panel set twindow_function simple_harmonic_function
The SIMPLE_HARMONIC_FUNCTION evaluates a simple harmonic function.
The following equation defines the function:
SHF = a * sin(w * (x-x0) - phi) + b
where:
x = independent variable expression
a = AMPLITUDE
w = fundmental FREQUENCY
x0 = phase SHIFT in the independent variable
phi = PHASE_SHIFT in the harmonic function
b = AVERAGE_VALUE_OF_DISPLACEMENT
Format:
panel set twindow_function simple_harmonic_function | |
|---|---|
x= | run time function |
shift= | real |
angular_shift= | angle |
amplitude= | real |
average_value_of_displacement= | real |
angular_amplitude= | angle |
angular_average_value_of_displacement= | angle |
frequency= | angle |
phase_shift= | angle |
Example:
panel set twindow_function simple_harmonic_function & | |
|---|---|
x = | time & |
shift = | 5 & |
amplitude = | 200 & |
average_value_of_displacement = | 256.6 & |
frequency = | 245 & |
phase_shift = | 45 |
Description:
Parameter | Value Type | Description |
|---|---|---|
X | Run Time Function | Specifies a run time function. |
shift | Real | Specifies a real variable that is a non-angular shift in a Chebyshev polynomial, Fourier Cosine series, Fourier Sine series, or polynomial function. Or, a phase shift in the independent variable x, for a simple_harmonic_function. |
angular_shift | Angle | Specifies a real variable that is a angular shift in a Chebyshev polynomial, Fourier Cosine series, Fourier Sine series, or polynomial function. Or, a phase shift in the independent variable x, for a simple_harmonic_function. |
amplitude | Real | Specifies the non-angular AMPLITUDE of the harmonic function. |
average_value_of_displacement | Real | Specifies the non-angular AVERAGE_VALUE_OF_DISPLACEMENT of the SIMPLE_HARMONIC_FUNCTION. |
angular_amplitude | Angle | Specifies the ANGULAR_AMPLITUDE of the harmonic function. |
angular_average_value_of_displacement | Angle | Specifies the ANGULAR_AVERAGE_VALUE_OF_DISPLACEMENT of the SIMPLE_HARMONIC_FUNCTION. |
frequency | Angle | Specifies the real variable that is the fundamental FREQUENCY of the series or harmonic function. |
phase_shift | Angle | Specifies a PHASE_SHIFT in the SIMPLE_HARMONIC_FUNCTION. |
Extended Definition:
1. The “amplitude” and the “angular_amplitude” parameters are used in the following SIMPLE_HARMONIC_ FUNCTION equation:
SHF = a * sin(w * (x-x0) - phi) + b
Where "a" is the AMPLITUDE parameter.
2. In the SIMPLE_HARMONIC_ FUNCTION, “b” represents the average_value_of_displacement.
SHF = a * sin(w * (x-x0) - phi) + b
where, b is the ANGULAR_AVERAGE_VALUE_OF_DISPLACEMENT parameter.
3. Adams assumes FREQUENCY is in radians per unit of the independent variable, unless you use a D after the value.
The FREQUENCY parameter is represented in the following functions as "w".
The SIMPLE_HARMONIC_FUNCTION
SHF = a * sin(w * (x-x0) - phi) + b
The FOURIER_COSINE_SERIES is defined :
where:
Tj (x-x0) = cos{j * w * (x-x0)}
The FOURIER_SINE_SERIES is defined as:
where the funtions Tj are defined as:
Tj (x-x0) = sin {j*
*(x-x0)}
*(x-x0)} 4. SHF = a * sin(w * (x-x0) - phi) + b
where, "phi" is the PHASE_SHIFT parameter.