11 spectrum analysis
- 2. 7/22/2019 2 Introduction • A spectrum analysis is one in which the results of a modal analysis are used with a known spectrum to calculate displacements and stresses in the model. • It is mainly used in place of a time-history analysis to determine the response of structures to random or time-dependent loading conditions such as earthquakes, wind loads, ocean wave loads, jet engine thrust, rocket motor vibrations, and so on
- 3. 7/22/2019 3 • The spectrum is a graph of spectral value versus frequency that captures the intensity and frequency content of time-history loads. Three types of spectra are available for a spectrum analysis: • Response Spectrum • Single-point Response Spectrum (SPRS) • Multi-point Response Spectrum (MPRS) • Dynamic Design Analysis Method (DDAM) • Power Spectral Density (PSD)
- 4. 7/22/2019 4 Response spectrum • A response spectrum represents the response of single-DOF systems to a time-history loading function. It is a graph of response versus frequency, where the response might be displacement, velocity, acceleration, or force. • Two types of response spectrum analysis are possible: • single-point response spectrum and • multi-point response spectrum.
- 5. 7/22/2019 5 Single-point Response Spectrum (SPRS) • In a single-point response spectrum (SPRS) analysis, you specify one response spectrum curve (or a family of curves) at a set of points in the model Multi-Point Response Spectrum (MPRS) • In a multi-point response spectrum (MPRS) analysis, you specify different spectrum curves at different sets of points
- 6. 7/22/2019 6 Dynamic Design Analysis Method (DDAM) : • The Dynamic Design Analysis Method (DDAM) is a technique used to evaluate the shock resistance of shipboard equipment. • The technique is essentially a response spectrum analysis in which the spectrum is obtained from a series of empirical equations and shock design
- 7. 7/22/2019 7 Power Spectral Density • Power spectral density (PSD) is a statistical measure defined as the limiting mean-square value of a random variable. • It is used in random vibration analyses in which the instantaneous magnitudes of the response can be specified only by probability distribution functions that show the probability of the magnitude taking a particular value. • A PSD spectrum is a statistical measure of the response of a structure to random dynamic loading conditions. • It is a graph of the PSD value versus frequency, where the PSD may be a displacement PSD, velocity PSD, acceleration PSD, or force PSD.
- 8. 7/22/2019 8 • Mathematically, the area under a PSD-versus-frequency curve is equal to the variance (square of the standard deviation of the response). • Similar to response spectrum analysis, a random vibration analysis may be single-point or multi-point. In a single-point random vibration analysis, you specify one PSD spectrum at a set of points in the model. In a multi-point random vibration analysis, you specify different PSD spectra at different points in the model. • Note-The sparse direct solver is not applicable to PSD spectrum analysis
- 9. 7/22/2019 9 Deterministic Vs. Probabilistic Analyses • Response spectrum and DDAM analyses are deterministic analyses because both the input to the analyses and output from the analyses are actual maximum values. • Random vibration analysis, on the other hand, is probabilistic in nature, because both input and output quantities represent only the probability that they take on certain values.