Theory for Two-Port Components
The equations for all the two port components are described below:
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Theory for Mass
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Theory for Spring
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Theory for Damper
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Theory for Impedance
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Theory for Displacement Source
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Theory for Force Source
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Theory for External Source
Theory for Mass
A mass component creates a difference in the forces between the two connecting nodes.
Figure 5-1: A mass component connected between the two nodes p1 and p2.
The following equations are used to relate force (fp1) and displacement (up1) of one node to the force (fp2) and displacement (up2) of another node:
where f and u are the force and displacement variables in the component. They are related by the following equations, where m is the component mass:
Frequency-Domain and Eigenfrequency Studies
Time-Dependent Studies
Stationary Studies
An additional gravity force is added in the component force when the gravity contribution is included:
Theory for Spring
A spring component creates a difference in the displacements between the two connecting nodes which is proportional to the force.
Figure 5-2: A spring component connected between the two nodes p1 and p2.
The following equations are used to relate force (fp1) and displacement (up1) of one node to the force (fp2) and displacement (up2) of another node:
where f and u are the force and displacement variables in the component. They are related by the following equation:
where k is the spring constant and u0 is the predeformation.
Theory for Damper
A damper component is similar to the spring component and creates a difference in the displacements of the two connecting nodes. The relative velocity is proportional to the force.
Figure 5-3: A damper component connected between the two nodes p1 and p2.
The following equations are used to relate force (fp1) and displacement (up1) of one node to the force (fp2) and displacement (up2) of another node:
where f and u are the force and displacement variables in the component. They are related by the following equations, where c is the damping coefficient:
Frequency-Domain and Eigenfrequency Studies
Time-Dependent Studies
Stationary Studies
Theory for Impedance
An impedance component creates a difference in the displacements as well as forces between the two connecting nodes.
Figure 5-4: An impedance component connected between the two nodes p1 and p2.
The following equations are used to relate force (fp1) and displacement (up1) of one node to the force (fp2) and displacement (up2) of another node:
where f1, f2 and u1, u2 are the force and displacement variables in the component. They are related by the following equations:
Frequency-Domain and Eigenfrequency Studies
Time-Dependent and Stationary Studies
Here Z11, Z12, Z21, and Z22 are the components of the impedance matrix.
Theory for Displacement Source
A displacement source creates a difference in the displacements of the two connecting nodes.
Figure 5-5: A displacement source connected between the two nodes p1 and p2.
The following equations are used to relate force (fp1) and displacement (up1) of one node to the force (fp2) and displacement (up2) of another node:
where f and u are the force and displacement variables in the component. The following equation prescribes the component displacement, u:
Frequency-Domain and Eigenfrequency Studies
Time-Dependent and Stationary Studies
Here usrc is the prescribed displacement value and ϕ is the phase angle.
Theory for Force Source
A force source creates a difference in the forces of the two connecting nodes.
Figure 5-6: A force source connected between the two nodes p1 and p2.
The following equations are used to relate force (fp1) and displacement (up1) of one node to the force (fp2) and displacement (up2) of another node:
where f and u are the force and displacement variables in the component. The following equation prescribes the component force, f:
Frequency-Domain and Eigenfrequency Studies
Time-Dependent and Stationary Studies
Here, fsrc is the prescribed force value and ϕ is the phase angle.
Theory for External Source
An external source is similar to the impedance component and creates a difference in the displacements as well as forces of the two connecting nodes.
Figure 5-7: An external source connected between the two nodes p1 and p2.
The following equations are used to relate force (fp1) and displacement (up1) of one node to the force (fp2) and displacement (up2) of another node:
where f1, f2 and u1, u2 are the force and displacement variables in the component. The following equation prescribes the component displacement (u1, u2)
where up10 and up20 are the displacement values obtained from the component level model.
The component force (f1, f2) obtained from the external source node of the system level model can be applied in the component level model as a feedback in order to complete the coupling between the two.