A spectrum analysis calculates displacements and stresses in a structural model using modal analysis results and a known spectrum representing time-dependent loads like earthquakes or wind. There are different types of spectra: response spectra graph response vs. frequency; single-point and multi-point response spectra use one or multiple curves; power spectral density spectra are statistical measures of response to random loads graphed against frequency. Spectrum analyses can be deterministic using maximum values or probabilistic representing probability of response quantities.

1. Structural Spectrum Analysis

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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

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• 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)

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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.

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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

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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

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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.

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• 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

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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.

10. Thank You
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