# Modeling and Analysis of Passive Viberation Isolation Systems

Passive vibration isolators are widely used in areas such as automotive, aerospace, manufacturing, heavy machinery, and civil structures. On the one hand, the design and development of passive vibration isolators is a mature technology.On the other hand, analytical modeling of such isolation systems is still evolving due to the multifaceted intersection of different disciplines.

The aim of this book is to serve as a reference for engineers and researchers involved in the design, development,modeling,analysis,and testing of passive
vibration isolation systems.
This book has been divided into seven chapters.Chapter 1 presents a brief review of vibration analysis and terminology. The aim of this chapter is to serve as a refresher; this chapter can be used in conjunction with Appendix A and Appendix B to recapitulate the content from an introductory course in vibration analysis.Chapter 2 presents several linear viscoelastic rheological models that can be used for a single-degree-of-freedom analysis of vibration isolation systems. The main attributes of each model are discussed in this chapter along with the governing relationships between critical model and design parameters. Chapter 3 presents linear viscoelastic models for planar (two- and three-degree-of-freedom) and spatial (six-degree-of-freedom) vibration isolation systems. Additional models for piecewise behavior and hysteretic systems are also presented in this chapter. Chapter 4 presents nonlinear models for single-degree-of-freedom systems as well as multiple-degree-of-freedom systems that can be used for the analysis of passive vibration isolation. Although nonlinearities can be attributed to multiple sources,this chapter primarily focuses on analytical models for a few specific nonlinearities associated with stiffness and damping characteristics. Chapter 5 presents models that are typically used for the analysis of elastomeric
vibration isolators.
Models that can be used to represent such phenomena as Mullins effect, Payne effect, hyperelasticity, aging, and creep have been discussed in this chapter. Chapter 6 presents models that can be used to account for the inertia effect that is typically observed in vibration isolation systems that need to withstand very high excitation frequencies. These models allow an evaluation of vibroacoustic characteristics well above 1 kHz while capturing internal resonance and wave effects.Chapter 7 presents examples and case studies that integrate concepts from the models presented in the previous chapters of the book while emonstrating the influence of the vibration isolation system on overall system dynamics. There are two brief appendices that may be used as a refresher on ordinary differential equations and matrix algebra. Each chapter has a few exercise problems that can be solved to test the understanding of the content presented in the chapter.

The models discussed in this book encompass a wide range that can be useful for the analysis of passive vibration isolation systems. While some of the models presented in this book have been used for quite some time, others are relatively new and offer useful options for gaining an analytical insight that can be used for design. Furthermore, some of the models are phenomenological, while others are semi-empirical; therefore allowing a
design or analysis engineer to customize the models during the product development process. Some of the models for elastomeric materials and nonlinear behavior that have been discussed in this book are active areas of research and continue to be discussed and investigated in the existing literature. A surge in the use of electric powertrains has resulted in new requirements for passive vibration isolation systems, a few models presented in this book are possible options for the analysis of internal resonance in such systems. I hope that the variety of models discussed in this book is useful in the design and development of passive vibration isolation systems by holistically accounting for vibration response, system dynamics, design parameters, and isolator design.