graphic

11R8. Fundamentals of Vibrations. - L Meirovitch (Col of Eng, VP1, Blacksburg VA 24061). McGraw-Hill, New York. 2001. 806 pp. ISBN 0-07-041345-2. $95.50.

Reviewed by RG Parker (Dept of Mech Eng, Ohio State Univ, 206 W 18th Ave, Columbus OH 43210-1107).

Professor Meirovitch has produced a number of widely-used textbooks on dynamics, vibration, and control over the last 35 years. This is especially true at the graduate level, where Analytical Methods in Vibrations (1967, Macmillan) became the standard reference for vibrations researchers. He subsequently produced additional undergraduate and graduate vibrations texts. The ones most relevant to the current book are Elements of Vibration Analysis (1975, 1986, McGraw-Hill) and Principles and Techniques of Vibrations (1997, Prentice-Hall). People familiar with Meirovitch’s books will find the same careful, concise, analytical treatment in this latest book that is the hallmark of his earlier ones. The similarity to Elements of Vibration Analysis is unmistakable in content and organization, though it has been adjusted in two ways. First, the book includes more graduate material, allowing greater flexibility in its use. Additionally, Matlab codes are given at the end of some chapters and used in some exercises.  

This book “is intended as a textbook for a number of courses on vibrations ranging from the junior level to the second-year graduate level.” This is an ambitious range for a single book. With this in mind, it begins with the basics; Chapter 1, Concepts from Vibrations, treats the basic laws of particle and planar rigid body dynamics, modeling simple vibratory systems, properties of linear systems, and the like. Undergraduates can see from this first chapter the emphasis on analysis that continues throughout. Chapters 2 through 4 are Response of Single-Degree-of-Freedom (SDOF) Systems to Initial Excitations, Response of SDOF Systems to Harmonic and Periodic Excitations, and Response of SDOF Systems to Nonperiodic Excitations. These chapters emphasize the analytical more than engineering applications; a characteristic of the book overall, but most evident in these undergraduate sections. Matlab is introduced at the ends of these chapters by giving codes to calculate free response, frequency response, and response to arbitrary forces. Matlab is not integrated throughout the text, but this is not necessarily a flaw. This is also true of later chapters. Each chapter begins with a well-written introduction and ends with a helpful summary.

Chapter 5, Two-Degree-of-Freedom Systems, is a bridge to the more general treatment of multi-DOF systems. Items such as matrix representation of the equations, natural frequencies, vibration modes, orthogonality, and modal analysis are introduced for this special case. Graduate classes would likely cover this quickly or omit it. Chapter 6, Elements of Analytical Dynamics, derives Hamilton’s Principle using virtual work and d’Alembert’s Principle and uses it to obtain Lagrange’s Equations. The condensed treatment is well-written and allows use of these key ideas in later chapters even if students have not had a dedicated course in analytical dynamics. Chapter 7, Multi-Degree-of-Freedom Systems, presents the classical matrix methods in a clear, mathematical exposition. The flow is natural: influence coefficients, properties of system matrices, the symmetric eigenvalue problem, orthogonality, modal decoupling, and response using modal analysis. Later sections present interesting material on geometric interpretation of the eigenvalue problem, Rayleigh’s Quotient, systems with arbitrary damping using a state-space representation with biorthogonality relations, and response using the state-transition matrix.

Chapters 8 (Distributed-parameter Systems: Exact Solutions) and 9 (Distributed-Parameter Systems: Approximate Methods) address continuous systems. There is an emphasis on careful formulation of the governing equations. This is demonstrated for the transverse string and beam vibration examples using the Newtonian formulation applied to a differential element and Hamilton’s Principle. The eigensolutions, orthogonality, and modal analysis are derived and interpreted on a case-by-case basis rather than introducing operators and treating general self-adjoint, positive-definite systems. Chapter 8 includes systems with masses at the boundaries, time-dependent boundary conditions, and wave propagation. Chapter 9 is a comprehensive, well-written treatment of lumping (Holzer, Myklestad) and series expansion (Rayleigh-Ritz, assumed modes, Galerkin and collocation) discretizations. There is enough here for a first-year graduate course.

Chapters 10 (Finite Element Method), 11 (Nonlinear Oscillations), and 12 (Random Vibrations) are excellent, concise introductions to advanced topics. These chapters allow good depth of coverage of typically optional topics in early graduate courses. They add considerably to the book’s utility as a reference. The finite element method is presented as a vibrational, Rayleigh-Ritz method. Both geometric and perturbation methods for nonlinear vibrations are covered. The treatment of random vibrations is a self-contained primer suitable for part of an advanced vibrations course or for self-study.

Meirovitch has produced another excellent book that this reviewer recommends highly. Fundamentals of Vibrations is well written with customary clarity and emphasis on analytical precision. Readers will find the style, content, and organization similar to his existing classical ones with a slightly different bias in potential class use. The book should find its best audience in first-year graduate courses and as a reference for practicing engineers. Its level is ambitious for junior-level undergraduates, though it can succeed in senior undergraduate courses, especially technical electives as a second course in vibrations. There is material here in sufficient depth for a second-year graduate course, but the author has other, more advanced offerings that might be better suited for these classes.