32 Vibration Design and Control Clarence W. de Silva

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The University of British Columbia

32.1 Introduction ..................................................................... 32-2

Shock and Vibration

32.2 Specification of Vibration Limits ................................... 32-3

Peak Level Specification † Root-Mean-Square Value

Specification † Frequency-Domain Specification

32.3 Vibration Isolation ........................................................... 32-5

Design Considerations † Vibration Isolation of Flexible

Systems

32.4 Balancing of Rotating Machinery ................................... 32-15

Static Balancing † Complex Number/Vector

Approach † Dynamic (Two-Plane) Balancing †

Experimental Procedure of Balancing

32.5 Balancing of Reciprocating Machines ............................ 32-26

Single-Cylinder Engine † Balancing the Inertia Load

of the Piston † Multicylinder Engines † Combustion/

Pressure Load

32.6 Whirling of Shafts ............................................................ 32-33

Equations of Motion † Steady-State Whirling †

Self-Excited Vibrations

32.7 Design through Modal Testing ....................................... 32-39

Component Modification † Substructuring

32.8 Passive Control of Vibration ........................................... 32-45

Undamped Vibration Absorber † Damped Vibration

Absorber † Vibration Dampers

32.9 Active Control of Vibration ............................................ 32-61

Active Control System † Control Techniques

32.10 Control of Beam Vibrations ............................................ 32-67

State-Space Model of Beam Dynamics † Control

Problem † Use of Linear Dampers

Appendix 32A MATLAB Control

Systems Toolbox ............................................................... 32-73

Summary

There are desirable and undesirable types and situations of mechanical vibration. Undesirable vibrations are those

that cause human discomfort and hazards, structural degradation and failure, performance deterioration and

malfunction of machinery and processes, and various other problems. This chapter discusses ways of either

eliminating or reducing the undesirable effects of vibration. Specifically, some useful topics on design for vibration

suppression and the control of vibration are addressed. General approaches to vibration mitigation may be

identified from the dynamic systems point of view. Typically, a set of vibration specifications is given as simple

threshold values (bounds) or frequency spectra, and the goal is to either design or control the system to meet these

32-1

© 2005 by Taylor & Francis Group, LLC

specifications. Frequency-domain techniques based on transfer functions such as transmissibility and time-domain

techniques using the state-space representation, optimal control, and modal control are presented. Applications

considered here include vibration isolation, balancing of rotating and reciprocating machinery, whirling

suppression, and passive and active control of vibration.

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