The Wave Elevation, eta, is given by

   eta  = a*cos(w*t + k*x*cos(beta) + k*y*sin(beta))

The resulting Vessel Response is then given by

   r   = R*cos(w*t + phi)
   RAO = R/a

If the -REFN option is specified, then the beam Y axis is defined as the vector cross product of the vector from the beginning of the beam to *REFNOD with the beam local X axis. The beam Z axis is then given by the cross product of the beam X axis with the beam Y axis.

If -REFN is not specified, then the local axes are defined based on the -STGAXIS option of a &MODEL_DEF command. This defines two vectors: SAV1 and SAV2 which define local Y and Z as follows:

• If the beam X axis is not parallel to the SAV1 vector, then the beam Y axis will be defined by the cross product of the SAV1 vector and the beam X axis.
• If the beam X axis is parallel to the SAV1 vector, then the beam Y axis is determined by the cross product of the SAV2 vector with the local X axis.

After the local system has been defined, it can be rotated about the local X axis with the -CA option. Here, CHANG is the beam chord angle (degrees). The rotation of the system is about the beam x axis, positive towards the beam negative Y axis (right hand rule). The relationship of the local coordinate system is shown;

Let

• e be a unit vector along the brace X axis acting from the joint toward the other end of the brace and

• c be a unit vector from the chord "left joint" to the joint

then e is the force direction and the directions for inplane (m_i) and out of plane bending (m_o) are given by:

• m_i = (exc) / ||exc||

• m_o = (exm_i)/ ||exm_i||