Ebook: Statistical Dynamics and Reliability Theory for Mechanical Structures

The theory of random processes is an integral part of the analysis and synthesis of complex engineering systems. This textbook systematically presents the fundamentals of statistical dynamics and reliability theory. The theory of Markovian processes used during the analysis of random dynamic processes in mechanical systems is described in detail. Examples are machines, instruments and structures loaded with perturbations. The reliability and lifetime of those objects depend on how properly these perturbations are taken into account. Random vibrations with finite and infinite numbers of degrees of freedom are analyzed as well as the theory and numerical methods of non-stationary processes under the conditions of statistical indeterminacy. This textbook is addressed to students and post-graduate of technical universities. It can be also useful to lecturers and mechanical engineers, including designers in different industries.

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The theory of random processes is an integral part of the analysis and synthesis of complex engineering systems. This textbook systematically presents the fundamentals of statistical dynamics and reliability theory. The theory of Markovian processes used during the analysis of random dynamic processes in mechanical systems is described in detail. Examples are machines, instruments and structures loaded with perturbations. The reliability and lifetime of those objects depend on how properly these perturbations are taken into account. Random vibrations with finite and infinite numbers of degrees of freedom are analyzed as well as the theory and numerical methods of non-stationary processes under the conditions of statistical indeterminacy. This textbook is addressed to students and post-graduate of technical universities. It can be also useful to lecturers and mechanical engineers, including designers in different industries.

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The theory of random processes is an integral part of the analysis and synthesis of complex engineering systems. This textbook systematically presents the fundamentals of statistical dynamics and reliability theory. The theory of Markovian processes used during the analysis of random dynamic processes in mechanical systems is described in detail. Examples are machines, instruments and structures loaded with perturbations. The reliability and lifetime of those objects depend on how properly these perturbations are taken into account. Random vibrations with finite and infinite numbers of degrees of freedom are analyzed as well as the theory and numerical methods of non-stationary processes under the conditions of statistical indeterminacy. This textbook is addressed to students and post-graduate of technical universities. It can be also useful to lecturers and mechanical engineers, including designers in different industries.
Content:
Front Matter....Pages I-XII
Introduction....Pages 1-9
Fundamentals of the Probability Theory and the Theory of Random Processes....Pages 11-43
Non-Stationary Random Functions (Processes)....Pages 45-71
Stationary Random Functions (Processes)....Pages 73-100
Fundamentals of the Markov Processes Theory....Pages 101-129
Random Vibrations of Systems with One Degree of Freedom....Pages 131-196
Random Vibrations of Systems with Finite Number of Degrees of Freedom....Pages 197-258
Random Vibrations of Strings; Longitudinal and Torsional Vibrations of Straight Rods....Pages 259-278
Random Vibrations of Rods....Pages 279-311
Fundamentals of Reliability Theory....Pages 313-347
Random Processes at the Action of Random Functions Bounded in Absolute Value....Pages 349-429
Back Matter....Pages 431-448

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The theory of random processes is an integral part of the analysis and synthesis of complex engineering systems. This textbook systematically presents the fundamentals of statistical dynamics and reliability theory. The theory of Markovian processes used during the analysis of random dynamic processes in mechanical systems is described in detail. Examples are machines, instruments and structures loaded with perturbations. The reliability and lifetime of those objects depend on how properly these perturbations are taken into account. Random vibrations with finite and infinite numbers of degrees of freedom are analyzed as well as the theory and numerical methods of non-stationary processes under the conditions of statistical indeterminacy. This textbook is addressed to students and post-graduate of technical universities. It can be also useful to lecturers and mechanical engineers, including designers in different industries.
Content:
Front Matter....Pages I-XII
Introduction....Pages 1-9
Fundamentals of the Probability Theory and the Theory of Random Processes....Pages 11-43
Non-Stationary Random Functions (Processes)....Pages 45-71
Stationary Random Functions (Processes)....Pages 73-100
Fundamentals of the Markov Processes Theory....Pages 101-129
Random Vibrations of Systems with One Degree of Freedom....Pages 131-196
Random Vibrations of Systems with Finite Number of Degrees of Freedom....Pages 197-258
Random Vibrations of Strings; Longitudinal and Torsional Vibrations of Straight Rods....Pages 259-278
Random Vibrations of Rods....Pages 279-311
Fundamentals of Reliability Theory....Pages 313-347
Random Processes at the Action of Random Functions Bounded in Absolute Value....Pages 349-429
Back Matter....Pages 431-448
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