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Research Papers

Passive and Switched Stiffness Vibration Controllers Using Fluidic Flexible Matrix Composites

[+] Author and Article Information

Otis Elevator Company, 5 Farm Springs. Road, Farmington, CT 06032amir.lotfi@gmail.com

Lloyd H. Scarborough, Christopher D. Rahn

Department of Mechanical Engineering, Pennsylvania State University, University Park, PA 16802

Edward C. Smith

Department of Aerospace Engineering, Pennsylvania State University, University Park, PA 16802

J. Vib. Acoust 134(2), 021001 (Jan 13, 2012) (8 pages) doi:10.1115/1.4002957 History: Received September 20, 2009; Revised June 26, 2010; Published January 13, 2012; Online January 13, 2012

Abstract

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.

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Figures

Figure 1

Schematic of an FMC laminate with two families of fibers wound at ±α angles with respect to the longitudinal axis

Figure 2

Schematic of the F2MC-mass dynamic system

Figure 3

Schematic of the F2MC tube model

Figure 4

Root Locus analysis of an example F2MC-mass system for changes in valve opening

Figure 5

Phase portrait of the example F2MC-mass system under skyhook control: open-valve (solid) and closed-valve (dashed) trajectories. Solid circles are the switching points. The thin lines indicate continuously open- or closed-valve trajectories and the heavy lines are the response under skyhook control.

Figure 6

Phase portrait of the example F2MC-mass system under ZV control: open-valve (solid) and closed-valve (dashed) trajectories. Solid circles are the switching points. The thin lines indicate continuously open- or closed-valve trajectories and the heavy lines are the response under ZV control.

Figure 7

ITAE performance index versus flow coefficient: (a) impulse and (b) step responses using skyhook (solid), ZV (dashed), and optimal passive (dotted) controllers

Figure 8

Impulse response of the example F2MC-mass system with optimal skyhook (solid), ZV (dashed), and passive (dotted) controllers

Figure 9

Step response of the example F2MC-mass system with optimal skyhook (solid), ZV (dashed), and passive (dotted) controllers

Figure 10

ITAE performance indices for Skyhook (solid), ZV (dashed), and optimal passive (dotted) controllers versus changes in Ko: (a) impulse and (b) step responses

Figure 11

Experimental setup

Figure 12

Experimental frequency response of the velocity to the force for experimental open (solid) and closed (dashed) valve and theoretical open (dash-dotted) and closed (dotted) valve

Figure 13

Experimental impulse response of the F2MC-mass system for optimal passive (dotted), skyhook (solid), and ZV (dashed) controllers and the closed-valve case (dash-dotted)

Figure 14

Experimental step response of the F2MC-mass system for optimal passive (dotted), skyhook (solid), and ZV (dashed) controllers and the closed-valve case (dash-dotted)

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