9R4. Optimal Protection from Impact, Shock, and Vibration. - DV Balandin (Res Inst of Appl Math and Cybernetics, Nizhny Novgorod State Univ, Russia), NN Bolotnik (Inst for Prob in Mech, Russian Acad of Sci, Moscow, Russia), and WD Pilkey (Dept of Mech and Aerospace Eng, Univ of Virginia, Charlottesville VA, Russia). Gordon Breach Sci Publ, Newark NJ. 2001. 436 pp. ISBN 90-5699-701-7. $110.00.

Reviewed by C Cetinkaya (Dept of Mech and Aeronaut Eng, Clarkson Univ, CAMP 241, Box 5725, Potsdam NY 13699-5725).

It is reported that only 5% of the total SUVs (sport utility vehicles) sold in the United States have ever been driven in off-road conditions even though the prime feature of an SUV, which has considerably higher price tag than an average sedan, is its off-road capabilities. A typical SUV is heavier and more rigid than a typical sedan. While a slew of explanations could be offered for this consumer behavior, one possible reason is their reportedly better impact protection. In light of this information, a driver of a none-SUV might rightfully wonder about the potential risk implications in case of his/her collision with an SUV, especially, when that driver is an engineer. The topics covered in this book are about how the principles of optimal control can be put to use to narrow risk gaps such as this one in impact protection by design of dynamic isolators.

As the title of the book clearly reflects, it is concerned with the problem of protection of structures under impulsive loading and vibration conditions. The subject matter has been the subject of long-term intensive research, and the size of the literature reflects that fact well. The book reports a wide spectrum of results in optimization techniques applied to finite-dof (degree-of-freedom) systems, and offers methodologies for design of optimal protection systems. The mathematical principles of optimality adopted in the book are based on the maximum principle and the principle of optimality by Pontryagin and Bellman, respectively, developed in the late ’50s and early ’60s. As stated by the authors, the focus of the book is on the application of the optimal control theory to multi-body dynamic systems. The book is concerned with idealized systems consisting of rigid base and the object to be protected from the impulsive load applied to the base. Two typical performance criteria utilized in the book are the maximum relative displacement of the object with respect to the base and the maximum force transmitted to the object. It appears that the main application field the authors have in mind is transportation systems (vehicles, airplanes, etc). The protection of civil engineering structures under seismic loads can also be maximized with the aid of the techniques presented. The target audience of the book is stated as “mathematically oriented researchers and engineers interested in the optimal design of systems for protection from shock and vibration.” To follow the derivations and proofs, a decent background in functional analysis should be sufficient.

This book could be used as text for a specialized graduate-level course following a graduate course in dynamics and vibration, as well as a basic course in control theory in which the state-space representation of systems is introduced. The practicing engineer working on protective systems and structures from impulsive loads and vibrations should also find the book useful as a valuable reference.

The brief background provided in Chapter 1 includes mathematical modeling of mechanical systems and isolators, and control theory for open and closed loop systems. The proofs to the basic theorems employed throughout the book are provided in the first chapter. Some readers would find a section devoted to a graphical method “for solving the fundamental problem of optimal isolation” rather interesting. Chapters 2 and 3 focus on the optimal protection of (single-dof) objects moving in rectilinear and rotational coordinates by designing optimal (passive) isolator under impulsive loading conditions. Chapters 4 and 5 deal with uncertainties in the impact process: uncertainty in loading conditions and the mass of the other object, respectively. The focus of Chapter 6 is on the isolation under harmonic loads. In addition to linear systems, vibration isolation with dry friction is covered in this chapter. In the first six chapters of the book, only single-dof systems are discussed.

Chapter 7 extends the concept of optimal damping of transient motion into multi-dof and distributed systems. Various computational methods for certain classes of disturbances are covered in Chapter 8. The main theme of Chapter 8 is the reduction of a continuous-time optimal control problem to a discreet time problem. Many practical applications, such as performance of a helicopter seat for the prevention of spinal injury and performance of seat belts for thoracic injury prevention, are included. Chapter 9 is on the optimal design of (single-dof) shock isolators using standard elements such as springs and dampers. It is shown that the limiting performance analysis requires that the shock absorber generates a constant force for minimizing the peak force to which the object is subjected. Chapter 10 demonstrates how optimal control can be achieved without the constant force controllers, thus a larger class of controllers are possible with the approach presented. This technique is also referred to as bang-bang control.

The notation adopted in the book seems consistent throughout the chapters. Even though the subject matter is mathematical in its nature, a typical reader should find the notation reasonably easy to follow and consistent. A brief section on the terminology used in the book is also included. Somewhat awkwardly large, but clear, plots are included in the text. System diagrams and figures in the book are clear. The book has a detailed table of contents, a rich subject index, and an extensive list of references. A detailed literature review is provided in Forward: Historical Perspective. A good introduction to Russian and Soviet research on the subject is also provided. Almost every chapter has a section making some closing remarks on the subject matter of the chapter, such as summary of basic results and practical recommendations.

It is somewhat surprising that this book has no coverage on some modern applications such as electronic equipment/device protection, electronic packaging, etc, even though the concepts and methods offered in the book should be directly applicable to such systems. It should be noted that the freedom in selection of the performance index provides a flexibility of the use of the book in a wider spectrum of applications than those covered in the text. Since mechanical systems tend to scale down well, the techniques covered in this book should find applications in the mechanical isolation of small-scale structures (eg, MEMS).

The book’s main focus is on linear finite-degree-of-freedom systems. The coverage for distributed systems is quite limited except for a brief reference in Chapter 7. In addition, the book neglects the effects of plastic deformations on the impact protection. For example, no mention of crumble zones in vehicles, which are often used in modern vehicles as energy absorbing elements, is made. This is partly because of the initial modeling assumption, a rigid base connected to an object to be protected through an isolator; crumbling zones and plastic deformations affect only the force exerted on the rigid base. The reader should keep in mind that more realistic analysis under impulsive loading conditions should include plastic effects. The coverage for nonlinear behavior is also limited. However, a dry-friction damper is introduced and discussed in Chapter 2.

If you are designing and/or analyzing systems which may be subjected to impulsive loads and vibrations during their operational life cycles, such as transportation systems, civil engineering structures, and protective systems (seat belts, helmets, airbags, seats, etc) and are concerned with their optimality, you must have a copy of this book, Optimal Protection from Impact, Shock, and Vibration. Also, control people who are interested in some good practical applications of the control theory in the subject matter might wish to have a look at this book. Vibrations engineers willing to expand their horizons into impact and transient response of systems could also find the book useful. Libraries should seriously consider the title for their collection.