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 ACOUSTICS - FINITE ELEMENT METHOD

Acoustic Pressure Oscillation in a Pipe via the Finite Element Method: aco__pipe_FEM.pdf
Acoustic Pressure Oscillation in a Two-Dimensional Pressure Field via the Finite Element Method using Triangular Elements: aco__triangle.pdf

 ROD VIBRATION - FINITE ELEMENT METHOD

Longitudinal Vibration of a Rod via the Finite Element Method: rod_FEM_long.pdf
Matlab Script: rod_FEA.m
Supporting function: materials.m
Longitudinal Vibration of a Tapered Rod via the Finite Element Method: taper_rod_FEM_long.pdf
--------

Matlab script

Calculate the longitudinal vibration, modal transient response to of a fixed-free rod an
arbitrary base input via the finite element method.

rod_modal_transient_FEA.m

Support functions:

materials.m
Generalized_Eigen.m
ODE_acceleration_input_rod.m
ramp_invariant_filter_coefficients.m
mdof_plot_rod.m
BEAM VIBRATION - FINITE ELEMENT METHOD
Transverse Vibration of a Beam via the Finite Element Method: beam_FEM.pdf

Vibration of a Beam-Column via the Finite Element Method: beam_column_FEM.pdf
Transverse Vibration of a Cantilever Beam Subjected to a Constant Axial Load: beam_FEM_cantilever_axial.pdf
Transverse Vibration of a Simply-Supported Beam Subjected to a Constant Axial Load: beam_FEM_ss_axial.pdf
Transverse Vibration of a Fixed-Fixed Beam Subjected to a Constant Axial Load: beam_FEM_ff_axial.pdf
PLANE TRUSS VIBRATION - FINITE ELEMENT METHOD
Vibration of a Plane Truss: plane_truss.pdf
Matlab scripts:
plane_truss.m
coordinate_transform.m
truss_example_1.txt
truss_example_2.txt

THIN PLATE BENDING VIBRATION WITH RECTANGULAR ELEMENTS

Transverse Vibration of a Plate Via the Finite Element Method, Four-Node, Two-Dimensional Rectangular Elements:  FEA_plate_bending.pdf

Matlab Scripts:

plate_fea.m
plate_mass_stiff.m

materials.m
Generalized_Eigen_semidefinite.m
Generalized_Eigen.m
progressbar.m
Generalized_Eigen_subspace.m

Optional Preprocessor for a Rectangular Plate:

plate_fea_pre.m


Alternate script:  rectangular_plate_fea.m
THICK PLATE BENDING VIBRATION WITH RECTANGULAR ELEMENTS

A Four Node, Thick Rectangular Plate Bending Element: FEA_thick_rectangular_plate_bending.pdf

Matlab scripts

thick_rectangular_plate_fea.m
thick_plate_mass_stiff.m

materials.m
Generalized_Eigen_semidefinite.m
Generalized_Eigen.m
progressbar.m
Generalized_Eigen_subspace.m
ISOPARAMETRIC THICK PLATE ELEMENT


A Four Node, Isoparametric Plate Bending Element Stiffness Matrix: iso_plate_bending_stiffness.pdf

A Four Node, Isoparametric Plate Bending Element Mass Matrix: iso_plate_bending_mass.pdf

Jacobian Matrix & Determinant:  Jacobian.pdf

Matlab Scripts: 

isoparametric thick_plate_fea.m
isoparametric_thick_plate_mass_stiff.m

materials.m
Generalized_Eigen_semidefinite.m
Generalized_Eigen.m
progressbar.m
Generalized_Eigen_subspace.m


STRUCTURAL DYNAMICS - FINITE ELEMENT METHOD

Linear Buckling Analysis Using an Eigenvalue Solution: eig_buck.pdf

Effective Modal Mass & Modal Participation Factors: ModalMass.pdf
The Mode Acceleration Method: MA_method.pdf

The Generalized Coordinate Method for Discrete Systems: gencoord.pdf

Notes on Finite Element Modeling of Isolated Components: FE_isolated.pdf
Shock Response Spectrum Analysis via the Finite Element Method: FEA_shock.pdf
Nastran File: srs_plate_frf_4k.nas
Additional Files: FEA_Shock_files.zip

Transfer Function from Modes, Tutorial & Matlab scripts:
transfer_from_modes.pdf

See also:  Transfer_Functions
COMPONENT MODE SYNTHESIS & CRAIG-BAMPTON METHOD
Ulf Sellgren, Component Mode Synthesis - A Method for Efficient Dynamic Simulation of Complex Technical Systems: CMS_wp5.pdf
Component Mode Synthesis, Fixed-Interface Model: component_mode_synthesis.pdf

Matlab scripts:
mdof_reduced_CB.m
Generalized_Eigen.m

Load Transfer Matrix: LTM.pdf

Craig-Bampton Method for a Two Component System: CB_two_component.pdf

Matlab Scripts:
Craig_Bampton.m
CB_partition.m
Generalized_Eigen.m

mass_stiffness_assembly.m

spring_mass_series.m

Scott Gordon, The Craig-Bampton Method, NASA/Goddard Space Flight Center: CraigBam.pdf
EIGENVALUE PROBLEM
The Generalized Eigenvalue Problem:  eigen.pdf

Mass Condensation (Guyan Reduction): mass_condensation.pdf

Matlab Script: mass_condensation.m

Matrix Deflation for Removing the Rigid-Body Mode from the Generalized Eigenvalue Problem: matrix_deflation.pdf

Matlab scripts:
matrix_deflation_rod.m
matrix_deflation_beam.m
Dr. Edward L. Wilson, The Eigenvalue Problem (Berkeley Link )
 ROTOR DYNAMICS - FINITE ELEMENT METHOD
Lateral Natural Frequency of a Shaft Rotor System by the Transfer Matrix Method: rotor.pdf

Lateral Natural Frequencies of Rotor Shaft Systems
via the Finite Element Method: rotorFEM.pdf
Submitted by P.H. Mathuria, graduate student, Indian Institute of Technology, Bombay. Vibrationdata student paper contests, Summer 1999 and Spring 2000, respectively.
APPLICATIONS
V.Hariharan, PSS.Srinivasan, Inertial and Vibration Characteristics of a Cricket bat: cricket_bat.pdf
(This paper may be download free of charge, without a subscription).

MASS PROPERTIES

Okuma, Heylen, Sas, Identification of Rigid Body Properties of 3-D Frame Structure by MCK Identification Method:  ident_MCK.pdf

Mass Properties from a Finite Element Model: mass_properties_FEA.pdf

MODAL GAIN FACTORS & AUTOPILOT STABILITY

Modal Gain Factors in Launch Vehicle Autopilot Stability Analysis: modal_gain_autopilot.pdf
Notes on Mode Shape and Bending Gain Units in Nastran: gain_units.pdf
MISCELLANEOUS

Nastran_Theoretical_Manual.pdf  (16 Mb)

Polynomial Interpolation for Finite Element Analysis: interpolation.pdf
Notes on Internal and Transmitted Forces in Vibrating Multi-degree-of-freedom Systems: mdof_transmitted.pdf
M. Donley & M. Baker, Improving the Dynamic Response Analysis Process: nafems_paper_donley_baker_update
T. Rolfe, Matrix Multiplication Optimization: Enforcement of Local Access and Array Access via Pointers: MatOpt.pdf
Source code: matrix_mult_source_code.txt

 

 EIGENVALUE SOFTWARE
Eigenvalues of the generalized eigen problem where the mass and stiffness matrices are symmetric with real coefficients. The eigenvalues are determined by the QR Householder method.
 QR_modal.exe QR_modal.cpp
Eigenvalues of the generalized eigen problem where the mass and stiffness matrices are symmetric with real coefficients. The eigenvalues are determined by the Jacobi method.
 Jacobi.exe
 Jacobi.cpp
The first eigenvalue and eigenvector via the inverse iteration method.
 inverse_iteration.exe
  inverse_iteration.cpp
Eigenvalues of the generalized eigen problem where the mass and stiffness matrices are symmetric with real coefficients. The eigenvalues are determined by calculating the roots of the determinant polynomial. The upper limit is fourth order.
 eigen.exe

  _
Eigenvalues of the generalized eigen problem via the slicing method, which is essentially the Sturm Sequence method.
 slice_eigenvalues.exe
  slice_eigenvalues.cpp

QR Householder Decomposition of a Matrix.

QR_Householder.exe

QR_Householder.cpp

Matrix Inverse QR Householder Decomposition.

QR_Householder_inverse.exe

QR_Householder_inverse.cpp

Householder Tridiagonalization

Householder_tridiagonal.exe

Householder_tridiagonal.cpp
Eigenvalues and eigenvectors of a two-degree-of-freedom system.
 twodof.exe
  twodof.cpp
Eigenvalues and eigenvectors of a three-degree-of-freedom system.
 threedof.exe
 threedof.cpp
Natural frequency of a rifle barrel with free-free boundary conditions.
 rifle_frequency.exe
rifle.pdf
  rifle_frequency.cpp
Natural frequency of a cantilever beam with an added point mass at an arbitary point along the length of the beam.
 cantilever_with_mass.exe
 cantilever_with_mass.cpp
Natural frequency of a cantilever tapered pipe with an added point mass at its free end and with an applied axial tensile load its free end.
 cantilever_mass_axial.exe
 cantilever_mass_axial.cpp

Mass properties of a dynamic system using Guyan reduction. i.e. center of gravity and moments of inertia.

mass_properties.exe

mass_properties.cpp

Mass properties of a dynamic system using geometric rigid-body modes. i.e center of gravity and moments of inertia

mass_properties_GRB.exe

mass_properties_GRB.cpp
Matrix multiplication use pure pointer access matrix_11.exe matrix_11.cpp
Unit conversion program.
units.exe
DLL files:
mfc100u.dll
msvcr100.dll

 

  Matlab Scripts

Transfer Functions from Modes 

 transfer_from_modes.zip

Mass properties of a dynamic system using Guyan reduction. i.e center of gravity and moments of inertia.   The required inputs are the mass and stiffness matrices.

mass_properties.m

Generalized_Eigen.m

Mass properties of a dynamic system using geometric rigid-body modes.  The required inputs are a mass matrix and the nodal coordinates.

mass_properties_GRB.m
Natural Frequencies and Mode Shapes of a Beam via the Finite Element Method, with three degrees-of-freedom per node.

This program also calculates the participation factors and effective modal mass values.
It allows for the addition of a point mass.
 beam.zip

Natural Frequencies and Mode Shapes of a Beam via the Finite Element Method with six degrees-of-freedom per node.

The input file is a Nastran *.bdf or *.nas file generated by Femap or some other preprocessor.

The beam elements may be in a three-dimensional frame.

beam_3D_nastran.m

Functions:

beam_3D_nastran_find.m
beam_3D_mass_condensation.m
Generalized_Eigen.m
beam_3D_modeplot.m

Natural Frequencies and Mode Shapes of a Beam via the Finite Element Method with six degrees-of-freedom per node.

It allows for the addition of a point mass.

The beam elements may be in a three-dimensional frame.

beam_3D.m

Functions:

beam_3D_mass_condensation.m
Generalized_Eigen.m
beam_3D_modeplot.m

User Guide

beam_3D_guide.pdf

Additional scripts are given at:  Matlab

 

 

COMMON NASTRAN SOFTWARE UTILITIES
Extract grid points, elements, and constraints from Nastran file for CBAR elements.
CBAR_extract.cpp
 CBAR_extract.exe
Extract grid points, elements, and constraints from Nastran file for CTRIA3 elements.
CTRIA3_extract.cppCTRIA3_extract.exe


NE/NASTRAN SOFTWARE UTILITIES
Convert acceleration time history to Nastran format as preprocessing step.
 ne_tabled2.cpp
 ne_tabled2.exe
The input file is the NE/Nastran output file where a base excitation frequency function was applied to the FE model.
The amplitude metrics must be in magnitude & phase format.
The analysis type is frequency response function, SOL SEMFREQ.
The program thus outputs transmissibility functions.
 ne_postprocess_all.cpp
 ne_postprocess_all.exe
The input file is the NE/Nastran output file where an applied force frequency function was applied to the FE model. The analysis type is frequency response function, SOL SEMFREQ.
ne_postprocess_force.cpp
 ne_postprocess_force.exe
Run this utility to check *.nas files prior to SOL SEMFREQ runs.
ne_base_check.cpp
ne_base_check.exe
The input file is a NE/Nastran output file from a SOL SEMODES or SEMFREQ analysis.
 ne_eigenvalues.cpp
 ne_eigenvalues.exe
Complex Force of Single Point Constraint
ne_postprocess_spc.cpp
 ne_postprocess_spc.exe
Bar stress FRF
ne_bar_stress_all.cpp 
 ne_bar_stress_all.exe
Bar stress Modal Transient 
 ne_bar_stress_th.cpp 
 ne_bar_stress_th.exe
Forces in a Beam,
Modal Transient (old)
ne_force_beam_th.cpp
 ne_force_beam_th.exe
Forces in a Beam,
Modal Transient
ne_force_beam_transient.cpp
ne_force_beam_transient.exe
Forces in a Beam, Static Analysis
ne_force_beam_static.cpp
ne_force_beam_static.exe
Acceleration and Displacement Response to Modal Transient
 ne_accel_th.cpp
 ne_accel_th.exe
Grid Point Stress in Volume, Modal Transient
 ne_stress_volume_th.cpp

ne_stress_volume_th.exe
Link to Noran Engineering / NEiNastran Website: nenastran

 

NX NASTRAN SOFTWARE UTILITIES

The input file is a NX Nastran output file from a SOL SEMODES or SEMFREQ analysis.

nx_eigenvalues.cpp

nx_eigenvalues.exe
The input file is the NX Nastran output file where a base excitation frequency function was applied to the FE model.
The amplitude metrics must be in magnitude & phase format.
The analysis type is frequency response function, SOL SEMFREQ.
The program thus outputs transmissibility functions.

nx_postprocess_all.cpp

nx_postprocess_all.exe
The input file is the NX Nastran output file where an applied force frequency function was applied to the FE model. The analysis type is frequency response function, SOL SEMFREQ.
nx_postprocess_force.cpp
nx_postprocess_force.exe
Acceleration and Displacement Response to Modal Transient

nx_accel_th.cpp
nx_accel_th.exe
Relative Displacement from Modal Transient Files

nx_relative_disp.cpp
nx_relative_disp.exe
MSC/NASTRAN SOFTWARE UTILITIES 

Bending gains from .f06 files for systems with an INS and TVC:
bend_gain.cpp
Extract natural frequencies and mode shapes from MSC/Nastran *.f06 files: msc_eigenvectors.cpp
Convert MSC/Nastran frequency domain punch files to useful format for acceleration output: msc_punch_three.cpp
Convert MSC/Nastran frequency domain punch files to useful format for displacement output: msc_punch_disp.cpp

Convert MSC/Nastran time history punch files to useful form at for acceleration output:
msc_punch_accel.cpp
Davenport, et al, An Integrated Approach to Random Analysis using MSC/Patran and MSC/Nastran: msc_random.pdf

 

 NASTRAN MODELS
SOL SEMODES
Modal Analysis of a Rectangular Plate via the Finite Element Method (using FEMAP & NE/Nastran): rplateFE.pdf
Nastran Input File: rplate.nas

Modal Analysis of a Free Circular Plate via the Finite Element Method (using FEMAP/Structural): cplateFE.pdf
Tuning Fork Input Files. Completely Free Boundary Conditions. Tuned for A4 Note, 440 Hz.
Nastran Input File: tf_440.nas
FEMAP Model File: tf_fe440.zip

Singing bowl: bowl6.nas

Conical Shell Modal Test and Finite Element Analysis: conical_shell.pdf
Nastran Input File: conical_shell3.nas
SOL LINEAR PRESTRESS MODAL

Cantilever beam with axial load: cant_beam_prestress.nas
SOL SEMFREQ
Base excitation of a single-degree-of-freedom system: sdof_m6_base.nas
SOL SEMTRAN

Initial velocity, transient response: bench5c_velox.nas

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