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Home / Technical Notes / Electric analysis / How to Examine the Results of Harmonic Vibration
How to Examine the Results of Harmonic Vibration
Fields Displayed in Resonant/Harmonic Analysis
In the resonant analysis or harmonic analysis, the fields can be displayed which show the temporal changes of the vibrations and the quantities related to the vibration.
On the [Results] tab,
by selecting 
phase box, the temporal changes of the vibrations and the quantities related to the vibration can be displayed.
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Some fields such as poynting vector and loss energy density are not supported for the display of temporal change. The phase box cannot be selected for such fields.
The average value of one period is displayed.
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Note that results such as the displacement, the electric potential etc solved in the stress/piezoelectric analysis are totally different from the experimental values.
Display of Temporal Changes in Vibration
Phase box can show the results for phases in 5-degree step.
A graph of the horizontal axis phase can also be displayed by the graph display function.
The vibrations can also be observed by advancing the phases in animation display.
Display of Quantities Related to Vibration
Phase box can show the following values. Some fields cannot be displayed.
They are displayable by contour diagram, but not by vector diagram.
|
Display Type |
Notes |
Remarks |
|
Absolute |
The absolute value of amplitude of harmonic vibration is displayed. |
Not displayable in the case of quantities which do not oscillate harmonically. |
|
Phase |
The argument (phase shift) of harmonic vibration is displayed. |
Not displayable in the case of quantities which do not oscillate harmonically. |
|
Real |
The value of the real part of complex number representing harmonic vibration is displayed. |
Not displayable in the case of quantities which do not oscillate harmonically. |
|
Imaginary |
The value of the imaginary part of complex number representing harmonic vibration is displayed. |
Not displayable in the case of quantities which do not oscillate harmonically. |
|
Maximum |
The maximum value of change in one period is displayed. |
Not displayed are; minimum principal stress, minimum principal stress, |
|
Minimum |
The minimum value of change in one period is displayed. |
Not displayed are; maximum principal stress, medium principal stress, maximum shearing stress, |
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See "Q10. Peak of Displacement is Divided at Resonant Frequency" for the example of Absolute.
Quantities Related to Vibration and Temporal Changes
A filed of harmonic vibrations is represented by complex number Φ*. It is called complex amplitude.
ΦAbsolute: absolute value of amplitude, ΦPhase: Argument (phase shift), ΦReal: real part, ΦImaginary: imaginary part
The temporal change of vibrations is represented by the following equation.
t: time, ω: angular frequency of harmonic vibration
In the equation above, Re means the real part. [ωt] corresponds to the phase selected in the "phase" box.
Some values, which are obtained by the calculations of harmonically-oscillating quantities, do not oscillate harmonically.
For example, X, Y, Z components and magnitude of displacement vector are shown below.
X, Y, and Z components of the vector oscillate harmonically, but the magnitude does not.
The quantities given by the vector components only (such as magnitude of vector) and quantities given by the tensor components only (such as maximum principal stress and Mises's equivalent stress) do not oscillate harmonically, and cannot be expressed with the complex number components.
They are calculated by the maximum and minimum values of the change in one period.
For the quantities related to the harmonic vibration, the maximum value is the same as the absolute value of amplitude, and the minimum value is equal to the absolute value of amplitude multiplied by -1.