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Book Review
These reviews of books and other forms of information express the opinions of the individual reviewers and are not necessarily endorsed by the Editorial Board of Acoustics Today or the Journal of the Acoustical Society of America.
Foundations of Statistical Energy Analysis in Vibroacoustics
Author: A. Le Bot Publisher: Oxford University Press, 2015 ISBN: 978–0198729235
Foundations of Statistical Energy Analysis in Vibro- acoustics is an excellent elaboration on its title subject, not only in terms of providing those specific foundations but also at connecting them to rele- vant deterministic concepts
while acknowledging the field’s many contributors to both sets of disciplines. Readers might also be advised, however, of generalized Polynomial Chaos as a complementary, and possibly supplementary approach to the “propagation”
of physical uncertainties throughout a complex system, including a structural one made up of lumped parameters (basic oscillators) coupled to wave-bearing distributed components.
Le Bot’s book begins by laying out the necessary mathemat- ics of Statistical Energy Analysis (SEA) and that makes the monograph self contained. There are occasional comments that one should take cum grano salis, as p. 7’s promotion of Eqs. 1.25 and 1.26 as more “useful” [in practice] than Eq. 1.24’s alternative, or Eq. 1.57’s clipping off of its dummy- time’s domain before t1⁄40 when its integral’s limits would have respected causality just as much had they been expand- ed, and generalized, to [-1,t]. Equation 2.74 could be modi- fied accordingly.
– Philip L. Marston, Book Review Editor
transients, for which -dE/dt in Eq. 12.19, and þdE/dt in Eq. 2.103, effectively replace Prad at either injecting or drawing energy into/from an equivalent group of resistive boundaries.
On the other side of the ledger, the book gives more than adequate attention to Skudrzyk’s similarly acting structural energy sinks derived from the product of a [nominal] loss factor and the system’s modal density (called a “fuzzy” in the later literature). The structure’s mean response is then accu- rately supplied by the former’s unbound version or behavior, often analytically available; cf. p. 203, which cites Skudrzyk’s 1968 paper, which was later summarized and added to in that author’s “The mean value method of predicting the dy- namic response of complex vibrators,” Journal of Acousti- cal Society of America 67(4), April 1980, pp. 1105–1135. I was particularly grateful for Le Bot’s analysis of the effects on modal density of a structural system’s two canonical, null (and therefore purely reactive) classes of boundaries, of which this reviewer was frankly unaware (Sec. 6.4, where Dirichlet boundaries embody zero stresses and maximum local displacements, versus Neumann ones, for which the reverse occurs).
Returning to the fundamental statistical mechanics under- lying much of SEA, the book explains clearly, both quanti- tatively and qualitatively, the important role of white-noise driving conditions in eliciting energy sharing and equi-par- titioning among a structure’s possible types of local consti- tutive and/or inertia response, both “self” and interactive: First on pp. 25 and 39 (Eqs. 2.87 and 2.88), and later in Eq. 3.64 at the level of power, or energy—thereby retroac- tively justifying Dick Lyon’s reference to these concepts in the book’s praising Foreword in the context of equilibrium Thermodynamics.
In summary, this reviewer highly recommends Le Bot’s new book to both students and seasoned analysts of the time- varying dynamics of complex structures. It does a fine job in its description of the insightful issue from the marriage of the deterministic to the statistical, the continuous to the discrete, and the sharp-harmonic to the spectral shot-gun blast of a frequency-flat stochastic input.
Reviewed by:
R. MARTINEZ
Applied Physical Sciences, Lexington, MA 02421 rmartinez@aphysci.com
[Published online August 9, 2016,
Journal of Acoustical Society of America. 140 (2)]
Another comment relates to Eq. 2.31’s power balance for an isolated structural system. It might have been mentioned that an unbound acoustic medium either partially or wholly engulfing the structure would have contributed a radiated power Prad to the left side of Eqs. 2.102 and 2.104. It is true that these expressions are later extended in the analysis of
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