# flat_plate_analytical¶

Computes the analytical frequency response of a plat plate for the input output sequences in input_seq and output_seq over the frequency points kv, if available.

The output complex values array Yan has shape (Nout, Nin, Nk); if an analytical solution is not available, the response is assumed to be zero.

If plunge_deriv is True, the plunge response is expressed in terms of first derivative dh.

param kv

Frequency range of length Nk.

type kv

np.array

param x_ea_perc

Elastic axis location along the chord as chord length percentage.

type x_ea_perc

float

param x_fh_perc

Flap hinge location along the chord as chord length percentage.

type x_fh_perc

float

param input_seq

List of Nin number of inputs. Supported inputs include:

• gust_sears: Response to a continuous sinusoidal gust.

• pitch: Response to an oscillatory pitching motion.

• plunge: Response to an oscillatory plunging motion.

type input_seq

list(str)

param output_seq

List of Nout number of outputs. Supported outputs include:

• Fy: Vertical force.

• Mz: Pitching moment.

type output_seq

list(str)

param output_scal

Array of factors by which to divide the desired outputs. Dimensions of Nout.

type output_scal

np.array

param plunge_deriv

If True expresses the plunge response in terms of the first derivative, i.e. the

type plunge_deriv

bool

:param rate of change of plunge $$d\dot{h}$$.:

returns

A (Nout, Nin, Nk) array containing the scaled frequency response for the inputs and outputs specified.

rtype

np.array

The lift coefficient due to pitch and plunging motions is calculated using sharpy.utils.analytical.theo_CL_freq_resp(). In turn, the pitching moment is found using sharpy.utils.analytical.theo_CM_freq_resp().
The response to the continuous sinusoidal gust is calculated using sharpy.utils.analytical.sears_CL_freq_resp().