core

model_setup

This module contains the functions for setting up the WFE model.

This includes:

• Creating the relevant dof dict data

• Applying the boundary conditions

• Sorting M, K and dofs to left and right faces

• Creating node dict data

pywfe.core.model_setup.generate_dof_info(dof: dict, axis=0)

Generates the dof dictionary, including which face each dof is on. Also rolls sets the waveguide axis and created index array if none given.

Parameters:

dofdict

DESCRIPTION.

axisTYPE, optional

DESCRIPTION. The default is 0.

Returns:

dofTYPE

DESCRIPTION.

pywfe.core.model_setup.apply_boundary_conditions(K, M, dof, null, nullf)

Applies boundary conditions according to null constraint matrices. Resorts and removes degrees of freedom as needed. (NOT FINISHED)

Parameters:

Kndarray

(ndof, ndof) sized array of type float or complex.

Mndarray

(ndof, ndof) sized array of type float or complex.

dofdict

dof dictionary.

nullndarray

(ndof, ndof) sized array of type float.

nullfndarray

(ndof, ndof) sized array of type float.

Returns:

Kndarray

(ndof, ndof) sized array of type float or complex.

Mndarray

(ndof, ndof) sized array of type float or complex.

dofdict

dof dictionary.

pywfe.core.model_setup.order_system_faces(K, M, dof)

Parameters:

Kndarray

(ndof, ndof) sized array of type float or complex.

Mndarray

(ndof, ndof) sized array of type float or complex.

dofdict

dof dictionary.

Returns:

Kndarray

(ndof, ndof) sized array of type float or complex.

Mndarray

(ndof, ndof) sized array of type float or complex.

dofdict

dof dictionary.

pywfe.core.model_setup.substructure_matrices(K, M, dof)

Creates dictionaries for the submatrices of K and M

Parameters:

Kndarray

(ndof, ndof) sized array of type float or complex.

Mndarray

(ndof, ndof) sized array of type float or complex.

dofdict

dof dictionary.

Returns:

K_subdict

dictionary of substructured stiffness matrices.

M_subdict

dictionary of substructured mass matrices.

pywfe.core.model_setup.create_node_dict(dof)

Creates node dictionary for nodes on the left face of the model

Parameters:

dofdict

dof dictionary.

Returns:

nodedict

node dictionary.

eigensolvers

This module contains different solvers for the WFE eigenproblem.

pywfe.core.eigensolvers.transfer_matrix(DSM)

Classical transfer matrix formulation of the WFE eigenproblem.

The transfer function is defined as

\[\begin{split}\mathbf{T} = \begin{bmatrix} -D_{LR}^{-1} D_{LL} & D_{LR}^{-1} \\ -D_{RL}+D_{RR} D_{LR}^{-1} D_{LL} & -D_{RR} D_{LR}^{-1} \end{bmatrix}\end{split}\]

which leads to the eigenvalue problem

\[T \mathbf{\Phi} = \lambda \mathbf{\Phi}\]

The left eigenvectors can be found by considering \(\mathbf{T}^{T}\)

Parameters:

DSM(N,N) ndarray (float or complex)

The dynamic stiffness matrix of the system. NxN array of type float or complex.

Returns:

valsndarray

1-D array of length N type complex.

left_eigenvectorsndarray

NxN array of type float or complex. Column i is vector corresponding to vals[i]

right_eigenvectorsndarray

NxN array of type float or complex. Column i is vector corresponding to vals[i]

pywfe.core.eigensolvers.polynomial(DSM)

[unfinished] Polynomial form of the eigenproblem

Parameters:

DSM(N,N) ndarray (float or complex)

The dynamic stiffness matristrucaxisym-x of the system. NxN array of type float or complex.

Returns:

valsndarray

1-D array of length N type complex.

left_eigenvectorsndarray

NxN array of type float or complex. Column i is vector corresponding to vals[i]

right_eigenvectorsndarray

NxN array of type float or complex. Column i is vector corresponding to vals[i]

classify_modes

This module contains the functionality needed to sort eigensolutions of the WFE method into positive and negative going waves.

pywfe.core.classify_modes.classify_wavemode(f, eigenvalue, eigenvector, threshold)

Identify if a wavemode is positive going or negative going

Parameters:

ffloat

frequency of eigensolution.

eigenvaluecomplex

Eigenvalue to be checked.

eigenvectornodarray, complex

Corresponding eigenvector.

thresholdfloat

Threshold for classification. How close to unity does an eigenvalue have to be?

Returns:

directionstr

'right' or 'left'.

pywfe.core.classify_modes.sort_eigensolution(f, eigenvalues, right_eigenvectors, left_eigenvectors)

Sort the eigensolution into positive and negative going waves

Parameters:

ffloat

Frequency of eigensolution.

eigenvaluesndarray, complex

Eigenvalues solved at this frequency.

right_eigenvectorsndarray, complex

Right eigenvectors solved at this frequency.

left_eigenvectorsTYPE

Left eigenvectors solved at this frequency..

Returns:

named tuple

Eigensolution tuple.

forced_problem

This module contains the functionality needed to apply forces to a WFE model.

pywfe.core.forced_problem.calculate_excited_amplitudes(eigensolution, force)

Calculates the directly excited amplitudes subject to a given force and modal solution.

Parameters:

eigensolutionnamedtuple

eigensolution.

forcenp.ndarray

force vector.

Returns:

e_plusnp.ndarray

directly excited modal amplitudes (positive).

e_minusnp.ndarray

directly excited modal amplitudes (negative).

pywfe.core.forced_problem.generate_reflection_matrices(eigensolution, A_right, B_right, A_left, B_left)

Calculates the reflection matrices from boundary matrices.

Parameters:

eigensolutionTYPE

DESCRIPTION.

A_rightnp.ndarray

A matrix on the right boundary.

B_rightnp.ndarray

B matrix on the right boundary.

A_leftnp.ndarray

A natrix on the left boundary.

B_leftnp.ndarray

B matrix on the left boundary.

Returns:

R_rightnp.ndarray

Right reflection matrix.

R_leftnp.ndarray

Left reflection matrix.

pywfe.core.forced_problem.calculate_propagated_amplitudes(e_plus, e_minus, k_plus, L, R_right, R_left, x_r, x_e=0)

Calculates the ampltiudes of waves after propagation to response point

Parameters:

e_plusnp.ndarray

positive directly excited amplitudes.

e_minusnp.ndarray

negative directly excited amplitudes.

k_plusnp.ndarray

wavenumber array.

Lfloat

Length of waveguide.

R_rightnp.ndarray

Right reflection matrix.

R_leftnp.ndarray

Left reflection matrix.

x_rfloat, np.ndarray

Response distance.

x_efloat,

Excitation distance. The default is 0.

Returns:

b_plusnp.ndarray

positive propagated amplitudes.

b_minusnp.ndarray

negative propagated amplitudes.

pywfe.core.forced_problem.calculate_modal_displacements(eigensolution, b_plus, b_minus)

Calculates the displacement of each mode (last axis is modal)

Parameters:

eigensolutionnamedtuple

eigensolution.

b_plusnp.ndarray

positive propagated amplitudes.

b_minusnp.ndarray

negative propagated amplitudes.

Returns:

q_j_plusnp.ndarray

positive going modal displacements.

q_j_minusnp.ndarray

negative going modal displacements.

pywfe.core.forced_problem.calculate_modal_forces(eigensolution, b_plus, b_minus)

Calculates the internal forces of each mode (last axis is modal)

Parameters:

eigensolutionnamedtuple

eigensolution.

b_plusnp.ndarray

positive propagated amplitudes.

b_minusnp.ndarray

negative propagated amplitudes.

Returns:

f_j_plusnp.ndarray

Positive going modal forces.

f_j_minusnp.ndarray

Negative going modal forces.