The FRF Calculator employs the Mode Superposition method to estimate the FRF between two given degrees of freedom (DOFs). FRF Mode Contribution is also extracted using this methodology, while Equivalent Radiated Power (ERP) and Equivalent Radiated Power Level (ERPL) use the formulation described in the Mechanical User’s Guide.

is the FRF between the i-th and j-th DOFs, where DOF i is the output and DOF j is the input.

can be understood as the output generalized displacement measured in DOF i when an input generalized force is imposed in DOF j as a function of frequency. Thus, depending on the nature of the DOFs (whether they are displacement or rotation DOFs), is measured as Displacement/Force, Rotation/Force, Displacement/Torque or Rotation/Torque.

The analogous relationships between generalized velocity (translational or rotational) and generalized force, or generalized acceleration (translational or rotational) and generalized force are called Mobility and Accelerance, respectively.

They are calculated as:

For a given pair of input and output nodes, a 3x3 FRF matrix can be computed relating the 3 input and 3 output DOFs measured at each node in the Global Coordinate System (GCS). If that matrix is denoted as , the FRF matrix expressed in the DOFs along two arbitrary coordinate systems centered in the input and output nodes is:

where and are the rotation matrices that transform from the GCS to the local output (O) and input (I) coordinate systems (CS), respectively.