Processing

Assembly Acoustic

class pulse.processing.assembly_acoustic.AssemblyAcoustic(mesh, frequencies)

This class creates a acoustic assembly object from input data.

Parameters

• mesh (Mesh object) – Acoustic finite element mesh.

• frequencies (array) – Frequencies of analysis.

get_global_matrices()

This method perform the assembly process of the acoustic FETM matrices.

Returns

• K (list) – List of admittance matrices of the free degree of freedom. Each item of the list is a sparse csr_matrix that corresponds to one frequency of analysis.

• Kr (list) – List of admittance matrices of the prescribed degree of freedom. Each item of the list is a sparse csr_matrix that corresponds to one frequency of analysis.

get_global_matrices_modal()

This method perform the assembly process of the acoustic FEM matrices.

Returns

• K (sparse csr_matrix) – Acoustic stiffness matrix.

• M (sparse csr_matrix) – Acoustic inertia matrix.

get_global_volume_velocity()

This method perform the assembly process of the acoustic load, volume velocity.

Returns

volume_velocity – Volume velocity load.

Return type

array

get_length_corretion(element)

This method evaluate the acoustic length correction for an element. The necessary conditions and the type of correction are checked.

Parameters

element (Acoustic element object) – Acoustic element.

Returns

Length correction.

Return type

float

get_lumped_matrices()

This method perform the assembly process of the acoustic FETM lumped matrices.

Returns

• K_lump (list) – List of lumped admittance matrices of the free degree of freedom. Each item of the list is a sparse csr_matrix that corresponds to one frequency of analysis.

• Kr_lump (list) – List of lumped admittance matrices of the prescribed degree of freedom. Each item of the list is a sparse csr_matrix that corresponds to one frequency of analysis.

get_pipe_and_unprescribed_indexes()

This method returns all the indexes of the free acoustic degrees of freedom.

Returns

Indexes of the free acoustic degrees of freedom.

Return type

array

See also

get_prescribed_values

Values of the prescribed pressure boundary condition.

get_prescribed_indexes

Indexes of the acoustic degrees with prescribed pressure boundary conditions.

get_prescribed_indexes()

This method returns all the indexes of the acoustic degrees of freedom with prescribed pressure boundary condition.

Returns

Indexes of the acoustic degrees with prescribed pressure boundary conditions.

Return type

array

See also

get_prescribed_values

Values of the prescribed pressure boundary condition.

get_unprescribed_indexes

Indexes of the free acoustic degrees of freedom.

get_prescribed_values()

This method returns all the values of the prescribed pressure boundary condition.

Returns

Values of the prescribed pressure boundary condition.

Return type

array

See also

get_prescribed_indexes

Indexes of the acoustic degrees with prescribed pressure boundary conditions.

get_unprescribed_indexes

Indexes of the free acoustic degrees of freedom.

get_unprescribed_indexes()

This method returns all the indexes of the free acoustic degrees of freedom.

Returns

Indexes of the free acoustic degrees of freedom.

Return type

array

See also

get_prescribed_values

Values of the prescribed pressure boundary condition.

get_prescribed_indexes

Indexes of the acoustic degrees with prescribed pressure boundary conditions.

pulse.processing.assembly_acoustic.length_correction_branch(branch_diameter, principal_diameter)

This function returns the acoustic length correction due to sidebranch in the acoustic domain. This discontinuity is characterized by three elements, two with the same diameters in line, and the other with different diameter connected to these two.

Parameters

• smaller_diameter (float) – Smaller diameter between the two elements diameters.

• larger_diameter (float) – Larger diameter between the two elements diameters.

Returns

Length correction due to side branch.

Return type

float

See also

length_correction_expansion

Length correction due to expansion in the acoustic domain.

pulse.processing.assembly_acoustic.length_correction_expansion(smaller_diameter, larger_diameter)

This function returns the acoustic length correction due to expansion in the acoustic domain. This discontinuity is characterized by two elements in line with different diameters.

Parameters

• smaller_diameter (float) – Smaller diameter between the two elements diameters.

• larger_diameter (float) – Larger diameter between the two elements diameters.

Returns

Length correction due to expansion.

Return type

float

See also

length_correction_branch

Length correction due to sidebranch in the acoustic domain.

Assembly Structural

class pulse.processing.assembly_structural.AssemblyStructural(mesh, frequencies, **kwargs)

This class creates a structural assembly object from input data.

Parameters

• mesh (Mesh object) – Acoustic finite element mesh.

• frequencies (array) – Frequencies of analysis.

• acoustic_solution (array, optional) – Solution of the acoustic FETM model. This solution is need to solve the coupled problem. Default is None.

get_bc_array_for_all_frequencies(there_are_table, boundary_condition)

This method perform the assembly process of the structural FEM force and moment loads.

Parameters

• pressure_external (float, optional) – Static pressure difference between atmosphere and the fluid in the pipeline. Default is 0.

• loads_matrix3D (boll, optional) – Default is False.

Returns

Loads vectors. Each column corresponds to a frequency of analysis.

Return type

array

get_global_loads(pressure_external=0, loads_matrix3D=False)

This method perform the assembly process of the structural FEM force and moment loads.

Parameters

• pressure_external (float, optional) – Static pressure difference between atmosphere and the fluid in the pipeline. Default is 0.

• loads_matrix3D (boll, optional) – Default is False.

Returns

Loads vectors. Each column corresponds to a frequency of analysis.

Return type

array

get_global_matrices()

This method perform the assembly process of the structural FEM matrices.

Returns

• K (list) – List of stiffness matrices of the free degree of freedom. Each item of the list is a sparse csr_matrix.

• M (list) – List of mass matrices of the free degree of freedom. Each item of the list is a sparse csr_matrix.

• Kr (list) – List of stiffness matrices of the prescribed degree of freedom. Each item of the list is a sparse csr_matrix.

• Mr (list) – List of mass matrices of the prescribed degree of freedom. Each item of the list is a sparse csr_matrix.

get_lumped_matrices()

This method perform the assembly process of the structural FEM lumped matrices.

Returns

• K_lump (list) – List of lumped stiffness matrices of the free degree of freedom. Each item of the list is a sparse csr_matrix that corresponds to one frequency of analysis.

• M_lump (list) – List of mass matrices of the free degree of freedom. Each item of the list is a sparse csr_matrix that corresponds to one frequency of analysis.

• C_lump (list) – List of lumped damping matrices of the free degree of freedom. Each item of the list is a sparse csr_matrix that corresponds to one frequency of analysis.

• Kr_lump (list) – List of lumped stiffness matrices of the prescribed degree of freedom. Each item of the list is a sparse csr_matrix that corresponds to one frequency of analysis.

• Mr_lump (list) – List of lumped mass matrices of the prescribed degree of freedom. Each item of the list is a sparse csr_matrix that corresponds to one frequency of analysis.

• Cr_lump (list) – List of lumped damping matrices of the prescribed degree of freedom. Each item of the list is a sparse csr_matrix that corresponds to one frequency of analysis.

• flag_Clump (boll) – This flag returns True if the damping matrices are non zero, and False otherwise.

get_prescribed_indexes()

This method returns all the indexes of the structural degrees of freedom with prescribed structural displacement or rotation boundary conditions.

Returns

Indexes of the structural degrees of freedom with prescribed displacement or rotation boundary conditions.

Return type

array

See also

get_prescribed_values

Vaslues of the structural degrees of freedom with prescribed displacement or rotation boundary conditions.

get_unprescribed_indexes

Indexes of the structural free degrees of freedom.

get_prescribed_values()

This method returns all the values of the structural degrees of freedom with prescribed structural displacement or rotation boundary conditions.

Returns

Values of the structural degrees of freedom with prescribed displacement or rotation boundary conditions.

Return type

array

See also

get_prescribed_indexes

Indexes of the structural degrees of freedom with prescribed displacement or rotation boundary conditions.

get_unprescribed_indexes

Indexes of the structural free degrees of freedom.

get_unprescribed_indexes()

This method returns all the indexes of the structural free degrees of freedom.

Returns

Indexes of the structural free degrees of freedom.

Return type

array

See also

get_prescribed_indexes

Indexes of the structural degrees of freedom with prescribed displacement or rotation boundary conditions.

get_prescribed_values

Values of the structural degrees of freedom with prescribed displacement or rotation boundary conditions.

Solution Acoustic

class pulse.processing.solution_structural.SolutionStructural(mesh, frequencies, **kwargs)

This class creates a Structural Solution object from input data.

Parameters

• mesh (Mesh object) – Structural finite element mesh.

• frequencies (array) – Frequencies of analysis.

• acoustic_solution (array, optional) – Solution of the acoustic FETM model. This solution is need to solve the coupled problem. Default is None.

_reinsert_prescribed_dofs(solution, modal_analysis=False)

This method reinsert the value of the prescribed degree of freedom in the solution. If modal analysis is performed, the values are zeros.

Parameters

• solution (array) – Solution data from the direct method, modal superposition or modal shapes from modal analysis.

• modal_analysis (boll, optional) – True if the modal analysis was evaluated.

Returns

Solution of all the degrees of freedom.

Return type

array

direct_method(global_damping)

This method evaluates the harmonic analysis through direct method. It is suitable for Viscous Proportional and Hysteretic Proportional damping models.

Parameters

global_damping (list of floats.) – Damping coefficients alpha viscous, beta viscous, alpha histeretic, and beta histeretic.

Returns

Solution. Each column corresponds to a frequency of analysis. Each row corresponds to a degree of freedom.

Return type

array

get_combined_loads(global_damping)

This method adds the effects of prescribed displacement and rotation into global loads vector.

Parameters

global_damping (list of floats.) – Damping coefficients alpha viscous, beta viscous, alpha histeretic, and beta histeretic.

Returns

Force and moment global loads. Each column corresponds to a frequency of analysis.

Return type

array

get_reactions_at_fixed_nodes(global_damping_values=(0, 0, 0, 0))

This method evaluates reaction forces and moments at fixed nodes.

Parameters

global_damping (list of floats.) – Damping coefficients alpha viscous, beta viscous, alpha histeretic, and beta histeretic.

Returns

Reactions. Each column corresponds to a frequency of analysis. Each row corresponds to a fixed degree of freedom.

Return type

array

get_reactions_at_springs_and_dampers()

This method evaluates reaction forces and moments at lumped springs and dampers connected the structure and the ground.

Returns

Reactions. Each column corresponds to a frequency of analysis. Each row corresponds to a spring and damper.

Return type

array

modal_analysis(K=[], M=[], modes=20, which='LM', sigma=0.01, harmonic_analysis=False)

This method evaluates the FEM acoustic modal analysis. The FETM formulation is not suitable to performe modal analysis.

Parameters

• modes (int, optional) – Number of acoustic modes to be evaluated. Default is 20.

• which (str, ['LM' | 'SM' | 'LR' | 'SR' | 'LI' | 'SI'], optional) –

  Which k eigenvectors and eigenvalues to find:

  ’LM’ : largest magnitude ‘SM’ : smallest magnitude ‘LR’ : largest real part ‘SR’ : smallest real part ‘LI’ : largest imaginary part ‘SI’ : smallest imaginary part

  Default is ‘LM’.

• sigma (float, optional) – Find eigenvalues near sigma in (rad/s)^2 using shift-invert mode.

• harmonic_analysis (boll, optional) – True when the modal analysis is used to perform mode superposition. False otherwise. Default is False.

Returns

• natural_frequencies (array) – Natural frequencies.

• modal_shapes (array) – Modal shapes

mode_superposition(modes, global_damping, F_loaded=None, fastest=True)

This method evaluates the harmonic analysis through mode superposition method. It is suitable for Viscous Proportional and Hysteretic Proportional damping models.

Parameters

• global_damping (list of floats.) – Damping coefficients alpha viscous, beta viscous, alpha histeretic, and beta histeretic.

• F_loaded (,optional.) – Default None.

• fastest (boll, optional.) – True if 3D matrix solution procedure must be used. False otherwise. Default True.

Returns

Solution. Each column corresponds to a frequency of analysis. Each row corresponds to a degree of freedom.

Return type

array

stress_calculate(global_damping, pressure_external=0, damping_flag=False, _real_values=False)

This method evaluates reaction forces and moments at lumped springs and dampers connected the structure and the ground.

Parameters

• global_damping (list of floats.) – Damping coefficients alpha viscous, beta viscous, alpha histeretic, and beta histeretic.

• pressure_external (float, optional) – Static pressure difference between atmosphere and the fluid in the pipeline. Default is 0.

• damping_flag (boll, optional.) – True if the damping must be considered when evaluating the stresses. False otherwise. Default is False

Returns

Stresses. Each column corresponds to a element. The rows corresponds to the:

Normal axial stress Normal bending-y stress Normal bending-z stress Hoop stress Torsional shear Transversal-xy shear Transversal-xz shear

Return type

array

Solution Structural

class pulse.processing.solution_acoustic.SolutionAcoustic(mesh, frequencies)

This class creates a Acoustic Solution object from input data.

Parameters

• mesh (Mesh object) – Acoustic finite element mesh.

• frequencies (array) – Frequencies of analysis.

_reinsert_prescribed_dofs(solution, modal_analysis=False)

This method reinsert the value of the prescribed degree of freedom in the solution. If modal analysis is performed, the values are zeros.

Parameters

• solution (array) – Solution data from the direct method, modal superposition or modal shapes from modal analysis.

• modal_analysis (boll, optional) – True if the modal analysis was evaluated.

Returns

Solution of all the degrees of freedom.

Return type

array

direct_method()

This method evaluate the FETM acoustic solution through direct method.

Returns

Solution. Each column corresponds to a frequency of analysis. Each row corresponds to a degree of freedom.

Return type

array

get_combined_volume_velocity()

This method adds the effects of prescribed acoustic pressure into volume velocity global vector.

Returns

Volume velocity. Each column corresponds to a frequency of analysis.

Return type

array

get_global_matrices()

This method updates the acoustic global matrices.

modal_analysis(modes=20, which='LM', sigma=0.01)

This method evaluate the FEM acoustic modal analysis. The FETM formulation is not suitable to performe modal analysis.

Parameters

• modes (int, optional) – Number of acoustic modes to be evaluated. Default is 20.

• which (str, ['LM' | 'SM' | 'LR' | 'SR' | 'LI' | 'SI'], optional) –

  Which k eigenvectors and eigenvalues to find:

  ’LM’ : largest magnitude ‘SM’ : smallest magnitude ‘LR’ : largest real part ‘SR’ : smallest real part ‘LI’ : largest imaginary part ‘SI’ : smallest imaginary part

  Default is ‘LM’.

• sigma (float, optional) – Find eigenvalues near sigma (in (rad/s)^2) using shift-invert mode. Default is 0.01.

Returns

• natural_frequencies (array) – Natural frequencies.

• modal_shapes (array) – Modal shapes