23.4 Practical Considerations and Related Topics

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23.4.1 Summary of Vibration-Control Design Steps and Procedures

In order to select a suitable vibration-control system, especially a vibration isolator, a number of factors

must be considered.

23.4.1.1 Static Deflection

The static deflection of the vibration-control system under the deadweight of the load determines to a

considerable extent the type of the material to be used in the isolator. Organic materials, such as rubber

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FIGURE 23.32 Numerical simulations for the case with PZT control: (a) base motion; (b) tip displacement;

(c) control force and (d) PZT voltage.

23-38 Vibration and Shock Handbook

© 2005 by Taylor & Francis Group, LLC

and cork, are capable of sustaining very large strains provided they are applied momentarily. However, if

large strains remain for an appreciable period of time, they tend to drift or creep. On the other hand,

metal springs undergo permanent deformation if the stress exceeds the yield stress of the material, but

show minimal drift or creep when the stress is maintained below the yield stress.

DAC

ADC

Amplifier

Shaker

PZT

Tip Laser Sensor

Base Laser Sensor

Starin sensor

Plant

FIGURE 23.34 High-level control-block diagram.

FIGURE 23.33 The experimental setup: (a) the whole system; (b) PZT actuator, ACX model No. QP21B;

(c) dynamic strain sensor (attached on the other side of the beam), model No. PCB 740B02.

Vibration Control 23-39

© 2005 by Taylor & Francis Group, LLC

23.4.1.2 Stiffness in Lateral Directions

Resilient materials strained in compression are most useful when the load is relatively large and the

static deflection is small. Such applications are difficult to design for a small load, unless the required

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FIGURE 23.35 Experimental results for the case without PZT control: (a) base motion; (b) tip displacement;

(c) control force and (d) PZT voltage.

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FIGURE 23.36 Experimental results for the case with PZT control: (a) base motion; (b) tip displacement;

(c) control force and (d) PZT voltage.

23-40 Vibration and Shock Handbook

© 2005 by Taylor & Francis Group, LLC

static deflection is small. Otherwise, the small area and great thickness tend to cause a condition of

instability. To a considerable extent, this limitation can be overcome by using sponge rubber, a

material of lower modulus. In general, when the load is small, it is preferable to use rubber springs

that carry the load in shear.

23.4.1.3 Environmental Conditions

It is highly common for vibration-control systems to be subjected to harsh environmental conditions.

Especially in military applications, extreme ambient temperatures are encountered in addition to

exposure to substances like ozone, rocket fuels, and so on. Organic materials are usually more susceptible

to these environmental conditions than metal materials. However, owing to the superior mechanical

properties of organic materials, such as lighter weight, smaller size, greater damping, and the ability to

store large amounts of energy under shock, organic materials that are capable of withstanding the harsh

conditions are being developed.

23.4.1.4 Damping Characteristics

In most of the vibration-control applications, the excitations cover a wide range of frequencies and may

have random properties requiring the vibration-control systems to possess adequate damping.

Elastomers possess very good damping properties when compared with metal springs, and they also

eliminate the trouble of standing waves that occurs at high frequencies. If a metal spring is used in

vibration-control applications requiring isolation of vibration at high frequencies, it is common to

employ rubber pads in series with the metal spring, which also results in the damping of vibrations due to

the addition of damping material.

23.4.1.5 Weight and Space Limitations

The amount of load-carrying resilient material is determined by the quantity of energy to be stored. In

most of the cases, the vibration amplitude tends to be small relative to the static deflection, and the

amount of material may be calculated by equating the energy stored in the material to the work done on

the vibration control system.

23.4.1.6 Dynamic Stiffness

In the case of organic materials like rubber, the natural frequency calculated using the stiffness

determined from a static-force deflection test of the spring is almost invariably lower than that

experienced during vibration; that is, the dynamic modulus is greater than static modulus. The ratio

between the dynamic and static modulus is generally between one and two. In many vibration-control

applications, it is not feasible to mount the equipment directly upon the vibration-control system

(isolator). Instead, a heavy, rigid block, usually made of concrete or heavy steel, supported by the

isolator is employed.

23.4.2 Future Trends and Developments

During recent years, there has been considerable interest in the design and implementation of a

variety of vibration-control systems. Recent developments in multivariable control design

methodology and microprocessor implementation of modern control algorithms have opened a

new era for the design of externally controlled passive systems for use in such systems: fuzzy

reasoning (Yoshimura, 1998); adaptive algorithms (Venhovens, 1994); observer design (Hedrick et al.,

1994); and many others.

Observing these developments combined with the substantial ongoing theoretical advances in the

areas of adaptive and nonlinear controls (Astrom and Wittenmark, 1989; Alleyne and Hedrick, 1995), it

is expected that the future will bring applications of these techniques in advanced vibration-control

system design. For practical implementation, however, it is preferable to simplify these strategies, thus

leading to simpler software implementations. Suboptimal policy neglecting some performance

requirements can serve as an example of such simplifications.

Vibration Control 23-41

© 2005 by Taylor & Francis Group, LLC

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