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 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.

One of the first engineering books to cover wavelet analysis, this classic text describes and illustrates basic theory, with a detailed explanation of the workings of discrete wavelet transforms. Computer algorithms are explained and supported by examples and a set of problems, and an appendix lists ten computer programs for calculating and displaying wavelet transforms. Starting with an introduction to probability distributions and averages, the text examines joint probability distributions, ensemble averages, and correlation; Fourier analysis; spectral density and excitation response relations for linear systems; transmission of random vibration; statistics of narrow band processes; and accuracy of measurements. Discussions of digital spectral analysis cover discrete Fourier transforms as well as windows and smoothing. Additional topics include the fast Fourier transform; pseudo-random processes; multidimensional spectral analysis; response of continuous linear systems to stationary random excitation; and discrete wavelet analysis. Numerous diagrams and graphs clarify the text, and complicated mathematics are simplified whenever possible. This volume is suitable for upper-level undergraduates and graduate students in engineering and the applied sciences; it is also an important 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 is a systematic presentation of several classes of analytical techniques in non-linear random vibration. The book also includes a concise treatment of Markovian and non-Markovian solutions of non-linear differential equations.