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 this Journal.Dynamics of shells, plates, and rods is an engineering problem, which involves complicated mathematics due to the fourth-order partial differential equations that describe flexural vibrations. As a result there are two types of books related to this problem: one is written by engineers or physicists and the other by mathematicians. The reviewed book is clearly written by a mathematician, and, in my view, is written for mathematicians who specialize in mechanics and structural dynamics.This book is based on a hybrid variational-asymptotic approach that reduces the three-dimensional equations of elastic theory of plates, shells, and rods to two-and one-dimensional approximate equations of motion using small parameters. This variational-asymptotic ͑VA͒ method was developed by Professor V. L. Berdichevsky about 20 years ago studying small amplitude long-wave vibrations. The method is a synthesis of two methods that are widely used in mechanics: asymptotic and variational. The VA method starts by approximating the system Lagrangian of the functional, instead of a system of differential equations. Neglecting a small term in the Lagrangian is equivalent to neglecting several terms in the differential equations, which are not always easy to recognize as small ones. Next, approximate differential equations are obtained by varying the approximated functional. This approach simplifies the analysis and provides greater flexibility for modifying and solving the equations.The author of the book, Professor Le, has extrapolated this method into the high-frequency short-wave range. Specifically, he applies the VA method to analyze vibrations of piezoelectric shells, plates, and rods, and devotes roughly half of the book to this topic.The book starts with two introductory chapters that discuss the historical and mathematical background of tensor analysis, the geometry of curves and surfaces, the dynamic theory of elasticity and piezoelectricity, and the variational-asymptotic method. After this introduction the book is divided into two equal parts: the first part describes low-frequency vibrations and the second high-frequency vibrations. Both parts contain four chapters with the same titles: Elastic Shells, Elastic Rods, Piezoelectric Shells, and Piezoelectric Rods. Each section ends with problems and exercises. The bibliography consists of 62 references mostly related to the methods described in the book.Overall, the book describes an interesting and powerful method of deriving and solving complicated equations of shell and rod vibrations. However, as a physicist and practitioner, I hestitate to recommend it to ''engineers who deal with vibrations of shells and rods in their everyday practice.'' I would rather agree that it is ''for mathematicians who seek applications of the variational and asymptotic methods in elasticity and piezoelectricity,'' as announ...
The objective is to use active control to suppress the acoustic energy that is radiated to the far field from a structure that has been excited by a short-duration pulse. The problem is constrained by the assumption that the far-field pressure cannot be directly measured. Therefore, a method is developed for estimating the total radiated energy from measurements on the structure. Using this estimate as a cost function, a feedback controller is designed using linear quadratic regulator theory to minimize the cost. Computer simulations of a clampedclamped beam show that there is appreciable difference in the total radiated energy between a system with a controller designed to suppress vibrations of the structure and a system with a controller that takes into account the coupling of these vibrations to the surrounding fluid. The results of this work provide a framework for a general, model-based method for actively suppressing transient structural acoustic radiation that can also be applied to steady, narrow, or broadband disturbances.
We present a catalog of 316 trans-Neptunian bodies detected by the Dark Energy Survey (DES ). These objects include 245 discoveries by DES (139 not previously published) detected in ≈ 60, 000 exposures from the first four seasons of the survey ("Y4" data). The survey covers a contiguous 5000 deg 2 of the southern sky in the grizY optical/NIR filter set, with a typical TNO in this part of the sky being targeted by 25 − 30 Y4 exposures. We describe the processes for detection of transient sources and the linkage into TNO orbits, which are made challenging by the absence of the fewhour repeat observations employed by TNO-optimized surveys. We also describe the procedures for determining detection efficiencies vs. magnitude and estimating rates of false-positive linkages. This work presents all TNOs which were detected on ≥ 6 unique nights in the Y4 data and pass a "subthreshold confirmation" test wherein we demand the the object be detectable in a stack of the individual images in which the orbit indicates an object should be present, but was not detected. This eliminates false positives and yields TNO detections complete to r 23.3 mag with virtually no dependence on orbital properties for bound TNOs at distance 30 AU < d < 2500 AU. The final DES TNO catalog is expected to yield > 0.3 mag more depth, and arcs of > 4 years for nearly all detections.
To add damping to systems, viscoelastic materials (VEM) are added to structures. In order to enhance the damping effects of the VEM, a constraining layer is attached, creating a passive constrained layer damping (PCLD) treatment. When this constraining layer is an active element, the treatment is called active constrained layer damping (ACLD). Recently, the investigation of ACLD treatments has shown it to be an effective method of vibration suppression. In this paper, the treatment of a beam with a separate active and PCLD element will be investigated. Two new hybrid variations will be introduced. A Ritz-Galerkin approach is used to obtain discretized equations of motion. The damping is modeled using the Golla-Hughes-McTavish (GHM) method and the system is analyzed in the time domain. By optimizing on the performance and control effort for both the active and passive case, it will be shown that hybrid treatment is capable of lower control effort with more inherent damping, and is therefore a better approach to suppressing vibration than ACLD.
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