Pipe Stress Engineering
13 Dynamic Analysis — Part 2: MDOF Systems and Applications
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This chapter, the second one on dynamic analysis, focuses on general applications of dynamic analysis to piping systems. It includes the response spectra method for earthquake analysis, harmonic analysis of steady-state vibration, and the time-history analysis for general fluid transient loads. We will start with the general formulations of the approaches of the analysis [1, 2].
A piping system is a continuous system that can deform into infinitely different ways and patterns. However, the patterns of deformation requiring sharp reflection between two closely located points are not likely to occur in the practical world. This allows the system to be divided into a finite number of discrete points without losing practical accuracy. The deformation between any two adjacent points is assumed to follow a certain pattern that requires the least energy or the pattern that is easiest to achieve. This approach is called the finite element method. Practically all dynamic analyses of piping system are done by this method and are performed via computers. A detailed discussion of the finite element method is beyond the scope of this book. Interested engineers should read relevant books [3, 4] for details. This chapter will cover only several basic concepts that are needed to accurately and effectively use the computerized tools.