Book contents
- Frontmatter
- Contents
- Preface
- 1 Preliminaries
- 2 Dynamics of Single-Degree-of-Freedom Linear Systems
- 3 Dynamics of Multi-Degree-of-Freedom Linear Systems
- 4 Finite Element Method
- 5 Stochastic Processes
- 6 Variance Spectrum
- 7 Environmental Loads
- 8 Random Environmental Processes
- 9 Response Spectrum
- 10 Response Statistics
- 11 Statistics for Nonlinear Problems
- 12 Short-Term and Long-Term Extremes
- 13 Dynamic Load Effects for Design Checks
- 14 Equations of Motion
- 15 Numerical Solution Techniques
- 16 Monte Carlo Methods and Extreme Value Estimation
- A Integrals
- B Poisson Process
- C Statistical Moments and Cumulants
- References
- Index
2 - Dynamics of Single-Degree-of-Freedom Linear Systems
Published online by Cambridge University Press: 05 February 2013
- Frontmatter
- Contents
- Preface
- 1 Preliminaries
- 2 Dynamics of Single-Degree-of-Freedom Linear Systems
- 3 Dynamics of Multi-Degree-of-Freedom Linear Systems
- 4 Finite Element Method
- 5 Stochastic Processes
- 6 Variance Spectrum
- 7 Environmental Loads
- 8 Random Environmental Processes
- 9 Response Spectrum
- 10 Response Statistics
- 11 Statistics for Nonlinear Problems
- 12 Short-Term and Long-Term Extremes
- 13 Dynamic Load Effects for Design Checks
- 14 Equations of Motion
- 15 Numerical Solution Techniques
- 16 Monte Carlo Methods and Extreme Value Estimation
- A Integrals
- B Poisson Process
- C Statistical Moments and Cumulants
- References
- Index
Summary
Introduction
This chapter deals with vibrations of structures that can be represented as a single degree-of-freedom (SDOF) system. This means that the oscillatory response can be completely described by one displacement variable. This may seem like a gross oversimplification for structures of engineering interest that leads to a theory of little practical significance. However, the theory of vibrations for systems of an SDOF is crucial for understanding the vibration response of more complex structures. Frequently, it is also the case that one may investigate the vibration response characteristics of apparently complex structures by directly applying the theory of vibrations of SDOF systems. This is demonstrated in Chapter 3 on multi-degrees-of-freedom (MDOF) structures.
The word “vibration” used in this chapter should be interpreted as meaning oscillatory response in a fairly general sense, e.g., as applied to marine structures.
Harmonic Oscillator – Free Vibrations
Free vibrations or oscillations occur when there are no external forces imposed on the structure, e.g., after an initial displacement and release. Two different situations are discussed: translational oscillations and rotational oscillations.
Motions of Marine Structures
Because the main focus of this book is the motion response of marine structures, it is expedient to define the terms commonly used to describe the rigid-body motions of floating structures. This is most easily done by referring to Fig. 2.1. For a shiplike structure, it is common practice to place the x-axis along the beam of the ship (for the body-fixed coordinate system), and call the corresponding translational motion for surge.
- Type
- Chapter
- Information
- Stochastic Dynamics of Marine Structures , pp. 6 - 56Publisher: Cambridge University PressPrint publication year: 2012