23.1 Introduction

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The problem of reducing the level of vibration in constructions and structures arises in various branches

of engineering, technology, and industry. In most of today’s mechatronic systems, a number of possible

devices such as reaction or momentum wheels, rotating devices, and electric motors are essential to the

system’s operation and performance. These devices, however, can also be sources of detrimental

vibrations that may significantly influence the mission performance, effectiveness, and accuracy of

operation. Therefore, there is a need for vibration control. Several techniques are utilized either to limit

or alter the vibration response characteristics of such systems. During recent years, there has been

considerable interest in the practical implementation of these vibration-control systems. This chapter

presents the basic theoretical concepts for vibration-control systems design and implementation,

followed by an overview of recent developments and control techniques in this subject. Some related

practical developments in variable structure control (VSC), as well as piezoelectric vibration control of

flexible structures, are also provided, followed by a summary of design steps and procedures for

vibration-control systems. A further treatment of the subject is found in Chapter 32.

23-1

© 2005 by Taylor & Francis Group, LLC

23.1.1 Vibration Isolation vs. Vibration Absorption

In vibration isolation, either the source of vibration is isolated from the system of concern (also called

“force transmissibility”; see Figure 23.1a), or the device is protected from vibration of its point of

attachment (also called “displacement transmissibility”, see Figure 23.1b). Unlike the isolator, a vibration

absorber consists of a secondary system (usually mass – spring – damper trio) added to the primary device

to protect it from vibrating (see Figure 23.1c). By properly selecting absorber mass, stiffness, and

damping, the vibration of the primary system can be minimized (Inman, 1994).

23.1.2 Vibration Absorption vs. Vibration Control

In vibration-control schemes, the driving forces or torques applied to the system are altered in order

to regulate or track a desired trajectory while simultaneously suppressing the vibrational transients in

the system. This control problem is rather challenging since it must achieve the motion tracking

objectives while stabilizing the transient vibrations in the system. Several control methods have been

developed for such applications: optimal control (Sinha, 1998); finite element approach (Bayo, 1987);

model reference adaptive control (Ge et al., 1997); adaptive nonlinear boundary control (Yuh, 1987); and

several other techniques including VSC methods (Chalhoub and Ulsoy, 1987; de Querioz et al., 1999; de

Querioz et al., 2000).

As discussed before, in vibration-absorber systems, a secondary system is added in order to mimic the

vibratory energy from the point of interest (attachment) and transfer it into other components or

dissipate it into heat. Figure 23.2 demonstrates a comparative schematic of vibration control (both

single-input control and multi-input configurations) on translating and rotating flexible beams, which

could represent many industrial robot manipulators as well as vibration absorber applications for

automotive suspension systems.

23.1.3 Classifications of Vibration-Control Systems

Passive, active, and semiactive (SA) are referred to, in the literature, as the three most commonly used

classifications of vibration-control systems, either as isolators or absorbers (see Figure 23.3; Sun et al.,

1995). A vibration-control system is said to be active, passive, or SA depending on the amount of

y(t) = Y sin(wdtt)

x(t) = X sin(wt)

F(t) = F0 sin(wt)

F(t) = F0 sin(wt)

xa(t)

m

Source of

vibration

Source of

vibration

Vibration

isolator

Vibration

isolator

c k c k

FT

Device

m

absorber

Absorber ma

subsection

Primary

device

Ca ka

(a) Fixed base (b) Moving base

(c)

FIGURE 23.1 Schematic of (a) force transmissibility for foundation isolation; (b) displacement transmissibility for

protecting device from vibration of the base and (c) application of vibration absorber for suppressing primary system

vibration.

23-2 Vibration and Shock Handbook

© 2005 by Taylor & Francis Group, LLC

external power required for the vibration-control system to perform its function. A passive vibration

control consists of a resilient member (stiffness) and an energy dissipater (damper) either to absorb

vibratory energy or to load the transmission path of the disturbing vibration (Korenev and Reznikov,

1993; Figure 23.3a). This type of vibration-control system performs best within the frequency region of

its highest sensitivity. For wideband excitation frequency, its performance can be improved considerably

by optimizing the system parameters (Puksand, 1975; Warburton and Ayorinde, 1980; Esmailzadeh and

Jalili, 1998a). However, this improvement is achieved at the cost of lowering narrowband suppression

characteristics.

The passive vibration control has significant limitations in structural applications where broadband

disturbances of highly uncertain nature are encountered. In order to compensate for these limitations,

active vibration-control systems are utilized. With an additional active force introduced as a part of

absorber subsection, uðtÞ (Figure 23.3b), the system is controlled using different algorithms to make it

more responsive to source of disturbances (Soong and Constantinou, 1994; Olgac and Holm-Hansen,

1995; Sun et al., 1995; Margolis, 1998). The SA vibration-control system, a combination of active

and passive treatment, is intended to reduce the amount of external power necessary to achieve the

desired performance characteristics (Lee-Glauser et al., 1997; Jalili, 2000; Jalili and Esmailzadeh, 2002),

see Figure 23.3c.

x y(x,t)

X

Y

X'

Y'

q (t)

A

h

b

Sec. A-A

Ο

A

U

ba

z1(t)

Sprung mass

m1

k2

Unsprung mass

m2

z2(t)

z0(t)

Absorber mass

ma

U

ka

za(t)

s(t)

w(x,t)

f (t)

mt

mb

l1

l2

L

t(t)

(a) (b)

Road surface irregularities

(c)

FIGURE 23.2 A comparative schematic of vibration-control systems: (a) single-input simultaneous tracking and

vibration control; (b) multi-input tracking and vibration control and (c) a two-DoF vehicle model with dynamic

vibration absorber.

m m m

x x x

c k c c(t) k(t)

u(t)

k

Suspension Point of attachment

Suspension

subsection

Primary or

foundation

system

(a) (b) (c)

FIGURE 23.3 A typical primary structure equipped with three versions of suspension systems: (a) passive; (b) active

and (c) SA configurations.

Vibration Control 23-3

© 2005 by Taylor & Francis Group, LLC

23.1.4 Performance Characteristics of Vibration-Control Systems

In the design of a vibration-control system, it often occurs that the system is required to operate over a

wideband load and frequency range that is impossible to meet with a single choice of required stiffness

and damping. If the desired response characteristics cannot be obtained, an active vibration-control

system may provide an attractive alternative vibration control for such broadband disturbances.

However, active vibration-control systems suffer from control-induced instability in addition to the large

control effort requirement. This is a serious concern, which prevents them from the common usage in

most industrial applications. On the other hand, passive systems are often hampered by a phenomenon

known as “detuning.” Detuning implies that the passive system is no longer effective in suppressing the

vibration it was designed for. This occurs due to one of the following reasons: (1) the vibration-control

system may deteriorate and its structural parameters can be far from the original nominal design, (2) the

structural parameters of the primary device itself may alter, or (3) the excitation frequency or the nature

of disturbance may change over time.

A semiactive (also known as adaptive-passive) vibration-control system addresses these limitations by

effectively integrating a tuning control scheme with tunable passive devices. For this, active force

generators are replaced by modulated variable compartments such as variable rate damper and stiffness

(see Figure 23.3c; Hrovat et al., 1988; Nemir et al., 1994; Franchek et al., 1995). These variable

components are referred to as “tunable parameters” of the suspension system, which are retailored via a

tuning control, thus resulting in semiactively inducing optimal operation. Much attention is being paid

to these systems because of their low energy requirement and cost. Recent advances in smart materials,

and adjustable dampers and absorbers have significantly contributed to applicability of these systems

(Garcia et al., 1992; Wang et al., 1996; Shaw, 1998).

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