5R11. Sinusoidal Vibration. Mechanical Vibration and Shock Series, Vol I. - C Lalanne (French Atomic Energy Authority, France). Hermes Sci Publ, Paris. Distributed in USA by Taylor & Francis Publ, New York NY. 2002. 312 pp. ISBN 1-56032-985-8. \$150.00.

Reviewed by AW Leissa (Dept of Mech Eng, Colorado State Univ., Fort Collins, CO 80523).

This book is Volume I of a five volume series entitled Mechanical Vibration and Shock. The subsequent four volumes are: II, Mechanical Shock; III, Random Vibration; IV, Fatigue Damage; V, Specification Development. As explained in a Foreword, the series is intended for engineers and technicians working in design teams, and for testing laboratories.

With the above users in mind, the narrowness of scope and the inaccuracy of explanations in the present book are tolerable. This book is limited to single-degree-of-freedom systems having linear springs and viscous damping. Excitations are entirely deterministic, without considering random input. Continuous systems (rods, beams, plates, etc) are not taken up.

The inaccuracies are clearly evident in Chapter 1 (Basic Mechanics), where the ordinary differential equation for the one-dof system is derived (from Newtons Second Law—not D’Alembert’s Principle, as mentioned there). Free body diagrams are never drawn. Instead, equations evolve through discussion (including the well-known formulas for springs in parallel and in series). The linear spring stiffness is (unusually) defined as $k=−ΔF/Δz,$ and an incorrect picture (Fig. 1.4) is shown to explain it. Some lengthy discussion of material behavior transpires, with improper terminology used in places (eg, “deformation velocity,” instead of “strain rate,” which is dimensionally different, and “longitudinal deflection” instead of “strain”). In spite of such carping criticisms, Chapter 1 does have considerable useful and interesting general information in it. One only hopes that readers lacking fundamental background in the subject will obtain it elsewhere, and not rely too heavily upon the explanations here.

The next four chapters present solutions in great detail for displacement, velocity and acceleration of single-dof vibrating masses subjected to various types of applied forces or base excitation, including impulse or step functions. For the latter, Laplace transforms are introduced. All of these solutions are found also in textbooks, although typically not presented in such detail.

This reviewer found Chapter 6 to be interesting. It is entitled “Non-Viscous Damping.” It explains that in reality the various types of nonviscous damping (dry friction, aerodynamic, velocity powers, hysteretic, etc) can usually be represented by equivalent viscous damping. This is because, in practice, “damping is fortunately rather weak, so that the motion can be approached using a sinusoid.” Another important statement is that attempting to solve the nonlinear equations of nonviscous damping “leads to--calculations complex in a way seldom justified by the result obtained.” This is at the beginning of the chapter. The rest of it derives the well-known equivalent viscous damping coefficients by evaluating energy dissipated in a cycle of motion, and looks at hysteresis loops.

The final two chapters examine the response of the simple system to swept sine excitation. By this, it is meant that in the sin $Ωt$ forcing function, the excitation frequency (Ω) is itself a function of time (t). The swept sine excitation is often used in laboratory tests. Three types of frequency variation are considered: linear, logarithmic (actually exponential), and hyperbolic. Extensive numerical examples are presented and discussed.

The book has an outstanding bibliography of almost 200 listings, with emphasis placed on papers, reports, and books dealing with vibration damping and testing. It covers the field very well and is an excellent source from which a good reference library could be developed.

Sinusoidal Vibration is recommended for technical libraries and also for readers who want to supplement their understanding of damped vibrations. But, as mentioned earlier, it should be used only after a good fundamental understanding is obtained elsewhere.