Boundary Stabilization Of Thin Elastic Plates

In this paper we shall consider the question of uniform stabilization of thin, elastic plates through the action of forces and moments on the edge of the plate (or on a part of the edge of the plate). Two particular plate models will be considered: The classical fourth order Kirchoff model, but incorporating rotational inertia, and the sixth order Mindlin-Timoshenko model. The difference in the two models, from a physical point of view, is that the M-T model incorporates transverse shear effects while the Kirchhoff model does not. Actually, the M-T model is a hyperbolic system three coupled second order partial differential equations in two dependent variables. The unknowns, denoted by w, psi, phi are the vertical component w of displacement and angles which are measures of the amount of transverse shear. The three equations are coupled through terms which are multiples of a factor K called the coefficient of elasticity in shear.

Presents research in the area of design and analysis of feedback stabilizers for distributed parameter systems in structural dynamics.

Contents: the history of the development of the theory of elastic thin plates, theory of elastic thin plates, problems associated with the cylindrical bending of long rectangular plates, bending of simply supported rectangular plates, equilibrium, stability and vibration of rectangular plates with fixed edges, rectangular plates with two adjacent edges fixed and two adjacent edges simply supported, equilibrium, stability and vibration of continuous rectangular plates, problems associated with rectangular plates supported at the corner points.

Elementary Theory of Elastic Plates deals with plate theory, particularly on the elastic behavior of initially flat thin plates subjected to loads, producing deflexions. This book discusses rectangular plates and circular plates subjected to different types of load conditions. This text describes the bending moment and curvature of beams, and gives the formula of principal axes, where the location of a neutral axis that experiences zero stress and strain, can be found. This book also notes how calculations can show small or negligible deflexions. The text discusses Possion's ratio effect and the Mohr's circle relationship. This text analyzes the various loads acting on different parts of the rectangular plate using the Navier method; the Levy's method is taken up when considerations are on other forms of boundary support on the rectangular plate. This book then addresses the circular plate that experiences bending moments and curvatures when it is placed under radially symmetric loads. This text explains the equation that is applicable in a radially symmetric case. This book also addresses understanding approximations of energy in stability problems when there is bending and twisting as shown in a strut with a certain thickness, radial length of the arms, and length of the strut. Engineers, physicists, architects, and designers of industrial equipment subject to heavy loads will appreciate the information found in this book.

This advanced and graduate-level text and self-tutorial teaches readers to understand and to apply analytical design principles across the breadth of the engineering sciences. Emphasizing fundamentals, the book addresses the stability of key engineering elements such as rigid-body assemblage, beam-column, beam, rigid frame, thin plate, arch, ring, and shell. Each chapter contains numerous worked-out problems that clarify practical application and aid comprehension of the basics of stability theory, plus end-of-chapter review exercises. Others key features are the citing and comparison of different national building standards, use of non-dimensional parameters, and many tables with much practical data and simplified formula, that enable readers to use them in the design of structural components. First six chapters most suitable for undergraduate-level study and remaining chapters for graduate-level courses.

The grant period 1 December 1966 to 30 November 1967 saw the successful development of the Edge-Function Method to plates with polygonal and/or curved boundaries with holes, and also a radically novel use of conformal mapping for the solution of plate problems. (Author).

This groundbreaking book resolves the main lacuna in Kirchhoff theory of bending of plates in the Poisson-Kirchhoff boundary conditions paradox through the introduction of auxiliary problem governing transverse stresses. The book highlights new primary bending problem which is formulated and analyzed by the application of developed Poisson theory. Analysis with prescribed transverse stresses along faces of the plate, neglected in most reported theories, is presented with an additional term in displacements. The book presents a systematic procedure for the analysis of unsymmetrical laminates. This volume will be a useful reference for students, practicing engineers as well as researchers in applied mechanics.

The subject discussed in this book is the stability of thin-walled elastic systems under static loads. The presentation of these problems is based on modern approaches to elastic-stability theory. Special attention is paid to the formulation of elastic-stability criteria, to the statement of column, plate and shell stability problems, to the derivation of basic relationships, and to a discussion of the boundaries of the application of analytic relationships. The author has tried to avoid arcane, nonstandard problems and elaborate and unexpected solutions, which bring real pleasure to connoisseurs, but confuse students and cause bewilderment to some practical engineers. The author has an apprehension that problems which, though interesting, are limited in application can divert the reader's attention from the more prosaic but no less sophisticated general problems of stability theory.