Module with subroutines for the system-level eigenvalue analysis. More...

Functions/Subroutines
subroutine, public	alloceigenmatrices (modes, neq, ierr)
	Allocates internal work arrays used by the eigenvalue solver. More...

subroutine	filleigensystem (modes, neq, M, C, K, ierr)
	Builds the full matrices of the generalized eigenvalue problem. More...

subroutine	bubbelsort (V, ind)
	Sorts a real array in ascending order. More...

subroutine	findrealeigenvalues (sam, modes, normFactor, modeOrder, iprint, io, ierr)
	Extracts the real eigenvalues and associated eigenvectors. More...

subroutine	findeigenvalues (sam, modes, iprint, io, ierr)
	Extracts the complex eigenvalues and associated eigenvectors. More...

subroutine, public	printmodes (sam, modes, time, iprint, io)
	Prints the eigenvalues and eigenvectors to unit IO. More...

subroutine, public	eigenmodes (sam, modes, sys, mech, iprint, ierr)
	Calculate damped or undamped eigenvalues and eigenvectors. More...

subroutine	modalmasses (sups, modes, sam, eigVectors, normFactors, modeOrder, ierr)
	Calculates effective modal masses for the eigenmodes. More...

subroutine	addunitdisplvector (samData, iel, eV, sysV, ierr)
	Adds an element unit displacement vector into the system vector. More...

subroutine, public	exportmodes (yamlFile, modelFile, modes, triads, sups, istep, time, ierr)
	Exports mode shapes with associated beam section forces to YAML. More...

subroutine	writeyamlheader (iYaml, prog, modelFile, istep, time)
	Writes the header of a YAML frequency response file. More...

subroutine	writeyamldispl (iYaml, triads, iMod, eigVal, eigVec)
	Writes the mode shape eigenvector to a YAML frequency response file. More...

subroutine	writeyamlforces (iYaml, sups, scale, iDbg, ierr)
	Writes beam sectional forces to a YAML frequency response file. More...

Detailed Description

Module with subroutines for the system-level eigenvalue analysis.

Author: Knut Morten Okstad

Date: 23 Mar 2000

Function/Subroutine Documentation

◆ addunitdisplvector()

subroutine modesroutinesmodule::addunitdisplvector	(	type(samtype), intent(in)	samData,
		integer, intent(in)	iel,
		real(dp), dimension(:,:), intent(in)	eV,
		real(dp), dimension(:,:), intent(inout)	sysV,
		integer, intent(out)	ierr
	)

Adds an element unit displacement vector into the system vector.

Parameters

[in]	samData	Data for managing system matrix assembly
[in]	iel	Element index
[in]	eV	Element displacement vector
	sysV	System displacement vector
[out]	ierr	Error flag

Author: Leif Ivar Myklebust

Date: 2 Jul 2003

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◆ alloceigenmatrices()

subroutine, public modesroutinesmodule::alloceigenmatrices	(	type(modestype), intent(inout)	modes,
		integer, intent(in), optional	neq,
		integer, intent(out), optional	ierr
	)

Allocates internal work arrays used by the eigenvalue solver.

Parameters

	modes	Eigenmode data container
[in]	neq	Number of equations, i.e., dimension of system matrices
[out]	ierr	Error flag

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◆ bubbelsort()

subroutine modesroutinesmodule::bubbelsort	(	real(dp), dimension(:), intent(in)	V,
		integer, dimension(:), intent(inout)	ind
	)

Sorts a real array in ascending order.

Parameters

[in]	V	Array of real values to sort
	ind	Array of indices defining the sorted order

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◆ eigenmodes()

subroutine, public modesroutinesmodule::eigenmodes	(	type(samtype), intent(in)	sam,
		type(modestype), intent(inout)	modes,
		type(systemtype), intent(inout)	sys,
		type(mechanismtype), intent(inout)	mech,
		integer, intent(in)	iprint,
		integer, intent(out)	ierr
	)

Calculate damped or undamped eigenvalues and eigenvectors.

Parameters

[in]	sam	Data for managing system matrix assembly
	modes	Eigenmode data
	sys	System level model data
	mech	Mechanism components of the model
[in]	iprint	Print switch for additional output
[out]	ierr	Error flag

This is the main driver of the system-level eigenvalue analysis. The parameter modestypemodule::modestype::solver determines which actual subroutine to be used, as follows:

0 : Use SPRLAN (undamped systems only)
1 : Use LANCZ1 (undamped systems only)
2 : Use LANCZ2 (undamped systems only)
3 : Use LAPACK::DGGEVX (undamped system)
4 : Use LAPACK::DGGEVX (damped system)
5 : Use LAPACK::DSYGVX (symmetric system)

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◆ exportmodes()

subroutine, public modesroutinesmodule::exportmodes	(	character(len=*), intent(in)	yamlFile,
		character(len=*), intent(in)	modelFile,
		type(modestype), intent(in)	modes,
		type(triadtype), dimension(:), intent(inout)	triads,
		type(supeltype), dimension(:), intent(inout)	sups,
		integer(i8), intent(in)	istep,
		real(dp), intent(in)	time,
		integer, intent(out)	ierr
	)

Exports mode shapes with associated beam section forces to YAML.

Parameters

[in]	yamlFile	Name of the YAML-file top write
[in]	modelFile	Name of the model file
[in]	modes	Eigenmode data
	triads	All triads in the model
	sups	All superelements in the model
[in]	iStep	Time increment counter
[in]	time	Current simulation time
[out]	ierr	Error flag

Author: Knut Morten Okstad

Date: 21 Jun 2017

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◆ filleigensystem()

subroutine modesroutinesmodule::filleigensystem	(	type(modestype), intent(inout)	modes,
		integer, intent(in)	neq,
		type(sysmatrixtype), intent(in)	M,
		type(sysmatrixtype), intent(in)	C,
		type(sysmatrixtype), intent(in)	K,
		integer, intent(out)	ierr
	)

Builds the full matrices of the generalized eigenvalue problem.

Parameters

	modes	Eigenmode data container
[in]	neq	Number of equations, i.e., dimension of system matrices
[in]	M	System mass matrix
[in]	C	System damping matrix
[in]	K	System stiffness matrix
[out]	ierr	Error flag

The generalized eigenvalue problem is on the form A z = λ B z

With damping:

     | K  0 |*{z} = lambda * | -C -M |*{z}
     | 0 -M |                | -M  0 |

Without damping:

     [K]*{z} = lambda*[M]*{z}

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◆ findeigenvalues()

subroutine modesroutinesmodule::findeigenvalues	(	type(samtype), intent(in)	sam,
		type(modestype), intent(inout)	modes,
		integer, intent(in)	iprint,
		integer, intent(in)	io,
		integer, intent(out)	ierr
	)

Extracts the complex eigenvalues and associated eigenvectors.

Parameters

[in]	sam	Data for managing system matrix assembly
	modes	Eigenmode data
[in]	iprint	Print switch for additional output
[in]	io	File unit number to write to
[out]	ierr	Error flag

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◆ findrealeigenvalues()

subroutine modesroutinesmodule::findrealeigenvalues	(	type(samtype), intent(in)	sam,
		type(modestype), intent(inout)	modes,
		real(dp), dimension(:), intent(out)	normFactor,
		integer, dimension(:), intent(out)	modeOrder,
		integer, intent(in)	iprint,
		integer, intent(in)	io,
		integer, intent(out)	ierr
	)

private

Extracts the real eigenvalues and associated eigenvectors.

Parameters

[in]	sam	Data for managing system matrix assembly
	modes	Eigenmode data
[out]	normFactor	Scaling factors for normalizing the eigenmode shapes
[out]	modeOrder	Order of the modes with respect to eigenfrequency
[in]	iprint	Print switch for additional output
[in]	io	File unit number to write to
[out]	ierr	Error flag

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◆ modalmasses()

subroutine modesroutinesmodule::modalmasses	(	type(supeltype), dimension(:), intent(in)	sups,
		type(modestype), intent(inout)	modes,
		type(samtype), intent(in)	sam,
		real(dp), dimension(:,:), intent(in)	eigVectors,
		real(dp), dimension(:), intent(in)	normFactors,
		integer, dimension(:), intent(in)	modeOrder,
		integer, intent(out)	ierr
	)

Calculates effective modal masses for the eigenmodes.

Parameters

[in]	sups	All superelements in the model
	modes	Eigenmode data
[in]	sam	Data for managing system matrix assembly
[in]	eigVectors	The eigenvectors
[in]	normFactors	Scaling factors for normalizing the eigenmode shapes
[in]	modeOrder	Order of the modes with respect to eigenfrequency
[out]	ierr	Error flag

This subroutine is used to judge the significance of each vibration mode for each translation- and rotation component. Modes with relatively high effective masses can be readily excited by base exitation in the actual direction, while modes with lower effective masses may not be that critical. This is a commonly used feature, e.g. in NASTRAN.

The calculation is as follows:

[temp] = [Φ]^t[M]*[R]

M_eff(i,j) = temp(i,j)^2

where the eigenvector matrix, [Φ], is transposed and assumed to be mass-normalized, [M] is the compact mass matrix, and [R] is the influence matrix representing a rigid body unit displacement of the mechanism. Finally, [M_eff] is a nModes×6 matrix of the effective modal masses. The results are stored in modestypemodule::modestype::effmass.

Todo:: It works now for LANCZ2 and for the -undamped solvers (although I encountered something that looks like a bug in the -undamped calculation of the eigenvectors). Furthermore, local orientation of triads are not (yet) taken into account, but should normally not be critical as long as the local triad masses are the same in all coordinate directions (for inertias it will induce errors, however). Component modes seems to be treated correctly, but has not been tested too much. Some more elegance could also be put into the creation of unit displacement vectors, just to make sure that all kinds of joints and boundary conditions are treated correctly. In fact, there might be a better and easier solution to this than the approach I have used here.

Author: Leif Ivar Myklebust

Date: 2 Jul 2003

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◆ printmodes()

subroutine, public modesroutinesmodule::printmodes	(	type(samtype), intent(in)	sam,
		type(modestype), intent(in)	modes,
		real(dp), intent(in)	time,
		integer, intent(in)	iprint,
		integer, intent(in)	io
	)

Prints the eigenvalues and eigenvectors to unit IO.

Parameters

[in]	sam	Data for managing system matrix assembly
	modes	Eigenmode data
[in]	time	Current simulation time
[in]	iprint	Print switch for additional output
[in]	io	File unit number to write to

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◆ writeyamldispl()

subroutine modesroutinesmodule::writeyamldispl	(	integer, intent(in)	iYaml,
		type(triadtype), dimension(:), intent(in)	triads,
		integer, intent(in)	iMod,
		real(dp), intent(in)	eigVal,
		real(dp), dimension(:), intent(in)	eigVec
	)

Writes the mode shape eigenvector to a YAML frequency response file.

Parameters

[in]	iYaml	File unit number of the YAML-file to write
[in]	triads	All triads in the model
[in]	iMod	Mode shape index
[in]	eigVal	Associated eigenvalue
[in]	eigVec	Associated eigenvector

Author: Knut Morten Okstad

Date: 21 Jun 2017

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◆ writeyamlforces()

subroutine modesroutinesmodule::writeyamlforces	(	integer, intent(in)	iYaml,
		type(supeltype), dimension(:), intent(inout)	sups,
		real(dp), intent(in)	scale,
		integer, intent(in)	iDbg,
		integer, intent(out)	ierr
	)

Writes beam sectional forces to a YAML frequency response file.

Parameters

[in]	iYaml	File unit number of the YAML-file to write
	sups	All superelements in the model
[in]	scale	Scaling factor for the eigenvector
[in]	iDbg	File unit number of debug output
[in]	ierr	Error flag

Author: Knut Morten Okstad

Date: /rev 21 Jun 2017

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◆ writeyamlheader()

subroutine modesroutinesmodule::writeyamlheader	(	integer, intent(in)	iYaml,
		character(len=*), intent(in)	prog,
		character(len=*), intent(in)	modelFile,
		integer(i8), intent(in)	istep,
		real(dp), intent(in)	time
	)

private

Writes the header of a YAML frequency response file.

Parameters

[in]	iYaml	File unit number of the YAML-file to write
[in]	prog	Program name
[in]	modelFile	Name of the model file
[in]	iStep	Time increment counter
[in]	time	Current simulation time

Author: Knut Morten Okstad

Date: /rev 21 Jun 2017

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Functions/Subroutines

Detailed Description

Function/Subroutine Documentation

◆ addunitdisplvector()

◆ alloceigenmatrices()

◆ bubbelsort()

◆ eigenmodes()

◆ exportmodes()

◆ filleigensystem()

◆ findeigenvalues()

◆ findrealeigenvalues()

◆ modalmasses()

◆ printmodes()

◆ writeyamldispl()

◆ writeyamlforces()

◆ writeyamlheader()