RFlex Modal Force

The user can apply a user - defined load to a RFlex body using RFlex Modal Force. The function of Rflex Modal Force consists of three parts as Modal Load Case, Modal Force and Modal Preload.

Mathematical definitions

A set of nodal force and torque is can be translated to a generalized force with respect to the reference frame of RFlex body as following equation. The 3rd part of equation (1)

 (1)

Where,

 is a generalized force with respect to the reference frame of RFlex body.

 is a generalized force with respect to the reference frame of RFlex body.

 is a generalized modal force with respect to the reference frame of RFlex body.

 is a force applied on  node with respect to the reference frame of RFlex body.

 is a torque applied on  node with respect to the reference frame of RFlex body.

 is a position vector applied on  node with respect to the reference frame of RFlex body.

 is a translational mode shape matrix. [3xnmode]

 is a rotational mode shape matrix. [3xnmode]

If a force and torque a acting on the  node

The force vector including torque [6x1] is acting on the  node.

Figure 1  Simple example for Modal force

Therefore, we can write Equation (2).

 (2)

Where,  is a mass matrix [3x3] on  node.  is a stiffness matrix [3x3] on the  node.

The  is defined as .. Where, is a mode shape matrix [6xnmode]. is modal coordinates.

 (3)

Multiply  to Equation (3)

 (4)

Finally we get a mathematical definition of Modal force as follows.

 (5)

 (6)

 (7)