scholarly journals Optimization of Multiple Tuned Mass Damper (MTMD) Parameters for a Primary System Reduced to a Single Degree of Freedom (SDOF) Through the Modal Approach

2020 ◽  
Author(s):  
Piotr Wielgos ◽  
Robert Geryło
Keyword(s):  
Degrees Of Freedom ◽  
Research Work ◽  
System Optimization ◽  
Degree Of Freedom ◽  
Primary System ◽  
Single Degree Of Freedom ◽  
Modal Approach ◽  
Single Degree ◽  
Stiffness And Damping ◽  
The Impact

The research paper presents a new approach towards constructing motion equations for structures with attached MTMDs (multiple tuned mass dampers). A primary system, with MDOF (multiple dynamic degrees of freedom) was reduced to an equivalent system with a SDOF (single degree of freedom) through the modal approach, and equations from additional MTMDs were added to a thus-created system. Optimization based on H2 and H∞ for the transfer function associated with the generalized displacement of an SDOF system. The research work utilized GA (genetic algorithms) and SA (simulated annealing method) optimization algorithms to determine the stiffness and damping parameters for individual TMDs. The effect of damping and stiffness (MTMD tuning) distribution depending on the number of TMDs was also analyzed. The paper also reviews the impact of primary system mass change on the efficiency of optimized MTMDs, as well as confirms the results of other authors involving greater MTMD effectiveness relative to a single TMD.

scholarly journals Optimization of Multiple Tuned Mass Damper (MTMD) Parameters for a Primary System Reduced to a Single Degree of Freedom (SDOF) through the Modal Approach

2021 ◽  
Vol 11 (4) ◽  
pp. 1389
Author(s):  
Piotr Wielgos ◽  
Robert Geryło
Keyword(s):  
Degrees Of Freedom ◽  
Research Work ◽  
System Optimization ◽  
Degree Of Freedom ◽  
Primary System ◽  
Single Degree Of Freedom ◽  
Modal Approach ◽  
Single Degree ◽  
Novel Approach ◽  
The Impact

The research paper presents a novel approach toward constructing motion equations for structures with attached MTMDs (multiple tuned mass dampers). A primary system with MDOF (multiple dynamic degrees of freedom) was reduced to an equivalent system with a SDOF (single degree of freedom) through the modal approach, and equations from additional MTMDs were added to a thus-created system. Optimization based on ℌ2 and ℌ∞ for the transfer function associated with the generalized displacement of an SDOF system was applied. The research work utilized GA (genetic algorithms) and SA (simulated annealing method) optimization algorithms to determine the stiffness and damping parameters for individual TMDs. The effect of damping and stiffness (MTMD tuning) distribution depending on the number of TMDs was also analyzed. The paper also reviews the impact of primary system mass change on the efficiency of optimized MTMDs, as well as confirms the results of other authors involving greater MTMD effectiveness relative to a single TMD.

Predicting the Impact Response of a Nonlinear Single-Degree-of-Freedom Shock-Absorbing System From the Measured Step Response

1997 ◽  
Vol 119 (3) ◽  
pp. 221-227 ◽  
Author(s):  
S. N. Robinovitch ◽  
W. C. Hayes ◽  
T. A. McMahon
Keyword(s):  
High Energy ◽  
Degree Of Freedom ◽  
Step Response ◽  
Single Degree Of Freedom ◽  
Single Degree ◽  
Impact Forces ◽  
Standard Linear Solid ◽  
Standard Linear ◽  
The Impact ◽  
Measured Response

We measured the step response of a surrogate human pelvis/impact pendulum system at force levels between 50 and 350 N. We then fit measured response curves with four different single-degree-of-freedom models, each possessing a single mass, and supports of the following types: standard linear solid, Voigt, Maxwell, and spring. We then compared model predictions of impact force during high-energy collisions (pendulum impact velocity ranging from 1.16 to 2.58 m/s) to force traces from actual impacts to the surrogate pelvis. We found that measured peak impact forces, which ranged from 1700 to 5600 N, were best predicted by the mass-spring, Maxwell, and standard linear solid models, each of which had average errors less than 3 percent. Reduced accuracy was observed for the commonly used Voigt model, which exhibited an average error of 10 percent. Considering that the surrogate pelvis system used in this study exhibited nonlinear stiffness and damping similar to that observed in simulated fall impact experiments with human volunteers, our results suggest that these simple models allow impact forces in potentially traumatic falls to be predicted to within reasonable accuracy from the measured response of the body in safe, simulated collisions.

scholarly journals Symmetric waterbomb origami

2016 ◽  
Vol 472 (2190) ◽  
pp. 20150846 ◽  
Author(s):  
Yan Chen ◽  
Huijuan Feng ◽  
Jiayao Ma ◽  
Rui Peng ◽  
Zhong You
Keyword(s):  
Degrees Of Freedom ◽  
Degree Of Freedom ◽  
Solar Panels ◽  
Deployable Structures ◽  
Single Degree Of Freedom ◽  
Folding Process ◽  
Multiple Degrees Of Freedom ◽  
Single Degree ◽  
Flat Roofs ◽  
Additional Constraints

The traditional waterbomb origami, produced from a pattern consisting of a series of vertices where six creases meet, is one of the most widely used origami patterns. From a rigid origami viewpoint, it generally has multiple degrees of freedom, but when the pattern is folded symmetrically, the mobility reduces to one. This paper presents a thorough kinematic investigation on symmetric folding of the waterbomb pattern. It has been found that the pattern can have two folding paths under certain circumstance. Moreover, the pattern can be used to fold thick panels. Not only do the additional constraints imposed to fold the thick panels lead to single degree of freedom folding, but the folding process is also kinematically equivalent to the origami of zero-thickness sheets. The findings pave the way for the pattern being readily used to fold deployable structures ranging from flat roofs to large solar panels.

A Probabilistic Analysis of Single-Degree-of-Freedom Blade Vibration

1993 ◽  
Author(s):  
Kenan Y. Sanliturk ◽  
Mehmet Imregun ◽  
David J. Ewins
Keyword(s):  
Natural Frequencies ◽  
Probabilistic Approach ◽  
Substantial Reduction ◽  
Forced Response ◽  
Degree Of Freedom ◽  
Cumulative Probability ◽  
Blade Vibration ◽  
Single Degree Of Freedom ◽  
Single Degree ◽  
Stiffness And Damping

The effects of random stiffness and damping variations on damped natural frequencies and response levels of turbomachinery blades are investigated by employing probabilistic approach using a single-degree-of-freedom (SDOF) model. An important feature of this study is the determination of the cumulative probability distributions for damped natural frequencies and receptance frequency response functions without having to compute their probability density distributions since it is shown that those of stiffness and damping can be used directly. The advantage of this approach is not only in the simplicity of problem formulation but also in the substantial reduction of computational requirements. Furthermore, results suggest that both stiffness and damping properties should be considered as random parameters in statistical analyses of forced response.

A guide to classical flutter

1988 ◽  
Vol 92 (919) ◽  
pp. 339-355 ◽  
Author(s):  
L. T. Niblett
Keyword(s):  
Degrees Of Freedom ◽  
Normal Modes ◽  
Degree Of Freedom ◽  
Single Degree Of Freedom ◽  
Structural Coupling ◽  
Two Degrees Of Freedom ◽  
Single Degree ◽  
Lifting Surface ◽  
Classical Flutter ◽  
Comprehensive Study

Summary First essentials of classical flutter are demonstrated by a comprehensive study of the behaviour of a lifting surface with two degrees of freedom under the action of airforces limited to those in phase with displacement. Structural coupling between the coordinates is eliminated by taking the normal modes to be the deflection coordinates, and this results in conditions for stability with particularly concise forms. It is shown that the flutter stability can be seen to be very much a matter of the relative amplitudes of heave and pitch in the normal modes. In-quadrature airforces are then introduced and it is shown that they have little effect when the flutter is severe. They are of more importance in the milder forms of flutter, the extreme of which are shown to be little different from instabilities in a single degree of freedom.

scholarly journals Shock Performance of Different Semiactive Damping Strategies

2010 ◽  
Vol 8 (02) ◽  
Author(s):  
D. F. Ledezma-Ramirez ◽  
N. Ferguson ◽  
M. Brennan
Keyword(s):  
Harmonic Excitation ◽  
Degree Of Freedom ◽  
Harmonic Vibration ◽  
Passive Stiffness ◽  
Single Degree Of Freedom ◽  
Single Degree ◽  
Variable Damping ◽  
Stiffness And Damping ◽  
Shock Pulses

The problem of shock generated vibration is presented and analyzed. The fundamental background is explained based on the analysis of a single degree-of-freedom model with passive stiffness and damping. The advantages and limitations of such a shock mount are discussed. Afterwards, different semi-active strategies involving variable damping are presented. These strategies have been used for harmonic excitation but it is not clear how they will perform during a shock. This paper analyzes the different variable damping schemes already used for harmonic vibration in order to find any potential advantages or issues for theoretical shock pulses.

Tunable-with-energy intense modal interactions induced by geometric nonlinearity

2020 ◽  
pp. 095440622090862
Author(s):  
Alireza Mojahed ◽  
Lawrence A Bergman ◽  
Alexander F Vakakis
Keyword(s):  
Geometric Nonlinearity ◽  
Degree Of Freedom ◽  
Primary System ◽  
Energy Relation ◽  
Initial Angle ◽  
Modal Interactions ◽  
Single Degree Of Freedom ◽  
Single Degree ◽  
Energy Transfers ◽  
Wave Tailoring

Modal interactions are distinct features of nonlinear systems that can be exploited in applications such as vibration and shock mitigation, targeted (irreversible) energy transfers (TET), and acoustic/stress wave tailoring. For such applications, different types of nonlinearities, e.g. hardening, softening, smooth, non-smooth, material or geometric, have been considered. In this work, we examine the geometric nonlinearity resulting from an initially inclined element consisting of a linear spring and a viscous damper connected in parallel, having an initial angle of inclination, [Formula: see text]. Because of its inclined configuration, this element possesses strong (and doubly tunable with respect to [Formula: see text] and energy) geometrically nonlinear stiffness and damping effects, despite the linear constitutive laws governing its constituent components. First, we consider a single-degree-of-freedom linearly grounded oscillator attached to the nonlinear inclined element. Omitting dissipative effects, we investigate the frequency–energy relation of this system by employing the canonical action-angle transformation and show that, depending on the initial angle of inclination and the energy-level, the resulting nonlinearity can be tuned to be softening, hardening or a combination of both. Next, we explore the efficacy of the geometric nonlinearity to induce strong modal interactions by considering a three-degree-of-freedom lightly damped primary system that is weakly coupled to a single-degree-of-freedom lightly damped attachment with the inclined nonlinear element, subjected to impulsive excitation. Varying [Formula: see text] and the input energy, we demonstrate strong modal energy-exchanges between the modes of the primary system and the nonlinear attachment over broad energy-dependent spans of [Formula: see text]. We show that the passive self-adaptiveness of the nonlinear damping and the hardening–softening geometric nonlinearity can induce narrowband or broadband frequency TET, including high-to-low frequency energy transfers. Interestingly, over a definitive range of [Formula: see text], these modal interactions may be limited only between the nonlinear mode of the attachment and the highest-frequency linear mode of the primary system, inducing strong high-frequency targeted energy transfer to the primary system.

Nonlinearities in Experimental System Identification of a Piezocomposite Beam Model

2017 ◽  
Author(s):  
Patrick S. Heaney ◽  
Onur Bilgen
Keyword(s):  
System Identification ◽  
Electromechanical Coupling ◽  
Degree Of Freedom ◽  
Parameter Estimates ◽  
Beam Model ◽  
Single Degree Of Freedom ◽  
Testing Procedures ◽  
Single Degree ◽  
Constitutive Relationships ◽  
The Impact

Piezocomposite beams are often modeled using linear constitutive equations describing the electromechanical coupling of the material. In nearly all experimental identification processes, nonlinearities in these equations are ignored, which can lead to significant errors in the identified models. Following a common practice in the literature, a piezocomposite cantilever beam is modeled as a single degree of freedom system, with strain induced harmonic excitation governed by linear piezoelectric constitutive relationships. The validity of the linear property assumptions is investigated. It is experimentally demonstrated that the relationship between input and response of the beam is significantly nonlinear. The impact of this nonlinear behavior on the parameter identification of the system is shown for three different testing methods, (1) Open Loop Excitation, (2) Constant Input, and (3) Constant Response. For each method, the command amplitude is varied which yields different parameter estimates for the single degree of freedom beam model. These results demonstrate that the assumed linear constitutive relationships lead to parameter estimates which are only accurate for the specific testing method and the specific commanded input or response amplitude, even under highly controlled testing procedures. The paper concludes with comments on the system identification of a single degree of freedom model given this nonlinear system behavior.

Fast Simulation of a Single Degree-of-Freedom System Consisting of An Iwan Element Using the Method of Averaging

2020 ◽  
Vol 142 (5) ◽  
Author(s):  
Drithi Shetty ◽  
Matthew Allen
Keyword(s):  
Equations Of Motion ◽  
Element Model ◽  
Degree Of Freedom ◽  
Single Degree Of Freedom ◽  
Weakly Nonlinear ◽  
Single Degree ◽  
Integration Schemes ◽  
Current Implementation ◽  
Modal Model ◽  
Stiffness And Damping

Abstract While Iwan elements have been used to effectively model the stiffness and energy dissipation in bolted joints, integrating the equations of motion of these elements is fairly expensive since implicit schemes, such as Newmark’s methods, need to be used. This paper presents a method of simulating dynamic systems containing nonlinear Iwan elements that significantly reduce the computation cost by using closed-form expressions for stiffness and damping in the microslip regime and an averaging method for regions of time in which no external force is applied. The proposed algorithm is demonstrated on a single degree-of-freedom (SDOF) system to evaluate the range over which it retains accuracy and the improvement in performance it offers. Although the current implementation is limited to SDOF systems, it can be used to simulate the response of each mode in structures exhibiting weak nonlinearity that can be modeled using the modal Iwan approach. To verify this, the dynamic response of a finite element model of a beam assembly, integrated using the Newmark-β method, has been compared with its equivalent modal model integrated using the proposed algorithm. The results show that the algorithm accurately predicts the response in a fraction of the time taken by implicit integration schemes, so long as the modes remain uncoupled and weakly nonlinear.

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