HousnerSpectrumIntensity

The HousnerSpectrumIntensity calculates the Housner Spectrum Intensity (HSI) for a set of response histories calculated by the ResponseHistoryBuilder VectorPostprocessor. Housner Spectrum Intensity is defined as the area under the velocity spectrum curve, when plotted with period on the X axis (Housner, 1952). Housner (1952) recommends that the area be calculated between the periods 0.25sec and 2.5sec, which are the default values for the start_period and end_period parameters in MASTODON (see parameter definitions below). The HSI values will be output into a csv file in the same order as the acceleration variables are entered in the input file.

Usage

For example, the input file below contains a ResponseHistoryBuilder VectorPostprocessor called 'accel_hist', which builds the response histories of the acceleration variables, accel_x and accel_y at nodes 8 and 9. It is desired that the HSIs for accel_x and accel_y at these nodes be calculated. These can be calculated by the HousnerSpectrumIntensity vectorpostprocessor called 'accel_hsi', as shown in the input file below.

[VectorPostprocessors<<<{"href": "../../syntax/VectorPostprocessors/index.html"}>>>]
  [./accel_hist]
    type = ResponseHistoryBuilder<<<{"description": "Calculates response histories for a given node and variable(s).", "href": "ResponseHistoryBuilder.html"}>>>
    variables<<<{"description": "Variable name for which the response history is requested."}>>> = 'accel_x accel_y'
    nodes<<<{"description": "Node number(s) at which the response history is needed."}>>> = '8 9'
  [../]
  [./accel_hsi]
    type = HousnerSpectrumIntensity<<<{"description": "Calculate the HSI for the requested acceleration variables.", "href": "HousnerSpectrumIntensity.html"}>>>
    vectorpostprocessor<<<{"description": "Name of the ResponseHistoryBuilder vectorpostprocessor, for which HSIs are calculated."}>>> = accel_hist
    regularize_dt<<<{"description": "dt for HSI calculation. The acceleration response will be regularized to this dt prior to the HSI calculation."}>>> = 0.005
    outputs<<<{"description": "Vector of output names where you would like to restrict the output of variables(s) associated with this object"}>>> = out
  [../]
[]

note

HousnerSpectrumIntensity assumes that the response histories calculated in the vectorpostprocessor, provided in the vectorpostprocessor parameter in the input are acceleration histories, and will not perform any checks to ensure that they are accelerations. The user should ensure this by defining the corresponding ResponseHistoryBuilder appropriately.

Special care must be taken to ensure that the HSI calculations are performed only at the end of the simulation (last time step) and not at every time step. In order to accomplish this, an 'Outputs' block must be created as shown below. This block (named 'out') ensures that the CSV output is only calculated at the final timestep.

[Outputs<<<{"href": "../../syntax/Mastodon/Outputs/index.html"}>>>]
  [./out]
    type = CSV<<<{"description": "Output for postprocessors, vector postprocessors, and scalar variables using comma seperated values (CSV).", "href": "../outputs/CSV.html"}>>>
    execute_on<<<{"description": "The list of flag(s) indicating when this object should be executed. For a description of each flag, see https://mooseframework.inl.gov/source/interfaces/SetupInterface.html."}>>> = 'final'
  [../]
[]

For such an input, the HSI calculation is performed only at the end of the simulation and the HSIs are output into a csv file as shown below. Note that the columns in the csv file are organized according to the node numbers and variable names. For example, the HSIs for accel_x at node 8 are under node_8_accel_x_hsi. In this case, the HSIs for nodes 8 and 9 for the variables, accel_x and accel_y are reported.

node_8_accel_x_hsi,node_8_accel_y_hsi,node_9_accel_x_hsi,node_9_accel_y_hsi
0.81488283652923,1.6297656730584,0.8148828365292,1.6297656730584

Input Parameters

regularize_dtdt for HSI calculation. The acceleration response will be regularized to this dt prior to the HSI calculation.
C++ Type:double
Unit:(no unit assumed)
Controllable:No
Description:dt for HSI calculation. The acceleration response will be regularized to this dt prior to the HSI calculation.
vectorpostprocessorName of the ResponseHistoryBuilder vectorpostprocessor, for which HSIs are calculated.
C++ Type:VectorPostprocessorName
Unit:(no unit assumed)
Controllable:No
Description:Name of the ResponseHistoryBuilder vectorpostprocessor, for which HSIs are calculated.

Required Parameters

damping_ratio0.05Damping ratio for HSI calculation.
Default:0.05
C++ Type:double
Unit:(no unit assumed)
Controllable:No
Description:Damping ratio for HSI calculation.
end_period2.5End period for the HSI calculation.
Default:2.5
C++ Type:double
Unit:(no unit assumed)
Controllable:No
Description:End period for the HSI calculation.
num_periods140Number of frequencies for the HSI calculation.
Default:140
C++ Type:unsigned int
Controllable:No
Description:Number of frequencies for the HSI calculation.
parallel_typeREPLICATEDSet how the data is represented within the VectorPostprocessor (VPP); 'distributed' indicates that data within the VPP is distributed and no auto communication is performed, this setting will result in parallel output within the CSV output; 'replicated' indicates that the data within the VPP is correct on processor 0, the data will automatically be broadcast to all processors unless the '_auto_broadcast' param is set to false within the validParams function.
Default:REPLICATED
C++ Type:MooseEnum
Options:DISTRIBUTED, REPLICATED
Controllable:No
Description:Set how the data is represented within the VectorPostprocessor (VPP); 'distributed' indicates that data within the VPP is distributed and no auto communication is performed, this setting will result in parallel output within the CSV output; 'replicated' indicates that the data within the VPP is correct on processor 0, the data will automatically be broadcast to all processors unless the '_auto_broadcast' param is set to false within the validParams function.
start_period0.25Start period for the HSI calculation.
Default:0.25
C++ Type:double
Unit:(no unit assumed)
Controllable:No
Description:Start period for the HSI calculation.

Optional Parameters

allow_duplicate_execution_on_initialFalseIn the case where this UserObject is depended upon by an initial condition, allow it to be executed twice during the initial setup (once before the IC and again after mesh adaptivity (if applicable).
Default:False
C++ Type:bool
Controllable:No
Description:In the case where this UserObject is depended upon by an initial condition, allow it to be executed twice during the initial setup (once before the IC and again after mesh adaptivity (if applicable).
execution_order_group0Execution order groups are executed in increasing order (e.g., the lowest number is executed first). Note that negative group numbers may be used to execute groups before the default (0) group. Please refer to the user object documentation for ordering of user object execution within a group.
Default:0
C++ Type:int
Controllable:No
Description:Execution order groups are executed in increasing order (e.g., the lowest number is executed first). Note that negative group numbers may be used to execute groups before the default (0) group. Please refer to the user object documentation for ordering of user object execution within a group.
force_postauxFalseForces the UserObject to be executed in POSTAUX
Default:False
C++ Type:bool
Controllable:No
Description:Forces the UserObject to be executed in POSTAUX
force_preauxFalseForces the UserObject to be executed in PREAUX
Default:False
C++ Type:bool
Controllable:No
Description:Forces the UserObject to be executed in PREAUX
force_preicFalseForces the UserObject to be executed in PREIC during initial setup
Default:False
C++ Type:bool
Controllable:No
Description:Forces the UserObject to be executed in PREIC during initial setup

Execution Scheduling 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:Yes
Description:Set the enabled status of the MooseObject.
outputsVector of output names where you would like to restrict the output of variables(s) associated with this object
C++ Type:std::vector<OutputName>
Controllable:No
Description:Vector of output names where you would like to restrict the output of variables(s) associated with this object
use_displaced_meshFalseWhether or not this object should use the displaced mesh for computation. Note that in the case this is true but no displacements are provided in the Mesh block the undisplaced mesh will still be used.
Default:False
C++ Type:bool
Controllable:No
Description:Whether or not this object should use the displaced mesh for computation. Note that in the case this is true but no displacements are provided in the Mesh block the undisplaced mesh will still be used.

Advanced Parameters

prop_getter_suffixAn optional suffix parameter that can be appended to any attempt to retrieve/get material properties. The suffix will be prepended with a '_' character.
C++ Type:MaterialPropertyName
Unit:(no unit assumed)
Controllable:No
Description:An optional suffix parameter that can be appended to any attempt to retrieve/get material properties. The suffix will be prepended with a '_' character.
use_interpolated_stateFalseFor the old and older state use projected material properties interpolated at the quadrature points. To set up projection use the ProjectedStatefulMaterialStorageAction.
Default:False
C++ Type:bool
Controllable:No
Description:For the old and older state use projected material properties interpolated at the quadrature points. To set up projection use the ProjectedStatefulMaterialStorageAction.

Material Property Retrieval Parameters

Input Files

(test/tests/vectorpostprocessors/housner_spectrum_intensity/housner_spectrum_intensity.i)

References

G. W. Housner. Spectrum intensities of strong-motion earthquakes. Symposium on Earthquake and Blast Effects on Structures, Los Angeles, California, 1952.

@article{housner1952hsi,
    author = "Housner, G. W.",
    title = "Spectrum intensities of strong-motion earthquakes",
    journal = "Symposium on Earthquake and Blast Effects on Structures, Los Angeles, California",
    year = "1952"
}

(test/tests/vectorpostprocessors/housner_spectrum_intensity/housner_spectrum_intensity.i)

#@requirement F8.3
[Mesh]
  type = GeneratedMesh
  dim = 3
  nx = 1
  ny = 1
  nz = 4
  xmin = 0.0
  xmax = 1.0
  ymin = 0.0
  ymax = 1.0
  zmin = 0.0
  zmax = 4.0
[]

[Controls]
   [./period0]
      type = TimePeriod
      disable_objects = 'Kernels/inertia_x Kernels/inertia_y Kernels/inertia_z AuxKernels/accel_x AuxKernels/accel_y AuxKernels/accel_z AuxKernels/vel_x AuxKernels/vel_y AuxKernels/vel_z'
      start_time = 0.0
      end_time = 0.005 # same as dt used in the analysis
   [../]
[]

[Variables]
  [./disp_x]
  [../]
  [./disp_y]
  [../]
  [./disp_z]
  [../]
[]

[AuxVariables]
  [./vel_x]
  [../]
  [./accel_x]
  [../]
  [./vel_y]
  [../]
  [./accel_y]
  [../]
  [./vel_z]
  [../]
  [./accel_z]
  [../]
  [./stress_zx]
    order = CONSTANT
    family = MONOMIAL
  [../]
  [./strain_zx]
    order = CONSTANT
    family = MONOMIAL
  [../]
  [./layer_id]
    family = MONOMIAL
    order = CONSTANT
  [../]
[]

[Kernels]
  [./DynamicTensorMechanics]
    displacements = 'disp_x disp_y disp_z'
    stiffness_damping_coefficient = 0.000781
    static_initialization = True
    use_displaced_mesh = True
  [../]
  [./inertia_x]
    type = InertialForce
    variable = disp_x
    velocity = vel_x
    acceleration = accel_x
    eta = 0.64026
    beta = 0.25
    gamma = 0.5
    use_displaced_mesh = True
  [../]
  [./inertia_y]
    type = InertialForce
    variable = disp_y
    velocity = vel_y
    acceleration = accel_y
    eta = 0.64026
    beta = 0.25
    gamma = 0.5
    use_displaced_mesh = True
  [../]
  [./inertia_z]
    type = InertialForce
    variable = disp_z
    velocity = vel_z
    acceleration = accel_z
    eta = 0.64026
    beta = 0.25
    gamma = 0.5
    use_displaced_mesh = True
  [../]
  [./gravity]
    type = Gravity
    variable = disp_z
    value = -9.81
    use_displaced_mesh = True
  [../]
[]

[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
  [../]
  [./stress_zx]
    type = RankTwoAux
    rank_two_tensor = stress
    variable = stress_zx
    index_i = 2
    index_j = 0
  [../]
  [./strain_zx]
    type = RankTwoAux
    rank_two_tensor = total_strain
    variable = strain_zx
    index_i = 2
    index_j = 0
  [../]
  [./layer_id]
     type = UniformLayerAuxKernel
     variable = layer_id
     interfaces = '20'
     direction = '0 0 1'
     execute_on = initial
  [../]
[]

[Materials]
   [./elasticity_tensor]
      type = ComputeIsotropicElasticityTensorSoil
      block = 0
      layer_variable = layer_id
      layer_ids = '0'
      poissons_ratio = '0.3'
      density = '2000.0'
      shear_modulus = '325e7'
   [../]
   [./stress1]
     #Computes the stress, using linear elasticity
     type = ComputeLinearElasticStress
     block = 0
    [../]
    [./strain1]
      #Computes the strain, assuming small strains
      type = ComputeSmallStrain
      block = 0
      displacements = 'disp_x disp_y disp_z'
  [../]
[]

[BCs]
  [./bottom_accel_x]
    type = PresetAcceleration
    boundary = back
    function = accel_bottom_x
    variable = disp_x
    beta = 0.25
    acceleration = accel_x
    velocity = vel_x
  [../]
  [./bottom_z]
    type = DirichletBC
    variable = disp_z
    boundary = back
    value = 0.0
  [../]
  [./bottom_accel_y]
    type = PresetAcceleration
    boundary = back
    function = accel_bottom_y
    variable = disp_y
    beta = 0.25
    acceleration = accel_y
    velocity = vel_y
  [../]
  [./Periodic]
    [./x_dir]
      primary = 'left'
      secondary = 'right'
      translation = '1.0 0.0 0.0'
    [../]
    [./y_dir]
      primary = 'bottom'
      secondary = 'top'
      translation = '0.0 1.0 0.0'
    [../]
  [../]
[]

[Functions]
  [./accel_bottom_x]
    type = PiecewiseLinear
    data_file = 'accel.csv'
    format = columns
    scale_factor = 1.0
  [../]
  [./accel_bottom_y]
    type = PiecewiseLinear
    data_file = 'accel.csv'
    format = columns
    scale_factor = 2.0
  [../]
[]

[Executioner]
  type = Transient
  solve_type = PJFNK
  nl_abs_tol = 1e-8
  nl_rel_tol = 1e-8
  l_tol = 1e-8
  start_time = 32
  end_time = 33
  dt = 0.005 # should be 0.005
  timestep_tolerance = 1e-6
  petsc_options = '-snes_ksp_ew'
  petsc_options_iname = '-ksp_gmres_restart -pc_type -pc_hypre_type -pc_hypre_boomeramg_max_iter'
  petsc_options_value = '201                hypre    boomeramg      4'
  line_search = 'none'
[]

[Outputs]
  [./out]
    type = CSV
    execute_on = 'final'
  [../]
[]

[VectorPostprocessors]
  [./accel_hist]
    type = ResponseHistoryBuilder
    variables = 'accel_x accel_y'
    nodes = '8 9'
  [../]
  [./accel_hsi]
    type = HousnerSpectrumIntensity
    vectorpostprocessor = accel_hist
    regularize_dt = 0.005
    outputs = out
  [../]
[]

(test/tests/vectorpostprocessors/housner_spectrum_intensity/housner_spectrum_intensity.i)

#@requirement F8.3
[Mesh]
  type = GeneratedMesh
  dim = 3
  nx = 1
  ny = 1
  nz = 4
  xmin = 0.0
  xmax = 1.0
  ymin = 0.0
  ymax = 1.0
  zmin = 0.0
  zmax = 4.0
[]

[Controls]
   [./period0]
      type = TimePeriod
      disable_objects = 'Kernels/inertia_x Kernels/inertia_y Kernels/inertia_z AuxKernels/accel_x AuxKernels/accel_y AuxKernels/accel_z AuxKernels/vel_x AuxKernels/vel_y AuxKernels/vel_z'
      start_time = 0.0
      end_time = 0.005 # same as dt used in the analysis
   [../]
[]

[Variables]
  [./disp_x]
  [../]
  [./disp_y]
  [../]
  [./disp_z]
  [../]
[]

[AuxVariables]
  [./vel_x]
  [../]
  [./accel_x]
  [../]
  [./vel_y]
  [../]
  [./accel_y]
  [../]
  [./vel_z]
  [../]
  [./accel_z]
  [../]
  [./stress_zx]
    order = CONSTANT
    family = MONOMIAL
  [../]
  [./strain_zx]
    order = CONSTANT
    family = MONOMIAL
  [../]
  [./layer_id]
    family = MONOMIAL
    order = CONSTANT
  [../]
[]

[Kernels]
  [./DynamicTensorMechanics]
    displacements = 'disp_x disp_y disp_z'
    stiffness_damping_coefficient = 0.000781
    static_initialization = True
    use_displaced_mesh = True
  [../]
  [./inertia_x]
    type = InertialForce
    variable = disp_x
    velocity = vel_x
    acceleration = accel_x
    eta = 0.64026
    beta = 0.25
    gamma = 0.5
    use_displaced_mesh = True
  [../]
  [./inertia_y]
    type = InertialForce
    variable = disp_y
    velocity = vel_y
    acceleration = accel_y
    eta = 0.64026
    beta = 0.25
    gamma = 0.5
    use_displaced_mesh = True
  [../]
  [./inertia_z]
    type = InertialForce
    variable = disp_z
    velocity = vel_z
    acceleration = accel_z
    eta = 0.64026
    beta = 0.25
    gamma = 0.5
    use_displaced_mesh = True
  [../]
  [./gravity]
    type = Gravity
    variable = disp_z
    value = -9.81
    use_displaced_mesh = True
  [../]
[]

[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
  [../]
  [./stress_zx]
    type = RankTwoAux
    rank_two_tensor = stress
    variable = stress_zx
    index_i = 2
    index_j = 0
  [../]
  [./strain_zx]
    type = RankTwoAux
    rank_two_tensor = total_strain
    variable = strain_zx
    index_i = 2
    index_j = 0
  [../]
  [./layer_id]
     type = UniformLayerAuxKernel
     variable = layer_id
     interfaces = '20'
     direction = '0 0 1'
     execute_on = initial
  [../]
[]

[Materials]
   [./elasticity_tensor]
      type = ComputeIsotropicElasticityTensorSoil
      block = 0
      layer_variable = layer_id
      layer_ids = '0'
      poissons_ratio = '0.3'
      density = '2000.0'
      shear_modulus = '325e7'
   [../]
   [./stress1]
     #Computes the stress, using linear elasticity
     type = ComputeLinearElasticStress
     block = 0
    [../]
    [./strain1]
      #Computes the strain, assuming small strains
      type = ComputeSmallStrain
      block = 0
      displacements = 'disp_x disp_y disp_z'
  [../]
[]

[BCs]
  [./bottom_accel_x]
    type = PresetAcceleration
    boundary = back
    function = accel_bottom_x
    variable = disp_x
    beta = 0.25
    acceleration = accel_x
    velocity = vel_x
  [../]
  [./bottom_z]
    type = DirichletBC
    variable = disp_z
    boundary = back
    value = 0.0
  [../]
  [./bottom_accel_y]
    type = PresetAcceleration
    boundary = back
    function = accel_bottom_y
    variable = disp_y
    beta = 0.25
    acceleration = accel_y
    velocity = vel_y
  [../]
  [./Periodic]
    [./x_dir]
      primary = 'left'
      secondary = 'right'
      translation = '1.0 0.0 0.0'
    [../]
    [./y_dir]
      primary = 'bottom'
      secondary = 'top'
      translation = '0.0 1.0 0.0'
    [../]
  [../]
[]

[Functions]
  [./accel_bottom_x]
    type = PiecewiseLinear
    data_file = 'accel.csv'
    format = columns
    scale_factor = 1.0
  [../]
  [./accel_bottom_y]
    type = PiecewiseLinear
    data_file = 'accel.csv'
    format = columns
    scale_factor = 2.0
  [../]
[]

[Executioner]
  type = Transient
  solve_type = PJFNK
  nl_abs_tol = 1e-8
  nl_rel_tol = 1e-8
  l_tol = 1e-8
  start_time = 32
  end_time = 33
  dt = 0.005 # should be 0.005
  timestep_tolerance = 1e-6
  petsc_options = '-snes_ksp_ew'
  petsc_options_iname = '-ksp_gmres_restart -pc_type -pc_hypre_type -pc_hypre_boomeramg_max_iter'
  petsc_options_value = '201                hypre    boomeramg      4'
  line_search = 'none'
[]

[Outputs]
  [./out]
    type = CSV
    execute_on = 'final'
  [../]
[]

[VectorPostprocessors]
  [./accel_hist]
    type = ResponseHistoryBuilder
    variables = 'accel_x accel_y'
    nodes = '8 9'
  [../]
  [./accel_hsi]
    type = HousnerSpectrumIntensity
    vectorpostprocessor = accel_hist
    regularize_dt = 0.005
    outputs = out
  [../]
[]

(test/tests/vectorpostprocessors/housner_spectrum_intensity/gold/housner_spectrum_intensity_out_accel_hsi.csv)

node_8_accel_x_hsi,node_8_accel_y_hsi,node_9_accel_x_hsi,node_9_accel_y_hsi
0.81488283652923,1.6297656730584,0.8148828365292,1.6297656730584

(test/tests/vectorpostprocessors/housner_spectrum_intensity/housner_spectrum_intensity.i)

#@requirement F8.3
[Mesh]
  type = GeneratedMesh
  dim = 3
  nx = 1
  ny = 1
  nz = 4
  xmin = 0.0
  xmax = 1.0
  ymin = 0.0
  ymax = 1.0
  zmin = 0.0
  zmax = 4.0
[]

[Controls]
   [./period0]
      type = TimePeriod
      disable_objects = 'Kernels/inertia_x Kernels/inertia_y Kernels/inertia_z AuxKernels/accel_x AuxKernels/accel_y AuxKernels/accel_z AuxKernels/vel_x AuxKernels/vel_y AuxKernels/vel_z'
      start_time = 0.0
      end_time = 0.005 # same as dt used in the analysis
   [../]
[]

[Variables]
  [./disp_x]
  [../]
  [./disp_y]
  [../]
  [./disp_z]
  [../]
[]

[AuxVariables]
  [./vel_x]
  [../]
  [./accel_x]
  [../]
  [./vel_y]
  [../]
  [./accel_y]
  [../]
  [./vel_z]
  [../]
  [./accel_z]
  [../]
  [./stress_zx]
    order = CONSTANT
    family = MONOMIAL
  [../]
  [./strain_zx]
    order = CONSTANT
    family = MONOMIAL
  [../]
  [./layer_id]
    family = MONOMIAL
    order = CONSTANT
  [../]
[]

[Kernels]
  [./DynamicTensorMechanics]
    displacements = 'disp_x disp_y disp_z'
    stiffness_damping_coefficient = 0.000781
    static_initialization = True
    use_displaced_mesh = True
  [../]
  [./inertia_x]
    type = InertialForce
    variable = disp_x
    velocity = vel_x
    acceleration = accel_x
    eta = 0.64026
    beta = 0.25
    gamma = 0.5
    use_displaced_mesh = True
  [../]
  [./inertia_y]
    type = InertialForce
    variable = disp_y
    velocity = vel_y
    acceleration = accel_y
    eta = 0.64026
    beta = 0.25
    gamma = 0.5
    use_displaced_mesh = True
  [../]
  [./inertia_z]
    type = InertialForce
    variable = disp_z
    velocity = vel_z
    acceleration = accel_z
    eta = 0.64026
    beta = 0.25
    gamma = 0.5
    use_displaced_mesh = True
  [../]
  [./gravity]
    type = Gravity
    variable = disp_z
    value = -9.81
    use_displaced_mesh = True
  [../]
[]

[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
  [../]
  [./stress_zx]
    type = RankTwoAux
    rank_two_tensor = stress
    variable = stress_zx
    index_i = 2
    index_j = 0
  [../]
  [./strain_zx]
    type = RankTwoAux
    rank_two_tensor = total_strain
    variable = strain_zx
    index_i = 2
    index_j = 0
  [../]
  [./layer_id]
     type = UniformLayerAuxKernel
     variable = layer_id
     interfaces = '20'
     direction = '0 0 1'
     execute_on = initial
  [../]
[]

[Materials]
   [./elasticity_tensor]
      type = ComputeIsotropicElasticityTensorSoil
      block = 0
      layer_variable = layer_id
      layer_ids = '0'
      poissons_ratio = '0.3'
      density = '2000.0'
      shear_modulus = '325e7'
   [../]
   [./stress1]
     #Computes the stress, using linear elasticity
     type = ComputeLinearElasticStress
     block = 0
    [../]
    [./strain1]
      #Computes the strain, assuming small strains
      type = ComputeSmallStrain
      block = 0
      displacements = 'disp_x disp_y disp_z'
  [../]
[]

[BCs]
  [./bottom_accel_x]
    type = PresetAcceleration
    boundary = back
    function = accel_bottom_x
    variable = disp_x
    beta = 0.25
    acceleration = accel_x
    velocity = vel_x
  [../]
  [./bottom_z]
    type = DirichletBC
    variable = disp_z
    boundary = back
    value = 0.0
  [../]
  [./bottom_accel_y]
    type = PresetAcceleration
    boundary = back
    function = accel_bottom_y
    variable = disp_y
    beta = 0.25
    acceleration = accel_y
    velocity = vel_y
  [../]
  [./Periodic]
    [./x_dir]
      primary = 'left'
      secondary = 'right'
      translation = '1.0 0.0 0.0'
    [../]
    [./y_dir]
      primary = 'bottom'
      secondary = 'top'
      translation = '0.0 1.0 0.0'
    [../]
  [../]
[]

[Functions]
  [./accel_bottom_x]
    type = PiecewiseLinear
    data_file = 'accel.csv'
    format = columns
    scale_factor = 1.0
  [../]
  [./accel_bottom_y]
    type = PiecewiseLinear
    data_file = 'accel.csv'
    format = columns
    scale_factor = 2.0
  [../]
[]

[Executioner]
  type = Transient
  solve_type = PJFNK
  nl_abs_tol = 1e-8
  nl_rel_tol = 1e-8
  l_tol = 1e-8
  start_time = 32
  end_time = 33
  dt = 0.005 # should be 0.005
  timestep_tolerance = 1e-6
  petsc_options = '-snes_ksp_ew'
  petsc_options_iname = '-ksp_gmres_restart -pc_type -pc_hypre_type -pc_hypre_boomeramg_max_iter'
  petsc_options_value = '201                hypre    boomeramg      4'
  line_search = 'none'
[]

[Outputs]
  [./out]
    type = CSV
    execute_on = 'final'
  [../]
[]

[VectorPostprocessors]
  [./accel_hist]
    type = ResponseHistoryBuilder
    variables = 'accel_x accel_y'
    nodes = '8 9'
  [../]
  [./accel_hsi]
    type = HousnerSpectrumIntensity
    vectorpostprocessor = accel_hist
    regularize_dt = 0.005
    outputs = out
  [../]
[]

Usage
Input Parameters
Input Files
References

Usage

Development

Demonstration

HousnerSpectrumIntensity

Usage

Input Parameters

Required Parameters

Optional Parameters

Execution Scheduling Parameters

Advanced Parameters

Material Property Retrieval Parameters

Input Files

References