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Single Degree-of-Freedom Vibration
| Content Provider | Scilit |
|---|---|
| Author | Benaroya, Haym Han, Seon Mi Nagurka, Mark |
| Copyright Year | 2013 |
| Description | Book Name: Probabilistic Models for Dynamical Systems |
| Abstract | A primary goal in the study of the dynamics of a structure or a system is to predict its behavior in response to environmental inputs such as forces. In complex environments this can be especially challenging because the inputs cannot be modeled exactly mathematically. If the inputs are characterized statistically,1 the outputs are also similarly characterized. It is important to distinguish between inherently random molecular forces due to Brown- ian motion, such as those experienced by atoms at that scale, and the environmental forces referred to above and of concern here. Environmental forces in dynamic problems are not inherently random, but they undergo complicated oscillations that cannot be modeled e¤ectively using deterministic techniques. Therefore, the tools of probability and statistics are adopted as a framework for organizing complex behavior. In this way, probabilistic models can be used to characterize complex dynamic environments, and these can then be used to predict structural or system response using probabilistic methods. In this chapter we demonstrate all these aspects of probabilistic modeling for the simplest of dynamic models, the single degree-of-freedom system. Applications of random vibration theory include ocean engineering, earthquake engi- neering, wind engineering (skyscrapers and bridges), machine design, and vehicle design (automotive, train, aircraft, and spaceship design). Even though the discussions here are couched in the terminology of mechanical vibration and dynamics, the tools developed in this chapter and elsewhere in this book are broadly applicable to engineering and the physical sciences. The convolution integral de…nes the linear dynamic response to a deterministic force. But, what mathematical tools are useful when the forcing, F (t), function oscillates in such a complex manner as in Figure 6.1? One possibility is to carry out many experiments and gather data on F (t) in the form of time histories. The time history with the largest amplitudes can then be used for the deterministic analysis and design. But, if the largest amplitude force occurs only infrequently, the structure would be overdesigned, and stronger than necessary, and therefore uneconomical. What if all the time histories are averaged and this averaged or mean value time history is used as a deterministic force that is used in the convolution integral? This would be a good start, but the response calculated in this |
| Related Links | https://content.taylorfrancis.com/books/download?dac=C2010-0-35191-X&isbn=9780429107610&doi=10.1201/b14880-14&format=pdf |
| Ending Page | 330 |
| Page Count | 60 |
| Starting Page | 271 |
| DOI | 10.1201/b14880-14 |
| Language | English |
| Publisher | Informa UK Limited |
| Publisher Date | 2013-05-02 |
| Access Restriction | Open |
| Subject Keyword | Book Name: Probabilistic Models for Dynamical Systems Mechanical Engineering Probabilistic Convolution Integral Mathematically Single Degree |
| Content Type | Text |
| Resource Type | Chapter |
