chapter 13, Dynamic Analysis — Part 2: MDOF Systems and Applications

from: Pipe Stress Engineering

Author(s)/Editor(s): Liang-Chuan Peng, Tsen-Loong Peng

Published: 2009

Author(s)/Editor(s): Liang-Chuan Peng, Tsen-Loong Peng

Chapter DOI: http://dx.doi.org/10.1115/1.802854.ch13

Chapter Page Count: 49 pages

Previous Chapter | Next Chapter

Front Matter

1. Introduction

2. Strength of Materials Basics

3. Thermal Expansion and Piping Flexibility

4. Code Stress Requirements

5. Discontinuity Stresses

6. Pipe Supports and Restraints

7. Flexible Connections

8. Interface with Stationary Equipment

9. Interface with Rotating Equipment

10. Transportation Pipeline and Buried Piping

11. Special Thermal Problems

12. Dynamic Analysis — Part 1: SDOF Systems and Basics

13. Dynamic Analysis — Part 2: MDOF Systems and Applications

Back Matter

Preview

Chapter Contents

13.1. Lumped-Mass Multi-Degree of Freedom Systems
13.1.1 Mass Lumping
13.1.2 Free Vibration and Modal Superposition
13.2. Piping Subject to Ground Motion
13.2.1 Response Spectra Method
13.2.2 Combination of Response Spectra Analysis Results
13.2.3 Comparison of Modal Combination Methods
13.2.4 Puzzles of Absolute Closely Spaced Modal Combination
13.2.5 Compensation for the Higher Modes Truncated
13.2.6 Design Response Spectra
13.3. Account for Uncertainties
13.4. Steady-State Vibration and Harmonic Analysis
13.4.1 Basic Vibration Patterns
13.4.2 Allowable Vibration Displacement and Velocity
13.4.3 Formulation of Harmonic Analysis
13.4.4 Evaluation of Vibration Stress
13.5. Time-History Analysis
13.5.1 Treatment of Damping
13.5.2 Integration Schemes
13.5.3 Time Step Stability and Accuracy
13.5.4 Example Time-History Analysis

Excerpt

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.

http://dx.doi.org/10.1115/1.802854.ch13