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Basic Random Analysis

First, the frequency response analysis is performed for sinusoidal loading conditions, {Pa}, each a

separate subcase, at a sequence of frequencies i. The results are output to a normal XDB results

file.

Subcases in Dynamic Analysis

Some of the statics options that are not available in dynamic response analysis and complex

eigenvalue analysis include:

Changes in boundary conditions between subcases

Grid point forces and element strain energy outputs

4.Multiple subcases are available for frequency response analysis (SOLs 108,111and 118) for the

purpose of solving multiple loading conditions more efficiently.(Each frequency requires a matrix

decomposition and each additional load vector may be processed at this time with small cost.)

Another use is in random analysis where several loads need to be combined, each with a

different spectral density distribution

Recommendations

The following guidelines should be observed when applying dynamic loads:

TABLEDi

1.Tables are extrapolated at each end from the first or last two points. If the load actually

goes to zero, add two points with values of y = 0.

2.Linear interpolation is used between tabular points.

3.If a jump occurs (two points with equal values of X), the value of Y at the jump is the

average of the two points.

Stress analysis should be performed at the detailed part level with the loads from the model. The

use of element stresses directly from the output of the model requires detailed review in most

cases.

Effective thicknesses or reduced bending properties may have been used to reflect panel cutouts

or partial beam and fixity.

This piece-part assessment ensures a check and balance of the finite element model and the stress

distributions visualized and treated by the element selection. Also, the source of the components

of stress are known, that is, whether the predominant stress component is due to bending or axial

loads.

One area in which an underestimation of load could occur is the local response of small masses

during a dynamic analysis. These should be addressed in the detailed stress analysis with both the

model predictions and an alternate loading such as a specified loading condition. For the model to

give correct loads for the local response of a mass, one needs all of the following:

Mass must be represented by enough points to characterize the energy of the critical

local mode (a single-point mass may not be sufficient).

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Mass must be supported by proper elastic elements to represent the local mode(RBE2 or

RBE3 may not be sufficient).

Mass must be in the ASET.

Model and all analysis (input spectra, etc.) must be carried beyond this local critical

mode (as far as frequency is concerned).

Setup for Random Analysis

An Nastran random analysis requires a preliminary frequency response analysis to generate the

proper transfer functions that define the output/input ratios. The squared magnitudes of the

results are then multiplied by the spectral density functions of the actual loads. Normally, theinputs are unit loads (e.g., one g constant magnitude base excitation or a unit pressure on a

surface).

VM Stress

Since these values are Root-Mean-Square (RMS) they will always be positive. This means that

combining these values to obtain a maximum resultant is not purely valid. Many FEA codes will

calculate maximum displacement, Von Mises stress or Principal stresses based on Random

Vibration results.

It is important to remember that these calculations are based on all positive component values

and will not be accurate.

Loads may be input as base accelerations or applied external loads. The base excitation option

assumes that the input load will excite any part of the structure that has a constraint or is attached

by a spring to ground. The excitation is always defined as a linear acceleration.

RMS measures in Random Vibration problems, because all frequencies are acting simultaneously

and the RMS values represent the square root of the area under the PSD curve. Statistically it

represents the 1-sigma results.

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For Dynamic Frequency and Random analysis studies damping will have a big impact on the

maximum response. Zero damping should not be used since the response will try to be infinite. For

Random studies damping will have less of an impact on RMS results since the RMS values equal

the square root of the area under the PSD response curves.

The critical components and their potential high stress areas (hot spots) are determined from the

strain energy density (SED) information of the normal mode analysis.

Von Mises Stress in Random Analysis

The RMS of basic stress tensor can not be used to calculate von Mises stresses. The probability

distribution of von Mises stress is not Gaussian, nor is it centered about zero as basic stress tensor

is.

EQUIVALENT VON MISES STRESS

When the excitation is random, the principal directions can rotate continuously with time ;

the von Mises stress is proportional to the root mean

square of the shear stress over all planes.

The first method is based on the definition

of the von Mises stress as a uniaxial random process for which the PSD function is computed. The

second one is a frequency domain formulation of the

multiaxial rainflow method. Both methods lead to

a similar implementation and damage maps, to localize the most critical elements.