Random Vibrations Of Elastic Systems

The subject of random vibrations of elastic systems has gained, over the past decades, great importance, specifically due to its relevance to technical problems in hydro- and aero-mechanics. Such problems involve aircraft, rockets and oil-drilling platforms; elastic vibrations of structures caused by acoustic radiation of a jet stream and by seismic disturbances must also be included. Appli cations of the theory of random vibrations are indeed numerous and the development of this theory poses a challenge to mathematicians, mechanicists and engineers. Therefore, a book on random vibrations by a leading authority such as Dr. V.V. Bolotin must be very welcome to anybody working in this field. It is not surprising that efforts were soon made to have the book translated into English. With pleasure I acknowledge the co-operation of the very competent translater, I Shenkman; of Mrs. C. Jones, who typeJ the first draft; and of Th. Brunsting, P. Keskikiikonen and R. Piche, who read it and suggested where required, corrections and changes. I express my gratitude to Martinus Nijhoff Publishers BV for entrust ing me with the task of editing the English translation, and to F.J. van Drunen, publishers of N. Nijhoff Publishers BV, who so kindly supported my endeavours. Special acknowledgement is due to Mrs. L. Strouth, Solid Mechanics Division, University of Waterloo, for her competent and efficient preparation of the final manuscript.

Modern engineering materials subjected to unfavorable mechanical and environmental conditions decrease in strength due to the accumulation of microstructural changes. For example, considering damage in metals we can mention creep damage, ductile plastic damage, embrittlement of steels and fatigue damage. To properly estimate the value of damage when designing reliable structures it is necessary to formulate the damage phenomenon in terms of mechanics. Then it is possible to analyse various engineering problems using analytical and computational techniques. During the last two decades the basic principles of continuum damage mechanics were formulated and some special problems were solved. Many scientific papers were published and several conferences on damage mechanics took place. Now continuum damage mechanics is rapidly developing branch of fracture mechanics. This book is probably the first one on the subject; it contains a sys tematic description of the basic aspects of damage mechanics and some of its applications. In general, a theoretical description of damage can be rather compli cated. The experiments in this field are difficult (especially under multiax ial stress and non-proportional loading). Therefore, experimental data, as a rule, are scarce. Determination of functions and constants, which play a role in the complex variants of the theory, from available experimental data is often practically impossible. ix L.M. Kachanov The problems of damage mechanics are mainly engineering ones. Therefore, the author tries to avoid superfluous mathematical formalism. Some more details of the book's subject can be found in the list of con tents.

Preface Acknowledgements List of Figures List of Tables List of Abbreviations/Photographs Chapter 1 Introduction Chapter 2 Basic Concept Chapter 3 Discrete System Chapter 4 Multi Degree of Freedom system Chapter 5 Numerical Methods-Free Vibrations Chapter 6 Numerical Methods-forced Vibrations Chapter 7 Continuous Systems and Elastic Media Chapter 8 Nonlinear Vibrations Chapter 9 Random Vibrations Chapter 10 Finite Element Method Chapter 11 Vibration Isolation and Control Appendices Name Index Subject Index.

This Book Presents The Topic Of Vibtations Comprehensively In Terms Of Principles Of Dynamics- Forces, Responses, Analysis, Solutions, Examples, Measurement, Interpretation, Control And Probabilistic Approaches. Idealised Discrete Systems As Well As Continuous Systems Are Discussed In Detail. A Wide Array Of Numerical Methods Used In Vibration Analysis Are Presented In View Of Their Enormous Popularity, Adaptability Using Personal Computers. A Large Number Of Examples Have Been Worked Out To Help An Easy Understanding Of Even The Difficult Topics In Vibration Analysis And Control.

This volume explains the dramatic effect of cross-correlations in forming the structural response of aircraft in turbulent excitation, ships in rough seas, cars on irregular roads, and other dynamic regimes. It brings into sharp focus the dramatic effect of cross correlations often neglected due to the analytical difficulty of their evaluation. Veteran author Professor Isaac Elishakoff illustrates how neglect of cross correlations could result in underestimation of the response by tens or hundreds of percentages the effect of the random vibrations of structures’ main elements, including beams, plates, and shells.

The topic of Random Vibrations is the behavior of structural and mechanical systems when they are subjected to unpredictable, or random, vibrations. These vibrations may arise from natural phenomena such as earthquakes or wind, or from human-controlled causes such as the stresses placed on aircraft at takeoff and landing. Study and mastery of this topic enables engineers to design and maintain structures capable of withstanding random vibrations, thereby protecting human life.Random Vibrations will lead readers in a user-friendly fashion to a thorough understanding of vibrations of linear and nonlinear systems that undergo stochastic—random—excitation. Provides over 150 worked out example problems and, along with over 225 exercises, illustrates concepts with true-to-life engineering design problems Offers intuitive explanations of concepts within a context of mathematical rigor and relatively advanced analysis techniques. Essential for self-study by practicing engineers, and for instruction in the classroom.

The most comprehensive text and reference available on the study of random vibrations, this book was designed for graduate students and mechanical, structural, and aerospace engineers. In addition to coverage of background topics in probability, statistics, and random processes, it develops methods for analyzing and controlling random vibrations. 1995 edition.

This work presents a unified approach to the vibrations of elastic systems as applied to MEMS devices, mechanical components, and civil structures. Applications include atomic force microscopes, energy harvesters, and carbon nanotubes and consider such complicating effects as squeeze film damping, viscous fluid loading, in-plane forces, and proof mass interactions with their elastic supports. These effects are analyzed as single degree-of-freedom models and as more realistic elastic structures. The governing equations and boundary conditions for beams, plates, and shells with interior and boundary attachments are derived by applying variational calculus to an expression describing the energy of the system. The advantages of this approach regarding the generation of orthogonal functions and the Rayleigh-Ritz method are demonstrated. A large number of graphs and tables are given to show the impact of various factors on the systems’ natural frequencies, mode shapes, and responses.