Ormsby Wavelet

Calculates an amplitude normalized Ormsby wavelet with the given input parameters.

This object generates an Ormsby wavelet defined by Eq. (1) below. The Ormsby wavelet is a wavelet function that has a near constant Fourier amplitude for a given frequency range. It is defined by four frequencies, $var element = document.getElementById("moose-equation-5499e57e-9956-4df1-8865-6d1c6e3dda29");katex.render("f_1", element, {displayMode:false,throwOnError:false});$ , $var element = document.getElementById("moose-equation-76bfd7dd-e3c8-4856-8ce4-faf66fdab106");katex.render("f_2", element, {displayMode:false,throwOnError:false});$ , $var element = document.getElementById("moose-equation-ed77d032-9eb9-4a35-82ad-c3890f9297ff");katex.render("f_3", element, {displayMode:false,throwOnError:false});$ , and $var element = document.getElementById("moose-equation-be287d7e-afb1-4020-be6c-ec0981ec169b");katex.render("f_4", element, {displayMode:false,throwOnError:false});$ , and the time of maximum amplitude, $var element = document.getElementById("moose-equation-e236d0b0-66f3-48f3-920d-2dacb4550ffe");katex.render("t_s", element, {displayMode:false,throwOnError:false});$ . The approximate shape of the fast Fourier transform (FFT) of the Ormsby wavelet is as follows: it starts at zero, increases linearly between $var element = document.getElementById("moose-equation-b680bbf6-35c2-4694-b8cb-7d505fe72fd4");katex.render("f_1", element, {displayMode:false,throwOnError:false});$ and $var element = document.getElementById("moose-equation-490acfeb-6184-4613-bbaf-ff51a60d40bc");katex.render("f_2", element, {displayMode:false,throwOnError:false});$ , stays constant between $var element = document.getElementById("moose-equation-29ad836d-b7d3-44a3-8a1c-e73bf31faf6b");katex.render("f_2", element, {displayMode:false,throwOnError:false});$ and $var element = document.getElementById("moose-equation-141e68da-7f2c-439f-b27d-f99eb9327d06");katex.render("f_3", element, {displayMode:false,throwOnError:false});$ , decreases linearly to zero between $var element = document.getElementById("moose-equation-d9a8f976-70e7-4bd1-8885-ba9973b9050e");katex.render("f_3", element, {displayMode:false,throwOnError:false});$ and $var element = document.getElementById("moose-equation-4df3b1fb-9c53-43fe-9684-471f255b28b3");katex.render("f_4", element, {displayMode:false,throwOnError:false});$ , and stays at zero after $var element = document.getElementById("moose-equation-9937f1b4-4308-4e76-8ca8-c21d9f7c6533");katex.render("f_4", element, {displayMode:false,throwOnError:false});$ . The OrmsbyWavelet function returns an amplitude-normalized wavelet with a maximum amplitude of 1.0.

$(1)var element = document.getElementById("moose-equation-f069808a-1ed2-4590-954a-011c12b738c5");katex.render(" \\begin{aligned} f(t)=\\left[\\frac{\\pi f_4^2}{f_4-f_3}sinc(\\pi f_4(t-t_s))-\\frac{\\pi f_3^2}{f_4-f_3}sinc(\\pi f_3(t-t_s))\\right]- \\\\ \\left[\\frac{\\pi f_2^2}{f_2-f_1}sinc(\\pi f_2(t-t_s))-\\frac{\\pi f_1^2}{f_2-f_1}sinc(\\pi f_1(t-t_s))\\right] \\end{aligned}", element, {displayMode:true,throwOnError:false});$

A sample Ormsby wavelet calculated using the $var element = document.getElementById("moose-equation-b87fb21c-4ed3-4f64-93dc-9bb0c54b7daa");katex.render("f_1", element, {displayMode:false,throwOnError:false});$ , $var element = document.getElementById("moose-equation-17d4f6f3-2072-4ec6-b34e-462a2476affa");katex.render("f_2", element, {displayMode:false,throwOnError:false});$ , $var element = document.getElementById("moose-equation-a2cf506f-3b26-4540-97ea-38caac608bd7");katex.render("f_3", element, {displayMode:false,throwOnError:false});$ , and $var element = document.getElementById("moose-equation-00bb2730-2945-4575-b32e-8a17015e7b23");katex.render("f_4", element, {displayMode:false,throwOnError:false});$ values of 0 $var element = document.getElementById("moose-equation-ca43e5d1-86f9-45ac-9366-7569a752f248");katex.render("Hz", element, {displayMode:false,throwOnError:false});$ , 0.2 $var element = document.getElementById("moose-equation-0c400b94-88ae-4ef9-9d3d-85e482d5aeb6");katex.render("Hz", element, {displayMode:false,throwOnError:false});$ , 20 $var element = document.getElementById("moose-equation-46a4fbb7-b95d-432e-a362-89474f790007");katex.render("Hz", element, {displayMode:false,throwOnError:false});$ , and 25 $var element = document.getElementById("moose-equation-84577b14-f581-4478-961e-a7efcb3bcd53");katex.render("Hz", element, {displayMode:false,throwOnError:false});$ , a $var element = document.getElementById("moose-equation-4326ac87-b9df-4c54-bf73-20141d4969ca");katex.render("t_s", element, {displayMode:false,throwOnError:false});$ value of 2.0 $var element = document.getElementById("moose-equation-284276e0-c5ed-4ba9-878c-b525587706c9");katex.render("sec", element, {displayMode:false,throwOnError:false});$ , and a scale factor of 0.5, is shown in Figure 1. The input syntax for generating this wavelet is shown below.

[Functions<<<{"href": "../../syntax/Functions/index.html"}>>>]
  [ormsby]
    type = OrmsbyWavelet<<<{"description": "Calculates an amplitude normalized Ormsby wavelet with the given input parameters.", "href": "OrmsbyWavelet.html"}>>>
    f1<<<{"description": "First frequency for defining the Ormsby wavelet."}>>> = 0.0
    f2<<<{"description": "Second frequency for defining the Ormsby wavelet."}>>> = 0.2
    f3<<<{"description": "Third frequency for defining the Ormsby wavelet."}>>> = 20.0
    f4<<<{"description": "Fourth frequency for defining the Ormsby wavelet."}>>> = 25.0
    ts<<<{"description": "Time of the peak of the Ormsby wavelet."}>>> = 2.0
    scale_factor<<<{"description": "Amplitude scale factor to be applied to wavelet."}>>> = 0.5
  []
[]

Figure 1: Time series of a sample Ormsby wavelet

More detailed information on the Ormsby wavelet can be found in Appendix B of Bolisetti and Whittaker (2015), as well as here.

Input Parameters

f1First frequency for defining the Ormsby wavelet.
C++ Type:double
Unit:(no unit assumed)
Controllable:No
Description:First frequency for defining the Ormsby wavelet.
f2Second frequency for defining the Ormsby wavelet.
C++ Type:double
Unit:(no unit assumed)
Controllable:No
Description:Second frequency for defining the Ormsby wavelet.
f3Third frequency for defining the Ormsby wavelet.
C++ Type:double
Unit:(no unit assumed)
Controllable:No
Description:Third frequency for defining the Ormsby wavelet.
f4Fourth frequency for defining the Ormsby wavelet.
C++ Type:double
Unit:(no unit assumed)
Controllable:No
Description:Fourth frequency for defining the Ormsby wavelet.
tsTime of the peak of the Ormsby wavelet.
C++ Type:double
Unit:(no unit assumed)
Controllable:No
Description:Time of the peak of the Ormsby wavelet.

Required Parameters

scale_factor1Amplitude scale factor to be applied to wavelet.
Default:1
C++ Type:double
Unit:(no unit assumed)
Controllable:No
Description:Amplitude scale factor to be applied to wavelet.

Optional Parameters

control_tagsAdds user-defined labels for accessing object parameters via control logic.
C++ Type:std::vector<std::string>
Controllable:No
Description:Adds user-defined labels for accessing object parameters via control logic.
enableTrueSet the enabled status of the MooseObject.
Default:True
C++ Type:bool
Controllable:No
Description:Set the enabled status of the MooseObject.

Advanced Parameters

Input Files

(test/tests/functions/ormsby_wavelet/ormsby.i)
(examples/ex11a/dynamic/3d_beam_dynamic_second_order.i)
(examples/ex11a/dynamic/3d_beam_dynamic_first_order.i)

References

C. Bolisetti and A. S. Whittaker. Site response, soil-structure interaction and structure-soil-structure interaction for performance assessment of buildings and nuclear structures. Technical Report MCEER-15-0002, Multidisciplinary Center for Earthquake Engineering Research, Buffalo, New York, 2015. doi:10.13140/RG.2.1.1951.7527/1.

BibTeX

@article{BolisettiandWhittakerMCEER2015,
    author = "Bolisetti, C. and Whittaker, A. S.",
    title = "Site response, soil-structure interaction and structure-soil-structure interaction for performance assessment of buildings and nuclear structures",
    journal = "Technical Report MCEER-15-0002, Multidisciplinary Center for Earthquake Engineering Research, Buffalo, New York",
    year = "2015",
    doi = "10.13140/RG.2.1.1951.7527/1"
}

RIS

TY  - JOUR
AU  - Bolisetti, C.
AU  - Whittaker, A. S.
TI  - Site response, soil-structure interaction and structure-soil-structure interaction for performance assessment of buildings and nuclear structures
JO  - Technical Report MCEER-15-0002, Multidisciplinary Center for Earthquake Engineering Research, Buffalo, New York
PY  - 2015
DO  - 10.13140/RG.2.1.1951.7527/1
ER  -

Plain Text

C. Bolisetti and A. S. Whittaker. Site response, soil-structure interaction and structure-soil-structure interaction for performance assessment of buildings and nuclear structures. Technical Report MCEER-15-0002, Multidisciplinary Center for Earthquake Engineering Research, Buffalo, New York, 2015. doi:10.13140/RG.2.1.1951.7527/1.

(test/tests/functions/ormsby_wavelet/ormsby.i)

[Mesh]
  type = GeneratedMesh
  dim = 1
[]

[Variables]
  [u]
  []
[]

[Functions]
  [ormsby]
    type = OrmsbyWavelet
    f1 = 0.0
    f2 = 0.2
    f3 = 20.0
    f4 = 25.0
    ts = 2.0
    scale_factor = 0.5
  []
[]

[Postprocessors]
  [func]
    type = FunctionValuePostprocessor
    function = ormsby
    execute_on = "INITIAL TIMESTEP_END"
  []
[]

[Problem]
  type = FEProblem
  solve = false
  kernel_coverage_check = false
[]

[Executioner]
  type = Transient
  num_steps = 400
  dt = 0.01
[]

[Outputs]
  csv = true
[]

(test/tests/functions/ormsby_wavelet/ormsby.i)

[Mesh]
  type = GeneratedMesh
  dim = 1
[]

[Variables]
  [u]
  []
[]

[Functions]
  [ormsby]
    type = OrmsbyWavelet
    f1 = 0.0
    f2 = 0.2
    f3 = 20.0
    f4 = 25.0
    ts = 2.0
    scale_factor = 0.5
  []
[]

[Postprocessors]
  [func]
    type = FunctionValuePostprocessor
    function = ormsby
    execute_on = "INITIAL TIMESTEP_END"
  []
[]

[Problem]
  type = FEProblem
  solve = false
  kernel_coverage_check = false
[]

[Executioner]
  type = Transient
  num_steps = 400
  dt = 0.01
[]

[Outputs]
  csv = true
[]

(examples/ex11a/dynamic/3d_beam_dynamic_second_order.i)

[Mesh]
  [mesh_gen]
    type = GeneratedMeshGenerator
    dim = 3
    nx = 20
    ny = 2
    nz = 2
    xmin = 0.0
    xmax = 5.0
    ymin = 0.0
    ymax = 1.0
    zmin = 0.0
    zmax = 1.0
    # elem_type = 'HEX8'
    elem_type = 'HEX20'
  []
  [nodeset_gen]
    type = ExtraNodesetGenerator
    new_boundary = 'base_node end_node'
    coord = '0.0 0.0 0.5; 5.0 0.0 0.5'
    input = 'mesh_gen'
  []
[]

[GlobalParams]
  displacements = 'disp_x disp_y disp_z'
[]

[Variables]
  [./disp_x]
    # order = FIRST
    order = SECOND
    family = LAGRANGE
  [../]
  [./disp_y]
    # order = FIRST
    order = SECOND
    family = LAGRANGE
  [../]
  [./disp_z]
    # order = FIRST
    order = SECOND
    family = LAGRANGE
  [../]
[]

[Kernels]
  [DynamicTensorMechanics]
  []
  [inertia_x]
    type = InertialForce
    variable = disp_x
    velocity = vel_x
    acceleration = accel_x
    beta = 0.25
    gamma = 0.5
  []
  [inertia_y]
    type = InertialForce
    variable = disp_y
    velocity = vel_y
    acceleration = accel_y
    beta = 0.25
    gamma = 0.5
  []
  [inertia_z]
    type = InertialForce
    variable = disp_z
    velocity = vel_z
    acceleration = accel_z
    beta = 0.25
    gamma = 0.5
  []
[]

[AuxVariables]
  [vel_x]
    # order = FIRST
    order = SECOND
  []
  [accel_x]
    # order = FIRST
    order = SECOND
  []
  [vel_y]
    order = SECOND
  []
  [accel_y]
    order = SECOND
  []
  [vel_z]
    order = SECOND
  []
  [accel_z]
    order = SECOND
  []
[]

[AuxKernels]
  [accel_x]
    type = NewmarkAccelAux
    variable = accel_x
    displacement = disp_x
    velocity = vel_x
    beta = 0.25
    execute_on = timestep_end
  []
  [vel_x]
    type = NewmarkVelAux
    variable = vel_x
    acceleration = accel_x
    gamma = 0.5
    execute_on = timestep_end
  []
  [accel_y]
    type = NewmarkAccelAux
    variable = accel_y
    displacement = disp_y
    velocity = vel_y
    beta = 0.25
    execute_on = timestep_end
  []
  [vel_y]
    type = NewmarkVelAux
    variable = vel_y
    acceleration = accel_y
    gamma = 0.5
    execute_on = timestep_end
  []
  [accel_z]
    type = NewmarkAccelAux
    variable = accel_z
    displacement = disp_z
    velocity = vel_z
    beta = 0.25
    execute_on = timestep_end
  []
  [vel_z]
    type = NewmarkVelAux
    variable = vel_z
    acceleration = accel_z
    gamma = 0.5
    execute_on = timestep_end
  []
[]

[BCs]
  [fix_x]
    type = DirichletBC
    variable = disp_x
    boundary = 'left'
    value = 0.0
  []
  [fix_z]
    type = DirichletBC
    variable = disp_z
    boundary = 'left'
    value = 0.0
  []
  [y_motion]
    type = PresetAcceleration
    acceleration = accel_y
    velocity = vel_y
    variable = disp_y
    beta = 0.25
    boundary = 'left'
    function = 'ormsby'
  []
[]

[Functions]
  [ormsby]
    type = OrmsbyWavelet
    f1 = 0.0
    f2 = 0.1
    f3 = 45.0
    f4 = 50.0
    ts = 1.5
    scale_factor = 0.5
  []
[]


[Materials]
  [elasticity]
    type = ComputeIsotropicElasticityTensor
    youngs_modulus = 10e9
    poissons_ratio = 0.3
  []
  [strain_1]
    type = ComputeSmallStrain
  []
  [stress_1]
    type = ComputeLinearElasticStress
  []
  [den_1]
    type = GenericConstantMaterial
    prop_names = density
    prop_values = 1200
  []
[]

[Preconditioning]
  [smp]
    type = SMP
    full = true
  []
[]

[Executioner]
  type = Transient
  solve_type = NEWTON
  petsc_options = '-ksp_snes_ew'
  petsc_options_iname = '-pc_type -pc_factor_mat_solver_package'
  petsc_options_value = 'lu       superlu_dist'
  line_search = 'none'
  nl_rel_tol = 1e-8
  nl_abs_tol = 1e-10
  dt = 0.01
  end_time = 3.0
  timestep_tolerance = 1e-6
[]

[VectorPostprocessors]
  [accel_hist]
    type = ResponseHistoryBuilder
    variables = 'accel_y'
    boundary = 'base_node end_node'
  []
  [accel_spec]
    type = ResponseSpectraCalculator
    vectorpostprocessor = accel_hist
    regularize_dt = 0.01
    damping_ratio = 0.05
    start_frequency = 0.1
    end_frequency = 100
    outputs = 2_2
  []
[]

[Outputs]
  perf_graph = true
  [./2_2]
    type = CSV
    execute_on = 'final'
  [../]
[]

(examples/ex11a/dynamic/3d_beam_dynamic_first_order.i)

[Mesh]
  [mesh_gen]
    type = GeneratedMeshGenerator
    dim = 3
    nx = 20
    ny = 2
    nz = 2
    xmin = 0.0
    xmax = 5.0
    ymin = 0.0
    ymax = 1.0
    zmin = 0.0
    zmax = 1.0
    # elem_type = 'HEX8'
    elem_type = 'HEX20'
  []
  [nodeset_gen]
    type = ExtraNodesetGenerator
    new_boundary = 'base_node end_node'
    coord = '0.0 0.0 0.5; 5.0 0.0 0.5'
    input = 'mesh_gen'
  []
[]

[GlobalParams]
  displacements = 'disp_x disp_y disp_z'
[]

[Variables]
  [./disp_x]
    # order = FIRST
    order = SECOND
    family = LAGRANGE
  [../]
  [./disp_y]
    # order = FIRST
    order = SECOND
    family = LAGRANGE
  [../]
  [./disp_z]
    # order = FIRST
    order = SECOND
    family = LAGRANGE
  [../]
[]

[Kernels]
  [DynamicTensorMechanics]
  []
  [inertia_x]
    type = InertialForce
    variable = disp_x
    velocity = vel_x
    acceleration = accel_x
    beta = 0.25
    gamma = 0.5
  []
  [inertia_y]
    type = InertialForce
    variable = disp_y
    velocity = vel_y
    acceleration = accel_y
    beta = 0.25
    gamma = 0.5
  []
  [inertia_z]
    type = InertialForce
    variable = disp_z
    velocity = vel_z
    acceleration = accel_z
    beta = 0.25
    gamma = 0.5
  []
[]

[AuxVariables]
  [vel_x]
    # order = FIRST
    order = SECOND
  []
  [accel_x]
    # order = FIRST
    order = SECOND
  []
  [vel_y]
    order = SECOND
  []
  [accel_y]
    order = SECOND
  []
  [vel_z]
    order = SECOND
  []
  [accel_z]
    order = SECOND
  []
[]

[AuxKernels]
  [accel_x]
    type = NewmarkAccelAux
    variable = accel_x
    displacement = disp_x
    velocity = vel_x
    beta = 0.25
    execute_on = timestep_end
  []
  [vel_x]
    type = NewmarkVelAux
    variable = vel_x
    acceleration = accel_x
    gamma = 0.5
    execute_on = timestep_end
  []
  [accel_y]
    type = NewmarkAccelAux
    variable = accel_y
    displacement = disp_y
    velocity = vel_y
    beta = 0.25
    execute_on = timestep_end
  []
  [vel_y]
    type = NewmarkVelAux
    variable = vel_y
    acceleration = accel_y
    gamma = 0.5
    execute_on = timestep_end
  []
  [accel_z]
    type = NewmarkAccelAux
    variable = accel_z
    displacement = disp_z
    velocity = vel_z
    beta = 0.25
    execute_on = timestep_end
  []
  [vel_z]
    type = NewmarkVelAux
    variable = vel_z
    acceleration = accel_z
    gamma = 0.5
    execute_on = timestep_end
  []
[]

[BCs]
  [fix_x]
    type = DirichletBC
    variable = disp_x
    boundary = 'left'
    value = 0.0
  []
  [fix_z]
    type = DirichletBC
    variable = disp_z
    boundary = 'left'
    value = 0.0
  []
  [y_motion]
    type = PresetAcceleration
    acceleration = accel_y
    velocity = vel_y
    variable = disp_y
    beta = 0.25
    boundary = 'left'
    function = 'ormsby'
  []
[]

[Functions]
  [ormsby]
    type = OrmsbyWavelet
    f1 = 0.0
    f2 = 0.1
    f3 = 45.0
    f4 = 50.0
    ts = 1.5
    scale_factor = 0.5
  []
[]


[Materials]
  [elasticity]
    type = ComputeIsotropicElasticityTensor
    youngs_modulus = 10e9
    poissons_ratio = 0.3
  []
  [strain_1]
    type = ComputeSmallStrain
  []
  [stress_1]
    type = ComputeLinearElasticStress
  []
  [den_1]
    type = GenericConstantMaterial
    prop_names = density
    prop_values = 1200
  []
[]

[Preconditioning]
  [smp]
    type = SMP
    full = true
  []
[]

[Executioner]
  type = Transient
  solve_type = NEWTON
  petsc_options = '-ksp_snes_ew'
  petsc_options_iname = '-pc_type -pc_factor_mat_solver_package'
  petsc_options_value = 'lu       superlu_dist'
  line_search = 'none'
  nl_rel_tol = 1e-8
  nl_abs_tol = 1e-10
  dt = 0.01
  end_time = 3.0
  timestep_tolerance = 1e-6
[]

[VectorPostprocessors]
  [accel_hist]
    type = ResponseHistoryBuilder
    variables = 'accel_y'
    boundary = 'base_node end_node'
  []
  [accel_spec]
    type = ResponseSpectraCalculator
    vectorpostprocessor = accel_hist
    regularize_dt = 0.01
    damping_ratio = 0.05
    start_frequency = 0.1
    end_frequency = 100
    outputs = 2_2
  []
[]

[Outputs]
  perf_graph = true
  [./2_2]
    type = CSV
    execute_on = 'final'
  [../]
[]

Input Parameters
Input Files
References

Usage

Development

Demonstration