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SD-Lecture06-Dynamics-of-Simple-Systems - CEGCEG-5065C Soil...

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CEG CEG-5065C Soil Dynamics 5065C Soil Dynamics Lecture #06 Dynamics of Simple Systems o Discrete elements: springs, masses and dash pots o Single-Degree-of-Freedom Systems (SDOF) Luis A. Prieto-Portar 2009
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Complex vibrations can usually be simplified from infinite points and infinite degrees of freedom into a finite group of discreet elements , such as point masses , massless springs and viscoelastic dash pots . Obviously, this approach yields very approximate solutions for deep soil deposits subjected to complex seismic loads. A better solution is forthcoming from numerical methods, such as the finite element method . This lecture, however, is a review of the classical closed-form mathematical method. This method forms the basis for most structural and geotechnical analysis and design of foundations and structures. Vibrating systems can be either rigid or compliant . In rigid systems, all points within the body remain fixed with respect to each other. This system is easy to describe. However, all real world systems involve compliant behavior, where the body is distorted by the seismic input. This is especially true of soils and rocks, and the foundations placed within them. The number of independent variables required to describe the position of all the masses of a system is called the dynamic degree of freedom of the system .
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SD-Lecture06-Dynamics-of-Simple-Systems - CEGCEG-5065C Soil...

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