Exact Solutions to H∞ and H2 Optimizations of Passive Resonant Shunt Circuit for Electromagnetic or Piezoelectric Shunt Damper

2019 ◽  
Vol 141 (3) ◽  
Author(s):  
Toru Ikegame ◽  
Kentaro Takagi ◽  
Tsuyoshi Inoue
Keyword(s):  
Exact Solutions ◽  
Piezoelectric Element ◽  
Electric Circuit ◽  
Primary System ◽  
Dynamic Vibration Absorber ◽  
Optimization Criteria ◽  
Closed Form Solutions ◽  
Norm Minimization ◽  
Resonant Shunt ◽  
Piezoelectric Shunt

In this work, exact closed-form solutions are derived for optimizing the resonant shunt circuits of electromagnetic shunt dampers (EMSDs), which use an electromagnetic transducer, and piezoelectric shunt dampers (PZSDs), which use a piezoelectric element, shunted with an electric circuit. Modeling of the EMSD and PZSD is unified by nondimensional parameters. The optimization criteria selected for the EMSD and PZSD are H∞-norm minimization, H2-norm minimization, and exponential time-decay rate maximization. The aim of this study is to derive for the first time the exact solutions that have not previously been investigated, including cases that consider the inherent damping of the primary system. This paper comprehensively summarizes the exact solutions based on the optimization criteria together with approximated solutions obtained by the fixed-point method, which is commonly used to optimize the dynamic vibration absorber (DVA).

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

2002 ◽  
Vol 124 (4) ◽  
pp. 576-582 ◽  
Author(s):  
Osamu Nishihara ◽  
Toshihiko Asami
Keyword(s):  
Exact Solutions ◽  
Closed Form ◽  
Maximum Amplitude ◽  
Primary System ◽  
Magnification Factor ◽  
Dynamic Vibration Absorber ◽  
Dynamic Vibration ◽  
Classic Problem ◽  
Resonance Frequencies ◽  
Minimum Amplitude

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

Multi-Resonant Electromagnetic Shunt Dampers for Vibration Suppression

2017 ◽  
Author(s):  
Yalu Pei ◽  
Lei Zuo
Keyword(s):  
Vibration Suppression ◽  
Optimal Designs ◽  
Primary System ◽  
Mean Square ◽  
Optimal Result ◽  
Tuned Mass Dampers ◽  
Closed Form Solutions ◽  
System Parameters ◽  
Double Mass ◽  
Resonant Shunt

This paper proposed multi-resonant electromagnetic (EM) shunt dampers and investigated the optimal designs and performances of shunt circuits for a single DOF primary system. The circuits are arranged in parallel or series based on the analogy of multiple tuned mass dampers (TMDs). The objective is to minimize the root-mean-square (RMS) vibration of the primary system subjected to random base excitations. For single resonant EM shunt damper, closed-form solutions of optimal system parameters are obtained. For multi-resonant EM shunt dampers, the system parameters are numerically optimized. The vibration suppression performance of multi-resonant EM shunt dampers are compared with double-mass TMDs under the same 5% total stiffness ratio. It shows that the parallel shunt damper can achieve slightly better performance than parallel TMDs while the series shunt damper behaves differently from series TMDs. The optimal result of the series shunt damper will be the same as the single resonant shunt damper. It is also found that the multi-resonant EM shunt damper is much more sensitive to the capacitance than the resistance in the shunt circuits.

scholarly journals TECHNIQUE AND DEVICE FOR THE EXPERIMENTAL ESTIMATION OF THE ACOUSTIC IMPEDANCE OF VISCOELASTIC MEDIUM

2017 ◽  
Vol 8 (4) ◽  
pp. 314-326 ◽  
Author(s):  
O. V. Murav’eva ◽  
V. V. Murav’ev ◽  
D. V. Zlobin ◽  
O. P. Bogdan ◽  
V. N. Syakterev ◽  
...  
Keyword(s):  
Acoustic Impedance ◽  
Experimental Evaluation ◽  
Piezoelectric Element ◽  
Electric Circuit ◽  
Biological Tissues ◽  
Ultrasonic Waves ◽  
Acoustic Parameters ◽  
Laboratory Equipment ◽  
Viscoelastic Media ◽  
Silicone Sealant

Measuring the characteristics of process fluids allows us to evaluate their quality, biological tissues – to differentiate healthy tissues and tissues with pathologies. Measuring the characteristics of process fluids allows us to evaluate their quality, biological tissues – to differentiate healthy tissues and tissues with pathologies. One of the complex acoustic parameters is the impedance, which allows one to fully evaluate the characteristics of viscoelastic media. Most of impedance methods of measurements require using two or more reference media and the availability of calibrated acoustic transducers. The aim of this work ware introduced a methods and construction for the experimental evaluation of the longitudinal and shear impedance of viscoelastic media based on measuring the parameters of the amplitude-frequency characteristics and calculating the elements of the electric circuit for replacing the piezoelectric element which vibrating in the test medium.The paper introduces a methods and construction of the experimental evaluation of the impedances of viscoelastic media. The suggested methods is allowed measuring longitudinal and shear impedances and determining velocities of longitudinal and transverse ultrasonic waves and the values of the elastic moduli of viscoelastic media, including in various aggregate states. The technique is fairly simple to implement and can be reproduced using simple laboratory equipment.The obtained values of the acoustic impedances of the investigated media are in satisfactory agreement with their reference data. In contrast to the known methods for determining the acoustic impedance, the developed technique allows us to estimate with sufficient accuracy the parameter of the shear impedance of viscoelastic media that is difficult to measure at the frequencies of the megahertz range, which determines the shear modulus of the material and characterizes its resistance to shear deformations. The results of the implementation of the developed technique for the estimation of acoustic parameters for a number of media with zero shear elasticity (alcohol, acetone) and viscoelastic media (glycerin, architectural clay, silicone sealant and glue МР-55 before and after polymerization) are presented.

scholarly journals Attenuation of Motorcycle Handle Vibration Using Dynamic Vibration Absorber

2018 ◽  
Vol 217 ◽  
pp. 01006
Author(s):  
Muhammad Iyad Al-Maliki Saifudin ◽  
Nabil Mohamad Usamah ◽  
Zaidi Mohd Ripin
Keyword(s):  
Vibration Absorber ◽  
Primary System ◽  
Additional Source ◽  
Dynamic Vibration Absorber ◽  
Vibration Absorption ◽  
The Road ◽  
Dynamic Vibration ◽  
Attenuation Level ◽  
Road Surface Roughness ◽  
Extended Exposure

Motorcycle riders are exposed to hand-transmitted vibration of the hand-arm system due to the vibration of the handle and extended exposure can result in numbness and trembling. One feasible solution to attenuate the handle vibration is by using a dynamic vibration absorber (DVA). In this work a DVA is designed and mounted on the motorcycle handle in order to reduce the vibration at the handle by transferring the vibration from the primary system handle to the secondary mass. Removal of elastomeric material at the DVA mounting locations, symmetry of secondary mass and the direction of DVA attachment influence the vibration absorption. A series of tests conducted show that the vibration on the handle is mainly induced by the engine and there is additional source of vibration from the road surface roughness. Installation of DVA at different locations on the handle resulted in various attenuation levels at different speed in the x and z directions. the attenuation level is between 59-68 % in the biodynamic x-directions for speed at 30-50 kmh-1.

Analytical Modeling of Mechanical Properties and Behavior of Nanotube-Based Nanocomposites

2013 ◽  
Author(s):  
Davood Askari ◽  
Mehrdad N. Ghasemi-Nejhad ◽  
Alexander L. Kalamkarov
Keyword(s):  
Exact Solutions ◽  
Closed Form ◽  
Axial Strain ◽  
Stress Distributions ◽  
Closed Form Solutions ◽  
Loading Case ◽  
Analytical Formulae ◽  
Plain Strain ◽  
And Behavior ◽  
Radial Loading

The objective of this paper is to introduce analytical closed form solutions for the prediction of effective axial and transverse Young’s modulus and Poisson ratios of a matrix-filled nanotube (i.e., a representative element of nanotube reinforced nanocomposites) as well as its mechanical behavior (i.e., displacements, strains and stress distributions) when it is subjected to externally applied uniform axial and radial loads. In this work, both the nanotube and its filler material are considered to be generally cylindrical orthotopic. For the derivation of exact solutions for radial loading case, no plain strain condition is assumed and effects of axial strain is taken into consideration to obtain a more precise set of solutions. Analytical formulae are developed based on the principles of linear elasticity and continuum mechanics and then exact solutions are obtained for displacements, strains and stress distributions within the domain of each individual constituent. To validate and verify the accuracy of the closed form solutions obtained from the analytical approach, a 3-D model of a matrix-filled nanotube is generated and solved for displacements, strains and stresses, numerically, using a finite element method. Excellent agreements were achieved between the results obtained from the analytical and numerical methods.

Analytical Solutions for Effective Transverse Mechanical Properties and Performance of Radially Loaded Nanotube Based Nanocomposites

2009 ◽  
Author(s):  
Davood Askari ◽  
Mehrdad N. Ghasemi-Nejhad
Keyword(s):  
Exact Solutions ◽  
Poisson Ratio ◽  
Axial Strain ◽  
Radial Pressure ◽  
Stress Distributions ◽  
Closed Form Solutions ◽  
Analytical Formulae ◽  
And Performance ◽  
Plain Strain ◽  
Close Form

It is frequently reported that carbon nanotubes (CNTs) can be filled with various materials in different states to create nanocomposites. These nanocomposite tubes are often incorporated in another host material for further reinforcement to attain properties enhancements. The objective of this paper is to introduce exact analytical close form solutions for the prediction of effective transverse Young’s modulus and Poisson ratio of a matrix-filled nanotube (i.e., a representative element of nanotube reinforced nanocomposites) as well as its mechanical behavior (i.e., displacements, strains and stress distributions) when it is subjected to externally applied uniform radial pressure. In this work, both the nanotube and its filler material are considered to be generally cylindrical orthotropic. For no loss of generality, no plain strain condition is used and axial strain is also taken into consideration to obtain a more precise set of solutions. Analytical formulae are developed based on the principles of linear elasticity and continuum mechanics and then exact solutions are obtained for displacements, strains and stress distributions within the domain of each individual constituent. To validate and verify the accuracy of the closed form solutions obtained from the analytical approach, a 3-D model of a matrix-filled CNT is generated and solved for displacements, strains and stresses numerically, using finite element method. Excellent agreements were achieved between the results obtained from the analytical and numerical methods verifying the analytically obtained exact solutions.

On the Approximate Solution of Viscous-Flow Problems

1963 ◽  
Vol 30 (2) ◽  
pp. 263-268 ◽  
Author(s):  
J. A. Schetz
Keyword(s):  
Approximate Solution ◽  
Exact Solutions ◽  
Viscous Flow ◽  
Closed Form ◽  
New Method ◽  
Two Dimensional ◽  
General Technique ◽  
Closed Form Solutions ◽  
Flow Problems

The need for a general technique for the approximate solution of viscous-flow problems is discussed. Existing methods are considered and a new method is presented which results in simple closed-form solutions. The accuracy of the method is demonstrated by comparisons with the results of known exact solutions, and finally the general technique is employed to determine a new solution for the fully expanded two-dimensional laminar nozzle problem.

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

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