32.1 Introduction

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Consider the schematic diagram of a vibratory

system shown in Figure 32.1. Forcing excitations

f(t) to the mechanical system S cause the vibration

responses y. Our objective is to suppress y to a level

that is acceptable. Clearly, there are three general

ways of doing this:

1. Isolation. Suppress the excitations of

vibration. This method deals with f.

2. Design modification. Modify or redesign the

mechanical system so that for the same

levels of excitation, the resulting vibrations

are acceptable. This method deals with S:

3. Control. Absorb or dissipate the vibrations using external devices, through implicit or explicit

sensing and control. This method deals with y.

Within each of these three categories, several approaches can be used to achieve the objective of

vibration mitigation. Essentially, each of these approaches involves designing (either complete through

redesign or incremental design modification) of the system on the one hand, and controlling the

vibration through external means (passive or active devices) on the other. Note that removal of faults

(e.g., misalignments and malfunctions by repair or parts replacement) can also remove vibrations. This

approach may fall into any of the three categories listed above.

The category of vibration isolation involves “isolating” a mechanical system (S) from vibration

excitations (f) so that the excitation signals are “filtered” out or dissipated prior to reaching the system.

The use of properly designed suspension systems, mounts, and damping layers falls within this category.

The category of design modification will involve making changes to the components and the structure of

a mechanical system according to a set of specifications and design guidelines. Balancing of rotating

machinery and structural modification through modal analysis and design techniques fall into this

category. The category of control will involve either passive devices (which do not use external power),

such as dynamic absorbers and dampers, or active control devices (which need external power for

operation). In the passive case, the control device implicitly senses the vibration response and dissipates it

(as in the case of a damper) or absorbs and stores its energy where it is slowly dissipated (as in the case of

a dynamic absorber). In the active case, the vibrations y are explicitly sensed through sensors and

transducers. The forces that should be acted on the system to counteract and suppress vibrations are

determined by a controller, and the corresponding forces or torques are applied to the system through

one or more actuators.

Note that there may be some overlap in the three general categories of vibration mitigation that were

mentioned above. For example, the addition of a mount (category 1) may also be interpreted as a design

modification (category 2) or as incorporating a passive damper (category 3). It should also be noted

that the general approach, commonly known as source alteration, may fall into either category 1 or

category 2. In this case, the purpose is to alter or remove the source of vibration. The source could

either be external (e.g., road irregularities that result in vehicle vibrations) — a category 1 problem, or

internal (imbalance or misalignment in rotating devices that results in periodic forces, moments, and

vibrations) — a category 2 problem. It can be more difficult to alter external vibration sources (e.g.,

resurfacing the roadways) than to modify the internal sources (e.g., balancing of rotating machinery).

m

k

b

Mechanical

Vibrating System (S)

Vibration

Excitation

f(t)

Vibration

Response

y

FIGURE 32.1 A vibrating mechanical system.

32-2 Vibration and Shock Handbook

© 2005 by Taylor & Francis Group, LLC

Furthermore, the external source of vibration may be quite random and may not be accessible for

alteration at all (e.g., aerodynamic forces on an aircraft).

32.1.1 Shock and Vibration

Sometimes, response to shock loads is considered separately from response to vibration excitations

for the purpose of design and control of mechanical systems. For example, shock isolation and

vibration isolation are treated under different headings in some literature. This is actually unnecessary.

Even though vibration analysis predominantly involves periodic excitations and responses, transient

and random oscillations (vibrations) are also commonly found in practice. The frequency band of

the latter two types of signals is much broader than that of a simple periodic signal. A shock signal is

transient by definition, and has a very short duration (in comparison to the predominant time constants

of the mechanical system to which the shock load is applied). Hence, it will possess a wide band of

frequencies. Consequently, frequency-domain techniques are still applicable. Furthermore, time-domain

techniques are particularly suited to dealing with transient signals in general and shock signals in

particular. In that context, a shock excitation may be treated as an impulse whose effect is to

instantaneously change the velocity of an inertia element. Then, in the time domain, a shock load may

also be treated as an initial-velocity excitation of an otherwise free (unforced) system.

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