Definitions
Natural Frequency—Number of cycles of motion that occur in one second. Calculated using the spring constant and the mass .
Natural Frequency
where,
natural frequency (Hz)
spring constant
mass (kg)
Zero Displacement—Position of a dynamic boundary during model set-up. Can include an offset from the set-up position, so that if displacement is zero, the dynamic boundary will not correspond to the set-up position.
Displacement (m)—Magnitude of the linear translation of a dynamic boundary relative to its zero-displacement position in the Translation (1 DOF) ODE. For prescribed motion condition, displacement corresponds to prescribed displacement.
Velocity (m)—Magnitude of the velocity of a dynamic boundary in the Translation (1 DOF) ODE. A positive velocity has the same direction as the movement. For prescribed motion, velocity corresponds to time derivative of the prescribed displacement.
Acceleration (m/s2)—Magnitude of the acceleration of a dynamic boundary. For prescribed motion, acceleration corresponds to time derivative of the velocity for the prescribed displacement.
Damping Force (N)—A force that controls the motion of a vibrating body. For example, in a spring, the air acts as a damping medium. A positive damping force has the same direction as the movement direction.
Spring Constant—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 (N)—Based on preload force, spring constant, and displacement. A positive spring force has the same direction as the movement direction.
Spring Preload Force (N)—Force of the spring when displacement equals zero displacement. Zero displacement is not the same as initial displacement. Spring force associated with this force opposes an increase in displacement.
Fluid Force (N)—The hydrodynamic force includes pressure and shear forces. A positive fluid force has the same direction as the movement.
Friction Force (N)—Normal component of the contact force and friction coefficient.
Net Force (N)—Contribution of force terms such as hydrodynamic force, damping force, spring force due to the spring preload force and spring constant , contact friction and any additional force on body. A positive net force has the same direction as the movement.
Net Force
where,
net force (N)
hydrodynamic force (N)
damping force (N)
spring force (N)
additional forces (N)
shear force (N)
Zero Angular Displacement—Position of a dynamic boundary during model set-up. Can include an offset from the set-up position, such that if the displacement is zero, the dynamic boundary will not correspond to the set-up position.
Angular Displacement (deg)—Magnitude of rotation of a dynamic boundary relative to its zero angular displacement position. Angle and positive direction of rotation is based on the rotational axis vector and the right-hand-rule, such that if the axis points at an observer, the angle is increases in the counterclockwise direction. For prescribed motion, the angular displacement corresponds to the prescribed angle displacement.
Angular Velocity (rad/s)—Magnitude of the angular velocity of a dynamic boundary. 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 points at an observer, a positive angular velocity occurs 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 (rad/s2)—Magnitude of the rotation of a dynamic boundary relative to its zero angular displacement position in the Rotation (1 DOF) ODE. Angle and positive direction of acceleration is based on the rotational axis vector and the right-hand-rule, such that if the axis points at an observer, the angle increase 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 (N–m)—Based on angular velocity and damping coefficient. Sign of the damping torque is based on the rotational axis vector and the right-hand-rule, such that if the axis points at an observer, a positive damping torque occurs in the counterclockwise direction.
Fluid Torque (N–m)—Hydrodynamic torque. Sign of the fluid torque is based on the rotational axis vector and the right-hand-rule, such that if the axis is points at an observer, a positive fluid torque occurs in the counterclockwise direction.
Spring Torque (N–m)—Based on displacement angle, torsion preload torque, and torsion constant. Sign of the spring torque is based on the rotational axis vector and the right-hand-rule, such that if the axis points at an observer, a positive spring torque occurs in the counterclockwise direction.
Retarding Torque (N-m)—Retarding torque due to damping. Depends on the rotational velocity and the user-defined damping coefficient.
Net Torque (N–m)—Contribution of torque terms such as hydrodynamic torque, damping force, spring torque due to the torsion preload torque and the torsion constant, and any additional torque and contact friction. Sign of the net torque is based on the rotational axis vector and the right-hand-rule, such that if the axis points at an observer, a positive net torque occurs in the counterclockwise direction.
Net Torque
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)