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PREFACE:
Understanding and modeling a vibration system and measuring and controlling its oscillation responses are important basic capacities for mechanical, structural, and earthquake engineers who deal with the dynamic responses of mechanical/structural systems. Generally speaking, this ability requires three components:
the basic theories of vibrations, experimental observations, and measurement of dynamic systems and analyses of the time-varying responses. Among these three efforts, the former two are comparatively easily learned by engineering students. However, the third component often requires a mathematical background of random processes, which is rather abstract for students to grasp.
One course covering stochastic processes and random vibrations with engineering applications is already too much for students to absorb because it is mathematically intensive and requires students to follow an abstract thinking path through “pure” theories without practical examples.
To carry out a real-world modeling and analysis of specific types of vibration systems while following through the abstract pure thinking path of mathematical logic would require an additional course; however, there is no room in curriculums for such a follow-up course.
This has been the observation of the first author during many years of teaching random vibration. He frequently asked himself, How can one best teach the material of all three components in a one-semester course? The authors, during the past 20 years, have engaged in an extensive research study to formulate bridge design limit states; first, for earthquake hazard and, subsequently, expanded to multiple extreme natural hazards for which the time-varying issue of rare-occurring extreme hazard events (earthquakes, flood, vehicular and vessel collisions, etc.) had to be properly addressed.
This experience of formulating real-world failure probability–based engineering design criteria provided nice examples of using the important basic ideas and principles of random process (e.g., correlation analysis, the basic relationship of the Wiener–Khinchine formula to transfer functions, the generality of orthogonal functions and vibration modes, and the principles and approaches of dealing with engineering random process). We thus decided to emphasize the methodology of dealing with random vibration.
In other words, we have concluded that it is possible to offer a meaningful course in random vibration to students of mechanical and structural engineering by changing the knowledge-based course approach into a methodology-based approach. The course will guide them in understanding the essence of vibration systems, the fundamental differences in analyzing the deterministic and dynamic responses, the way to handle random variables, and the way to account for random process.
This is the basic approach that underlines the material developed in this book. By doing so, we give up coverage of the rigorous mathematical logic aspect and greatly reduce the portion of random process.
Instead, many real-world examples and practical engineering issues are used immediately following the abstract concepts and theories. As a result, students might gain the basic methodology to handle the generality of engineering projects and develop a certain capability to establish their own logic to systematically handle the issues facing the theory and application of random vibrations.
After such a course, students are not expected to be proficient in stochastic process and to model a random process, but they will be able to design the necessary measurement and observation, to understand the basic steps and validate the accuracy of dynamic analyses, and to master and apply newly developed knowledge in random vibrations and corresponding system reliabilities
