This self-contained volume explains the general method of statistical linearization and its use in solving random vibration problems. Numerous examples show advanced undergraduate and graduate students many practical applications. 1990 edition.

This second edition of the book, Nonlinear Random Vibration: Analytical Techniques and Applications, expands on the original edition with additional detailed steps in various places in the text. It is a first systematic presentation on the subject. Its features include: • a concise treatment of Markovian and non- Markovian solutions of nonlinear stochastic differential equations, • exact solutions of Fokker-Planck-Kolmogorov equations, • methods of statistical linearization, • statistical nonlinearization techniques, • methods of stochastic averaging, • truncated hierarchy techniques, and • an appendix on probability theory. A special feature is its incorporation of detailed steps in many examples of engineering applications. Targeted audience: Graduates, research scientists and engineers in mechanical, aerospace, civil and environmental (earthquake, wind and transportation), automobile, naval, architectural, and mining engineering.

This classic describes and illustrates basic theory, with a detailed explanation of discrete wavelet transforms. Suitable for upper-level undergraduates, it is also a practical resource for professionals.

Focuses on the Basic Methodologies Needed to Handle Random Processes After determining that most textbooks on random vibrations are mathematically intensive and often too difficult for students to fully digest in a single course, the authors of Random Vibration: Mechanical, Structural, and Earthquake Engineering Applications decided to revise the current standard. This text incorporates more than 20 years of research on formulating bridge design limit states. Utilizing the authors’ experience in formulating real-world failure probability-based engineering design criteria, and their discovery of relevant examples using the basic ideas and principles of random processes, the text effectively helps students readily grasp the essential concepts. It eliminates the rigorous math-intensive logic training applied in the past, greatly reduces the random process aspect, and works to change a knowledge-based course approach into a methodology-based course approach. This approach underlies the book throughout, and students are taught the fundamental methodologies of accounting for random data and random processes as well as how to apply them in engineering practice. Gain a Deeper Understanding of the Randomness in Sequences Presented in four sections, the material discusses the scope of random processes, provides an overview of random processes, highlights random vibrations, and details the application of the methodology. Relevant engineering examples, included throughout the text, equip readers with the ability to make measurements and observations, understand basic steps, validate the accuracy of dynamic analyses, and master and apply newly developed knowledge in random vibrations and corresponding system reliabilities. Comprising 11 Chapters, this text: Reviews the theory of probability and applies it from an engineering perspective Introduces basic concepts and formulas to prepare for discussions of random processes Emphasizes the essence of probability as the chance of occurrence in sample space Covers two important issues in engineering practice, the uncertainty of data and the probability of failure Explores the random processes in the time domain Explains the nature of time-varying variables by joint PDF through the Kolmogorov extension Examines random processes in the frequency domain Discusses several basic and useful models of random processes Presents a new set of statistics for random processes Employs an approach to present important processes within the context of practical engineering problems Includes the generality of dealing with randomness and the difference between random variables and processes Focuses on the topic of vibration problems Addresses the basic parameters of linear single-degree-of-freedom (SDOF) systems Stresses a new method of random process referred to as time series Details linear multi-degree-of-freedom (MDOF) systems Describes the statistical analyses of direct approach based on model decoupling of proportionally and nonproportionally-damped systems Provides materials on the applications of random processes and vibration Discusses statistical studies on random data and model identifications Describes the nonlinear phenomena and the general approach of linearization Highlights a special method of Monte Carlo simulation, and more Random Vibration: Mechanical, Structural, and Earthquake Engineering Applications effectively integrates the basic ideas, concepts, principles, and theories of random processes. This enables students to understand the basic methodology and establish their own logic to systematically handle the issues facing the theory and application of random vibrations.

This systematic treatment examines linear and nonlinear dynamical systems subject to parametric random vibrations. It formulates stochastic stability theorems and analytical techniques for determining random response of nonlinear systems. 1985 edition.

This second edition of the book, Nonlinear Random Vibration: Analytical Techniques and Applications, expands on the original edition with additional detailed steps in various places in the text. It is a first systematic presentation on the subject. Its features include: ¿ a concise treatment of Markovian and non- Markovian solutions of nonlinear stochastic differential equations, ¿ exact solutions of Fokker-Planck-Kolmogorov equations, ¿ methods of statistical linearization, ¿ statistical nonlinearization techniques, ¿ methods of stochastic averaging, ¿ truncated hierarchy techniques, and ¿ an appendix on probability theory. A special feature is its incorporation of detailed steps in many examples of engineering applications. Targeted audience: Graduates, research scientists and engineers in mechanical, aerospace, civil and environmental (earthquake, wind and transportation), automobile, naval, architectural, and mining engineering.

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.