Definitions

5.12.1 Definitions

Natural Frequency: The number of cycles of motion happening in one second. This is calculated using the spring constant () and the mass ().
5.570
where
Natural frequency (Hz)
Spring constant
Mass (kg)

Translation

Zero Displacement: The position of a dynamic boundary during model set-up. It could include an offset from the set-up position, such that even if the displacement was zero, the dynamic boundary would not correspond to the set-up position. Correct correlation between zero displacement in the ODE and the geometry or position of the boundary or volume is important when considering the spring constant and spring preload force since both involve displacement in their formulation. It is also important when including Flow, since the contribution of the pressure forces at a physical linear position should correspond to the correct mathematical displacement in the ODE.
Displacement: The magnitude of the linear translation of a dynamic boundary relative to its zero-displacement position in the Translation (1 DOF) ODE. The unit for displacement is m. For prescribed motion condition, the displacement corresponds to the prescribed displacement.
Velocity: The magnitude of the velocity of a dynamic boundary in the Translation (1 DOF) ODE. The unit for velocity is m/s. A positive velocity is in the same direction as the movement direction. For prescribed motion, the velocity corresponds to the time derivative of the prescribed displacement.
Acceleration: The magnitude of the acceleration of a dynamic boundary. The unit for acceleration is m/s². For prescribed motion, the acceleration corresponds to the time derivative of the velocity for the prescribed displacement.
Damping Force: A force that controls the motion of a vibrating body. For example, in a spring, the air acts as a damping medium. The unit for damping force is N. A positive damping force is in the same direction as the movement direction.

Spring Constant: It is a variable in the spring force in the force balance equation. The spring force associated with the spring constant opposes an increase in displacement.
Spring Force: It is based on the preload force, spring constant and displacement. The unit for spring force is N. A positive spring force is in the same direction as the movement direction.
Spring Preload Force: The force of the spring when the displacement equals the zero displacement. Zero displacement is not the same as the initial displacement. The spring force associated with this force opposes an increase in displacement. The unit for spring preload force is N.
Fluid Force: The hydrodynamic force includes both the pressure and the shear forces. The unit for fluid force is N. A positive fluid force is in the same direction as the movement direction.

Friction Force: The normal component of the contact force and friction coefficient. The unit for friction force is N.
Net Force: The contribution of force terms: the hydrodynamic force, the damping force, the spring force (due to the spring preload force and spring constant (), contact friction and any additional force on body. The unit for net force is N. A positive net force is in the same direction as the movement direction.

5.571

where

Net force (N)

Hydrodynamic force (N)

Damping force (N)

Spring force (N)

Additional forces (N)

Shear force (N)

Rotation

Zero Angular Displacement: The position of a dynamic boundary during model set-up. It could include an offset from the set-up position, such that even if the displacement was zero, the dynamic boundary would not correspond to the set-up position. Correct correlation between zero angular displacement in the ODE and the geometry or position of the boundary or volume is important when considering the torsion constant and torsion preload torque since both involve angular displacement in their formulation. It is also important when including Flow, since the contribution of the pressure forces at a physical linear position should correspond to the correct mathematical angular displacement in the ODE.
Angular Displacement: The magnitude of rotation of a dynamic boundary relative to its zero angular displacement position. The unit for angular displacement is deg (as opposed to rad). The angle and positive direction of rotation is based on the rotational axis vector and the right-hand-rule, such that if the axis is pointing at an observer, the angle is increasing in the counterclockwise direction. For prescribed motion, the angular displacement corresponds to the prescribed angle displacement.

Angular Velocity: The magnitude of the angular velocity of a dynamic boundary. The unit for angular velocity is rad/s (as opposed to deg, used for angle displacement). The sign of the angular velocity is based on the right-hand-rule and the rotational axis vector for the Rotation (1 DOF) module, such that if the axis is pointing at an observer, a positive angular velocity in the counterclockwise direction. For prescribed motion, the angular velocity corresponds to the time derivative of the prescribed angle, converted to rad/s.

Angular Acceleration: The magnitude of the rotation of a dynamic boundary relative to its zero angular displacement position in the Rotation (1 DOF) ODE. The unit for angular acceleration is rad/s². The angle and positive direction of acceleration is based on the rotational axis vector and the right-hand-rule, such that if the axis is pointing at an observer, the angle is increasing in the counterclockwise direction. For prescribed motion, the angular acceleration corresponds to the change in angular velocity based on the prescribed angle displacement.

Damping Torque: The damping torque is based on the angular velocity and the damping coefficient. The unit for damping torque is N-m. The sign of the damping torque is based on the rotational axis vector and the right-hand-rule, such that if the axis is pointing at an observer, a positive damping torque in the counterclockwise direction.

Fluid Torque: The hydrodynamic torque. The unit for fluid torque is N-m. The sign of the fluid torque is based on the rotational axis vector and the right-hand-rule, such that if the axis is pointing at an observer, a positive fluid torque in the counterclockwise direction.
Spring Torque: The spring torque is based on the displacement angle, torsion preload torque and torsion constant. The unit for spring torque is N-m. The sign of the spring torque is based on the rotational axis vector and the right-hand-rule, such that if the axis is pointing at an observer, a positive spring torque in the counterclockwise direction.
Retarding Torque: The retarding torque due to damping. It depends on the rotational velocity () and the user defined damping coefficient. The unit for retarding torque is N-m.

Net Torque: The contribution of torque terms: the hydrodynamic torque, the damping force, the spring torque due to the torsion pre-load torque and the torsion constant and any additional torque and/or contact friction. The unit for net torque is N-m. The sign of the net torque is based on the rotational axis vector and the right-hand-rule, such that if the axis is pointing at an observer, a positive net torque in the counterclockwise direction.

5.572

where

Net torque (N-m)

Hydrodynamic torque (N-m)

Damping torque (N-m)

Spring torque (N-m)

Additional torque (N-m)

Shear torque (N-m)

	Net force (N)
	Hydrodynamic force (N)
	Damping force (N)
	Spring force (N)
	Additional forces (N)
	Shear force (N)

	Net torque (N-m)
	Hydrodynamic torque (N-m)
	Damping torque (N-m)
	Spring torque (N-m)
	Additional torque (N-m)
	Shear torque (N-m)

	Natural frequency (Hz)
	Spring constant
	Mass (kg)