2014 ◽  
Vol 721 ◽  
pp. 464-467
Author(s):  
Tao Fu ◽  
Qin Zhong Gong ◽  
Da Zhen Wang
Keyword(s):  
Robust Optimization ◽  
Objective Function ◽  
Robust Design ◽  
Optimization Design ◽  
Optimization Methods ◽  
Optimization Method ◽  
Design Parameters ◽  
Hybrid Particle Swarm Optimization ◽  
Design Variables ◽  
Robust Optimization Design

In view of robustness of objective function and constraints in robust design, the method of maximum variation analysis is adopted to improve the robust design. In this method, firstly, we analyses the effect of uncertain factors in design variables and design parameters on the objective function and constraints, then calculate maximum variations of objective function and constraints. A two-level optimum mathematical model is constructed by adding the maximum variations to the original constraints. Different solving methods are used to solve the model to study the influence to robustness. As a demonstration, we apply our robust optimization method to an engineering example, the design of a machine tool spindle. The results show that, compared with other methods, this method of HPSO(hybrid particle swarm optimization) algorithm is superior on solving efficiency and solving results, and the constraint robustness and the objective robustness completely satisfy the requirement, revealing that excellent solving method can improve robustness.

scholarly journals Optimal parameters of dynamic vibration absorber for linear damped rotary systems subjected to harmonic excitation

2020 ◽  
Author(s):  
Vu Duc Phuc ◽  
Tong Van Canh ◽  
Pham Van Lieu
Keyword(s):  
Vibration Suppression ◽  
Fixed Point Theory ◽  
Damping Ratio ◽  
Harmonic Excitation ◽  
Tuning Parameter ◽  
Vibration Absorber ◽  
Optimal Parameters ◽  
Dynamic Vibration Absorber ◽  
Practical Applications ◽  
Dynamic Vibration

Dynamic vibration absorber (DVA) is a simple and effective device for vibration absorption used in many practical applications. Determination of suitable parameters for DVA is of significant importance to achieve high vibration reduction effectiveness. This paper presents a   method to find the optimal parameters of a DVA attached to a linear damped rotary system excited by harmonic torque. To this end, a closed-form formula for the optimum tuning parameter is derived using the fixed-point theory based on an assumption that the damped rotary systems are lightly or moderately damped. The optimal damping ratio of DVA is found by solving a set of non-linear equations established by the Chebyshev's min-max criterion. The performance of the proposed optimal DVA is compared with that obtained by existing optimal solution in literature. It is shown that the proposed optimal parameters are possible to obtain superior vibration suppression compared to existing optimal formula. Extended simulations are carried out to examine the performance of the optimally designed DVA and the sensitivity of the optimum parameters. The simulation results show that the improvement of the vibration performance on damped rotary system can be as much as 90% by using DVA.

scholarly journals A PROCEDURE FOR OPTIMAL DESIGN OF A DYNAMIC VIBRATION ABSORBER INSTALLED IN THE DAMPED PRIMARY SYSTEM BASED ON TAGUCHI’S METHOD

2018 ◽  
Vol 56 (5) ◽  
Author(s):  
Nguyen Van Khang
Keyword(s):  
Optimal Design ◽  
Vibration Absorber ◽  
Primary System ◽  
Taguchi’S Method ◽  
Optimal Parameters ◽  
Dynamic Vibration Absorber ◽  
Dynamic Vibration ◽  
Comparison Results

The dynamic vibration absorber (DVA) has been widely applied in various technical fields. This paper presents a  procedure for designing the optimal parameters of  a dynamic vibration absorber attached to a damped primary system. The values of the optimal parameters of the DVA obtained by the Taguchi’s method are compared by the results obtained by other methods. The comparison results show the advantages of the procedure presented in this study

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.

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

2020 ◽  
pp. 107754632094017
Author(s):  
Marcial Baduidana ◽  
Aurelien Kenfack-Jiotsa
Keyword(s):  
Transfer Function ◽  
Vibration Absorber ◽  
Engineering Practice ◽  
Primary System ◽  
Optimal Parameters ◽  
Dynamic Vibration Absorber ◽  
Ground Acceleration ◽  
Dynamic Vibration ◽  
Optimum Parameters ◽  
Peak Value

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 system s and series inerter system s are two commonly used configurations of inerter-based system s . 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 function s 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 function s , 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 system s are superior to the traditional dynamic vibration absorber . The results of the studied systems show that m ore than 23% and 16% improvement are attained in terms of minimizing the compliance and mobility transfer function s 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.

Optimal Distribution of Damping Coefficients for Viscous Dampers in Buildings

2017 ◽  
Vol 17 (04) ◽  
pp. 1750054 ◽  
Author(s):  
Tzu Kang Lin ◽  
Jenn Shin Hwang ◽  
Kuan Hui Chen
Keyword(s):  
Damping Ratio ◽  
Optimization Method ◽  
Design Guidelines ◽  
Damping Coefficient ◽  
Optimal Distribution ◽  
Viscous Dampers ◽  
Moment Frame ◽  
Practical Applications ◽  
Soft Story ◽  
Damping Coefficients

Design guidelines for implementing viscous dampers to buildings have been broadly included in seismic design codes worldwide. Although the relationship between the damping coefficient of viscous dampers and the added damping ratio to the structure has been theoretically studied, the process of distributing the damping coefficient onto each story of a building has not been regulated by the codes. For practical applications, some distribution methods have been previously proposed. However, no comparison has been made between these proposed methods considering the controllability and design economy. In this paper, two search methods based on the genetic algorithms (GAs) are adopted to examine the optimal distribution of damping coefficients. The results are then compared with a variety of existing distribution methods. A comparison is made for the distribution methods assuming the same added damping ratio for the structure. Three two-dimensional frames are adopted in the comparison: a regular moment frame, a moment frame with a soft-story, and a setback building. The results indicated that similar seismic response reduction can be achieved by using different distribution methods if the supplemental damping ratio is the same, while the optimal story damping coefficient can be obtained by using the proposed optimization method. Moreover, the “story shear strain energy to efficient stories” (SSSEES) method, among others, offers advantages in terms of seismic reduction efficiency, economical design, and practical application simplicity.

scholarly journals Calibration of the modified Bartlett-Lewis model using global optimization techniques and alternative objective functions

2012 ◽  
Vol 16 (3) ◽  
pp. 873-891 ◽  
Author(s):  
W. J. Vanhaute ◽  
S. Vandenberghe ◽  
K. Scheerlinck ◽  
B. De Baets ◽  
N. E. C. Verhoest
Keyword(s):  
Global Optimization ◽  
Optimization Methods ◽  
Optimization Method ◽  
Optimization Techniques ◽  
Objective Functions ◽  
Local Search Algorithms ◽  
Stochastic Point Process ◽  
Shuffled Complex Evolution ◽  
Global Optimization Methods ◽  
Downhill Simplex

Abstract. The calibration of stochastic point process rainfall models, such as of the Bartlett-Lewis type, suffers from the presence of multiple local minima which local search algorithms usually fail to avoid. To meet this shortcoming, four relatively new global optimization methods are presented and tested for their ability to calibrate the Modified Bartlett-Lewis Model. The list of tested methods consists of: the Downhill Simplex Method, Simplex-Simulated Annealing, Particle Swarm Optimization and Shuffled Complex Evolution. The parameters of these algorithms are first optimized to ensure optimal performance, after which they are used for calibration of the Modified Bartlett-Lewis model. Furthermore, this paper addresses the choice of weights in the objective function. Three alternative weighing methods are compared to determine whether or not simulation results (obtained after calibration with the best optimization method) are influenced by the choice of weights.

scholarly journals Calibration of the modified Bartlett-Lewis model using global optimization techniques and alternative objective functions

2011 ◽  
Vol 8 (6) ◽  
pp. 9707-9756 ◽  
Author(s):  
W. J. Vanhaute ◽  
S. Vandenberghe ◽  
K. Scheerlinck ◽  
B. De Baets ◽  
N. E. C. Verhoest
Keyword(s):  
Time Series ◽  
Global Optimization ◽  
Optimization Methods ◽  
Optimization Method ◽  
Optimization Techniques ◽  
Rainfall Time Series ◽  
Stochastic Point Process ◽  
Shuffled Complex Evolution ◽  
Global Optimization Methods ◽  
Downhill Simplex

Abstract. The use of rainfall time series for various applications is widespread. However, in many cases historical rainfall records lack in length or quality for certain practical purposes, resulting in a reliance on rainfall models to supply simulated rainfall time series, e.g., in the design of hydraulic structures. One way to obtain such simulations is by means of stochastic point process rainfall models, such as the Bartlett-Lewis type of model. It is widely acknowledged that the calibration of such models suffers from the presence of multiple local minima which local search algorithms usually fail to avoid. To meet this shortcoming, four relatively new global optimization methods are presented and tested for their abilities to calibrate the Modified Bartlett-Lewis Model (MBL). The list of tested methods consists of: the Downhill Simplex Method (DSM), Simplex-Simulated Annealing (SIMPSA), Particle Swarm Optimization (PSO) and Shuffled Complex Evolution (SCE-UA). The parameters of these algorithms are first optimized to ensure optimal performance, after which they are used for calibration of the MBL model. Furthermore, this paper addresses the issue of subjectivity in the choice of weights in the objective function. Three alternative weighing methods are compared to determine whether or not simulation results (obtained after calibration with the best optimization method) are influenced by the choice of weights.

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