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:
Single-Point Response Spectrum (SPRS)
Multi-Point Response Spectrum (MPRS)
Power Spectral Density (PSD)
A response spectrum input represents the maximum response of single-degree-of-freedom 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. The output of a response spectrum analysis is the maximum response of each mode to the input spectrum. While the maximum response of each mode is known, the relative phase of each mode is unknown. To account for this, various mode combination methods are used (rather than simply summing these maximum modal responses).
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, such as at all supports, as shown in Figure 6.1: Single-Point and Multi-Point Response Spectra (a).
In a multi-point response spectrum (MPRS) analysis, you specify different spectrum curves at different sets of points, as shown in Figure 6.1: Single-Point and Multi-Point Response Spectra (b).
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 tables provided in the U.S. Naval Research Laboratory Report NRL-1396.
Power spectral density (PSD) is a statistical measure defined as the limiting root mean-square (rms) 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. It is assumed that the dynamic input has a zero mean value and the range of values takes the form of a Gaussian or normal probability distribution.
A PSD is a graph of the PSD value versus frequency, where the PSD may be a displacement PSD, velocity PSD, acceleration PSD, or force PSD, that captures both the power or intensity of the input vibration and its frequency content. The PSD value is in (unit)2 / Hz, such as g2 / Hz. . Mathematically, the area under a PSD-versus-frequency curve is equal to the variance (square of the standard deviation) of the input vibration. Likewise, the output also takes on a Gaussian distribution and zero mean value. The output values of a PSD analysis are the response PSDs, with the area under the response PSD curve being the variance (the 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.
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.
The calculation of the element results in a spectral analysis for large models
(large number of modes and/or large number of degrees of freedoms) can be time
consuming. The most effective method is to combine the modal element results
(Elcalc = YES on SPOPT) during
solution, which can be done in SPRS, MPRS, and DDAM.