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Structural Dynamics - Finite Element Method Page

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

BEAM VIBRATION - FINITE ELEMENT METHOD Longitudinal Vibration of a Rod via the Finite Element Method: rod_FEM_long.pdf Longitudinal Vibration of a Tapered Rod via the Finite Element Method: taper_rod_FEM_long.pdf 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

STRUCTURAL DYNAMICS - FINITE ELEMENT METHOD Linear Buckling Analysis Using an Eigenvalue Solution: eig_buck.pdf Effective Modal Mass & Modal Participation Factors: ModalMass.pdf The Generalized Coordinate Method for Discrete Systems: gencoord.pdf Notes on Finite Element Modeling of Isolated Components: FE_isolated.pdf Notes on Mode Shape and Bending Gain Units in Nastran: gain_units.pdf Shock Response Spectrum Analysis via the Finite Element Method: FEA_shock.pdf Nastran File: srs_plate_frf_4k.nas

COMPONENT MODE SYNTHESIS 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 Load Transfer Matrix: LTM.pdf 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 Matrix Deflation for Removing the Rigid-Body Mode from the Generalized Eigenvalue Problem: matrix_deflation.pdf 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.com 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).

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 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
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

Matlab Scripts
Natural Frequencies and Mode Shapes of a Beam via the Finite Element Method. This program also calculates the participation factors and effective modal mass values. It allows for the addition of a point mass.	beam.m Functions: beam_data_entry.m local_stiffness.m local_mass.m assembly.m plot_modes.m

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 PSD was applied to the FE model. The analysis type is frequency response function, SOL SEMFREQ. The program thus outputs transmissibility functions.  ne_postprocess_all.cpp  ne_postprocess_all.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

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 format 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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