Passive and Switched Stiffness Vibration Controllers Using Fluidic Flexible Matrix Composites

2012 ◽  
Vol 134 (2) ◽  
Author(s):  
Amir Lotfi-Gaskarimahalle ◽  
Lloyd H. Scarborough ◽  
Christopher D. Rahn ◽  
Edward C. Smith
Keyword(s):  
Passive Control ◽  
Axial Strain ◽  
Damping Ratio ◽  
Equations Of Motion ◽  
Absolute Error ◽  
Step Response ◽  
Axial Stiffness ◽  
Matrix Composites ◽  
Mass System ◽  
Valve Orifice

This paper investigates passive and semi-active vibration control using fluidic flexible matrix composites (F2MC). F2MC tubes filled with fluid and connected to an accumulator through a fixed orifice can provide damping forces in response to axial strain. If the orifice is actively controlled, the stiffness of F2MC tubes can be dynamically switched from soft to stiff by opening and closing an on/off valve. Fiber reinforcement of the F2MC tube kinematically relates the internal volume to axial strain. With an open valve, the fluid in the tube is free to move in or out of the tube, so the stiffness is low. With a closed valve, however, the high bulk modulus fluid resists volume change and produces high axial stiffness. The equations of motion of an F2MC-mass system are derived using a 3D elasticity model and the energy method. The stability of the unforced dynamic system is proven using a Lyapunov approach. A reduced-order model for operation with either a fully open or fully closed valve motivates the development of a zero vibration (ZV) controller that suppresses vibration in finite time. Coupling of a fluid-filled F2MC tube to a pressurized accumulator through a fixed orifice is shown to provide significant passive damping. The open-valve orifice size is optimized for optimal passive, skyhook, and ZV controllers by minimizing the integral time absolute error cost function. Simulation results show that the optimal open valve orifice provides a damping ratio of 0.35 compared with no damping in closed-valve case. The optimal ZV controller outperforms optimal passive and skyhook controllers by 32.9% and 34.2% for impulse and 34.7% and 60% for step response, respectively. Theoretical results are confirmed by experiments that demonstrate the improved damping provided by optimal passive control F2MC and fast transient response provided by semi-active ZV control.

Switched Stiffness Vibration Controllers for Fluidic Flexible Matrix Composites

2009 ◽  
Author(s):  
Amir Lotfi-Gaskarimahalle ◽  
Christopher D. Rahn
Keyword(s):  
Equations Of Motion ◽  
Active Vibration Control ◽  
Flexible Structures ◽  
Variable Stiffness ◽  
Flow Coefficient ◽  
Step Response ◽  
Semiactive Control ◽  
Matrix Composites ◽  
Mass System ◽  
3D Elasticity

This paper investigates semi-active vibration control using Fluidic Flexible Matrix Composites (F2MC) as variable stiffness components of flexible structures. The stiffness of F2MC tubes can be dynamically switched from soft to stiff by opening and closing an on/off valve. Fiber reinforcement of the F2MC tube changes the internal volume when externally loaded. With an open valve, the fluid in the tube is free to move in or out of the tube, so the stiffness is low. When the valve is closed, the high bulk modulus fluid resists volume change and produces high stiffness. The equations of motion of an F2MC-mass system is derived using a 3D elasticity model and the energy method. The stability of the unforced dynamic system is proven using a Lyapunov approach. To capture the important system parameters, nondimensional full order and reduced order models are developed. A Zero Vibration (ZV) state switch technique is introduced that suppresses vibration in finite time, and is compared to conventional Skyhook semiactive control. The ITAE performance of the controllers is optimized by adjusting the open valve flow coefficient. Simulation results show that the optimal ZV controller outperforms the optimal Skyhook controller by 13% and 60% for impulse and step response, respectively.

Passive Control of Vibration of Elastically Supported Beams Subjected to Moving Loads

2005 ◽  
Author(s):  
D. Younesian ◽  
E. Esmailzadeh ◽  
M. H. Kargarnovin
Keyword(s):  
High Speed ◽  
Passive Control ◽  
Vibration Suppression ◽  
Damping Ratio ◽  
Equations Of Motion ◽  
Compressive Force ◽  
Moving Loads ◽  
Axial Compressive Force ◽  
Before And After ◽  
Elastically Supported

Vibration suppression of elastically supported beams subjected to moving loads is investigated in this work. For a Timoshenko beam with an arbitrary number of elastic supports, subjected to a constant axial compressive force, and having a tuned mass damper (TMD) installed at the mid-span, the equations of motion are derived and using the Galerkin approach the solution is sought. The optimum values of the frequency and damping ratio are determined both analytically and numerically and presented as some design curves directly applicable in the TMD design for bridge structures. To show the efficiency of the designed TMD, computer simulation for two real bridges, subjected to a S.K.S Japanese high-speed train, is carried out and the results obtained are compared for before and after the installation of the TMD system.

Spherical Compliant Model for Vibration Estimation and Control

1995 ◽  
Author(s):  
Thomas J. Thompson
Keyword(s):  
Passive Control ◽  
Equations Of Motion ◽  
Spherical Model ◽  
Control Element ◽  
Test Accuracy ◽  
Control Force ◽  
Lumped Mass ◽  
Mass System ◽  
Model Control ◽  
And Control

Abstract Proposed space missions involve large structures which must maintain precise dimensional tolerances during dynamic maneuvers. In order to attenuate disturbances in the many modes of vibration of such structures, active and passive vibration control has been proposed. Passive control is to be achieved by placing viscous or viscoelastic members in a structure to absorb energy, while active control similarly could involve structural members (struts) capable of sensing axial displacement and exerting axial control force. With conventional modal analysis, the effect of a control element on a system is computed by summing its influence on many immutable modes. Since changes in mode shape must be described by this summation, truncation of higher modes results in inaccuracies. The compliant model of vibration to be presented accurately accounts for the effects of locally-acting control elements without inclusion of high-frequency modes. The motion of each spring-mass system representing a structural mode is modified by a control element in series with another stiffness inherent to the structure for that mode and control position. In order to predict the influence of several control elements or dampers on closely-spaced modes, the compliant models for those modes are integrated into a spherical model in which one lumped mass is acted upon by orthogonal modal stiffnesses. In the spherical model, control elements influent the lumped mass from orientations determined by mode participation factors. The resulting equations of motion are stated in standard state-space form. To test accuracy, the compliant model is used to predict eigenvalue shifts due to springs and dampers acting upon an axially-vibrating rod, and the spherical model is used to predict damping accurately in a lumped-mass system with closely-spaced modes.

Fluidic Composite Tuned Vibration Absorbers

2009 ◽  
Author(s):  
Amir Lotfi-Gaskarimahalle ◽  
Lloyd H. Scarborough ◽  
Christopher D. Rahn ◽  
Edward C. Smith
Keyword(s):  
Forced Vibration ◽  
Axial Strain ◽  
Flow Coefficient ◽  
Resonant Peak ◽  
Matrix Composites ◽  
Mass System ◽  
Isolation Frequency ◽  
Primary Mass ◽  
Tuned Vibration Absorbers ◽  
Internal Volume

This paper presents a novel Tuned Vibration Absorber (TVA) using Fluidic Flexible Matrix Composites (F2MC). Fiber reinforcement of the F2MC tube kinematically links the internal volume with axial strain. Coupling of a fluid-filled F2MC tube through a fluid port to a pressurized air accumulator can suppress primary mass forced vibration at the tuned absorber frequency. 3-D elasticity model for the tube and a lumped fluid mass develops a 4th-order model of an F2MC-mass system. The model provides a closed form isolation frequency that depends mainly on the port inertance, orifice flow coefficient, and the tube parameters. A small amount of viscous damping in the orifice increases the isolation bandwidth. With a fully closed orifice, the zero disappears and the system has a single resonant peak. Variations in the primary mass do not change the isolation frequency, making the F2MC TVA robust to mass variations. Experimental results validate the theoretical predictions in showing a tunable isolation frequency that is insensitive to primary mass variations, and a 94% reduction in forced vibration response relative to the closed-valve case.

scholarly journals Seismic Performance Analysis of Tuned Mass Rocking Wall (TMRW)-Frame Building Structures

Buildings ◽  
2021 ◽  
Vol 11 (7) ◽  
pp. 293
Author(s):  
Andong Wang ◽  
Shanghong Chen ◽  
Wei Lin ◽  
Ai Qi
Keyword(s):  
Seismic Performance ◽  
Frequency Ratio ◽  
Passive Control ◽  
Damping Ratio ◽  
Equations Of Motion ◽  
Control Device ◽  
Building Structures ◽  
Frame Building ◽  
Host Structure ◽  
Rocking Wall

A tuned mass rocking wall (TMRW) is a passive control device that combines the merits of a traditional tuned mass damper (TMD) and a traditional rocking wall (RW). TMRWs not only help avoid weak story failure of the host structure but can also be regarded as a largely tuned mass substructure in the building structure. Through the appropriate design of the frequency ratio, the host structure can dissipate much more energy under earthquake excitations. In this paper, the basic equations of motion for the mechanical model of an SDOF structure-rigid rocking wall are established, and the optimization formulas of frequency ratio and damping ratio of TMRW are derived. Through the dynamic elastoplastic analysis of a six-story TMRW-frame model, the applicability of the derived parameter optimization formulas and the effectiveness of the TMRW in seismic performance control are investigated. The results demonstrate that the TMRW can coordinate the uneven displacement angle between stories of the host structure. Additionally, the TMRW is found to possess the merit of reducing both the peak and root-mean-square (RMS) structural responses when subjected to different types of earthquake excitations.

Stiffness Shaping for Zero Vibration Fluidic Flexible Matrix Composites

2008 ◽  
Author(s):  
Amir Lotfi-Gaskarimahalle ◽  
Ying Shan ◽  
Suyi Li ◽  
Christopher D. Rahn ◽  
Charles E. Bakis ◽  
...  
Keyword(s):  
Equations Of Motion ◽  
Active Vibration Control ◽  
Variable Stiffness ◽  
Matrix Composites ◽  
Mass System ◽  
Apparent Stiffness ◽  
Active Vibration ◽  
3D Elasticity ◽  
High Bulk ◽  
Orifice Valve

This paper studies semi-active vibration control using Fluidic Flexible Matrix Composites (F2MC) as variable stiffness structures. The apparent stiffness of F2MC tubes can be changed using a variable orifice valve. With fiber reinforcement, the volume inside the tube may change with external load. With an open valve, the liquid is free to move in or out of the tube, so the apparent stiffness will not changed. When the valve is closed, the high bulk modulus liquid is confined, which resists the volume change and causes the apparent stiffness of the tube to increase. The equations of motion of an F2MC-mass system is derived using a 3D elasticity model and the energy method. A reduced order model is then developed for fully-open or fully-closed valves. A Skyhook valve that cycles the valve between open and closed, asymptotically decays the vibration. A Zero Vibration (ZV) Stiffness Shaping technique is introduced to suppress the vibration in finite time. A sensitivity analysis of the ZV Stiffness Shaper studies the robustness to parameteric uncertainties.

The Dynamic Behaviour of Passively Compensated, Hydrostatic Journal Bearings with Various Numbers of Recesses

1976 ◽  
Vol 18 (6) ◽  
pp. 292-302 ◽  
Author(s):  
P. B. Davies
Keyword(s):  
Dynamic Behaviour ◽  
Damping Ratio ◽  
Equations Of Motion ◽  
Steady State Solution ◽  
Flow Equation ◽  
External Excitation ◽  
Signal Flow Graphs ◽  
Flow Compensation ◽  
Circular Functions ◽  
Flow Graphs

A previously established small-perturbation analysis is developed to express the unsteady-state continuity-of-flow equation for an isolated recess in a passively compensated, multirecess, hydrostatic journal bearing in terms of generalized co-ordinates. The concise form of this equation enables motion of the shaft about the concentric position to be described by equations which are derived in closed form for bearings with orifice, capillary or constant flow compensation and any number of recesses. These equations of motion, and hence the expressions for the receptances which describe the response of a bearing to external excitation, are shown to be of exactly the same form for all bearings of the type considered. Furthermore, the damping ratio and natural frequency in any particular case are determined by a single dynamic constant which is shown to be equal to a linear combination of circular functions and a limited number of coefficients which may be found explicitly by routine use of signal flow graphs. The results of the analysis, which is exact within the stated assumptions, are compared with those of other workers and the steady-state solution of the equations of motion is shown to give an expression for static stiffness which is useful for design purposes. Numerical values of the dynamic constant for bearings with between 3 and 20 recesses are given graphically.

Optimal Design of Vibration Absorber Systems Supported by Elastic Base

1991 ◽  
Author(s):  
Hashem Ashrafiuon
Keyword(s):  
Dynamic Models ◽  
Damping Ratio ◽  
Equations Of Motion ◽  
Elastic Base ◽  
Design Parameters ◽  
Primary System ◽  
Vibration Absorbers ◽  
Equivalent Damping ◽  
System Equations ◽  
Different Levels

Abstract This paper presents the effect of foundation flexibility on the optimum design of vibration absorbers. Flexibility of the base is incorporated into the absorber system equations of motion through an equivalent damping ratio and stiffness value in the direction of motion at the connection point. The optimum values of the uncoupled natural frequency and damping ratio of the absorber are determined over a range of excitation frequencies and the primary system damping ratio. The design parameters are computed and compared for the rigid, static, and dynamic models of the base as well as different levels of base flexibility.

Influence of Material Damping on In-Plane Modal Parameters for Rotating Disks

2012 ◽  
Author(s):  
Hamid R. Hamidzadeh ◽  
Ehsan Sarfaraz
Keyword(s):  
Elastic Moduli ◽  
Damping Ratio ◽  
Equations Of Motion ◽  
Elastic Stability ◽  
Rotating Disks ◽  
Governing Equations ◽  
Annular Disk ◽  
Stress Theory ◽  
Hysteretic Damping ◽  
Circumferential Wave

The linear in-plane free vibration of a thin, homogeneous, viscoelastic, rotating annular disk is investigated. In the development of an analytical solution, two dimensional elastodynamic theory is employed and the viscoelastic material for the medium is allowed by assuming complex elastic moduli. The general governing equations of motion are derived by implementing plane stress theory. Natural frequencies are computed for several modes at specific radius ratios with fixed-free boundary conditions and modal loss factors for different damping ratios are determined. The computed results were compared to previously established results. It was observed that the effects of rotational speed and hysteretic damping ratio on natural frequency and elastic stability of the rotating disks were related to the mode of vibration and type of circumferential wave occurring.

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