T1-1                  www.vibrationmounts.com  Phone:  516.328.3662  Fax:  516.328.3365 Table of Contents   1.0  FUNDAMENTALS OF VIBRATION AND SHOCK 1.1 What Is Vibration?  ...................................................................................................................................... T1-2 1.1.1 Damping  ........................................................................................................................................ T1-2 1.2 What is Shock? ........................................................................................................................................... T1-3 1.3 What is Noise?  ........................................................................................................................................... T1-3 1.4 Principles of Vibration Isolation................................................................................................................... T1-4 1.5 Principles of Noise Reduction ..................................................................................................................... T1-5   2.0  BASIC DEFINITIONS AND CONCEPTS IN VIBRATION AND SHOCK ANALYSIS 2.1 Kinematic Characteristics ........................................................................................................................... T1-5 2.2 Rigid-Body Characteristics  ......................................................................................................................... T1-6 2.3 Spring and Compliance Characteristics  ..................................................................................................... T1-6 2.4 Damping, Friction and Energy-Dissipation Characteristics  ........................................................................ T1-7 2.5 Vibration Characteristics of Mechanical Systems ....................................................................................... T1-7 2.5.1 Amplitude-Frequency Characteristics of Forced Vibrations ........................................................... T1-8   3.0  VIBRATION ISOLATION ...................................................................................................................................... T1-9 3.1 Vibration Isolation of Vibration-Producing Products  ................................................................................... T1-10 3.2 Vibration Isolation of Vibration-Sensitive Objects ....................................................................................... T1-12 3.3 Shock Isolation  ........................................................................................................................................... T1-14 3.3.1  Shock Motion of Base (Base Suddenly Stops or Accelerates)  ......................................................... T1-16 3.3.2  Sudden Impact on Equipment ........................................................................................................... T1-17   4.0  NONLINEARITIES ................................................................................................................................................ T1-17   5.0  MULTIDEGREE OF FREEDOM SYSTEMS, COUPLED MODES ....................................................................... T1-19   6.0  STATIC LOAD DISTRIBUTION CALCULATION ................................................................................................. T1-20 6.1 Advantages of CNF Vibration Isolators....................................................................................................... T1-21   7.0  CONNECTIONS OF SPRING ELEMENTS .......................................................................................................... T1-22 7.1 Springs in Parallel ....................................................................................................................................... T1-22 7.2 Springs in Series  ........................................................................................................................................ T1-22 7.3 Spring Connected Partly in Parallel and Partly in Series ............................................................................ T1-22   8.0  3-D OBJECT DRIVEN BY VIBRATORY FORCE AND TORQUES...................................................................... T1-23 8.1 Displacement of the Object  ........................................................................................................................ T1-23 8.2 Undamped Natural Frequencies ................................................................................................................. T1-24 8.3 Mount Deflections ....................................................................................................................................... T1-24   9.0  COMPLEX DRIVING FORCES ............................................................................................................................ T1-25 10.0  DESIGN PROBLEM EXAMPLES......................................................................................................................... T1-26   REFERENCES  .................................................................................................................................................... T1-34   APPENDIX   1 Useful Formulas in Vibration Analysis  ........................................................................................................ T1-35   2 Properties of Rubber and Plastic Materials  ................................................................................................ T1-37   3 Hardness Conversion Charts  ..................................................................................................................... T1-38 Technical Section: Vibration and Shock Isolation