Welcome to Vibrationdata
Structural Dynamics -  Beam Vibration

 Dear Guest,
Writing tutorials and maintaining a website are expensive endeavors. I need your help to continue this effort. Your subscription will allow me to continue this site and to add new materials.

The software and tutorials require a username and password which are given by subscription. The subscription instructions are given below.
The subscription entitles the user to download all of the items on this page, as well as other Vibrationdata pages.
http://www.vibrationdata.com/Resources/subscribebutton.jpg

Thank you for your support.
Sincerely, Tom Irvine
Email: tomirvine@aol.com
CD DISK
As an alternative, guests may purchase a CD disk containing all of the downloadable files on the Vibrationdata website. CD Offer

 
BEAMS - BENDING VIBRATION - BERNOULLI-EULER BEAMS

Bending Frequencies of Beams, Rods, and Pipes: beam.pdf  
Bending Frequency of a Fixed-Fixed Beam via the Rayleigh Method: fixed_fixed_beam.pdf
Natural Frequencies of Composite Beams: compbeam.pdf  
Matlab script:  composite_beam.m
Bending Frequencies of a Beam Supported on an Elastic Foundation: beam_elastic_foundation.pdf
Free Vibration of a Cantilever Beam: free_cant.pdf

Vibration of a Simply Supported Beam with Concentrated Mass: ss_beam_cm.pdf
Matlab script:  ss_beam_mass.m


BEAMS - BENDING VIBRATION - BERNOULLI-EULER BEAMS - BASE EXCITATION
Steady-State Vibration Response of a Cantilever Beam Subjected to Base Excitation: steady_cant.pdf
Steady-State Vibration Response of a Simply-Supported Beam Subjected to Base Excitation: steady_ss_beam.pdf
Steady-State Vibration Response of a Fixed-Fixed Beam Subjected to Base Excitation: steady_fixed_fixed_beam.pdf

Modal Transient Vibration Response of a Cantilever Beam Subjected to Base Excitation:  cantilever_modal_transient_base.pdf

  __________________

Matlab Script with optional frequency response function, half-sine base excitation & arbitrary base excitation:
continuous_beam_base_accel.m

Supporting functions:

plot_PSD.m
plot_PSD_two.m

srs_coefficients avd.m
continuous_beam_base_PSD.m
psd_mult_trans.m
find_plot_limits.m
calculate_PSD_slopes.m

continuous_beam_base_arbitrary.m

continuous_beam_base_sine.m
continuous_beam_base_half_sine.m
continuous_beam_base_frf.m
enter_modal_damping.m
continuous_beam_bc.m
geometry_entry.m
materials.m

BEAMS - BENDING VIBRATION - BERNOULLI-EULER BEAMS -
APPLIED CONCENTRATED FORCE 

Vibration Response of a Cantilever Beam Subjected to a Concentrated Force at Its Free End: cant_beam_force.pdf

Matlab scripts:
cant_beam_force_frf.m

geometry_materials.m

The Response of a Cantilever Beam Subjected to a Concentrated Half-Sine Force Pulse: cant_beam_half_sine_force.pdf

Matlab scripts:  
cant_beam_half_sine_force.m

geometry_materials.m

frf_from_th.m
fix_size.m
progressbar.m

frf_median_filter.m

The Response of a Cantilever Beam Subjected to a Concentrated Sine Force

Matlab scripts:
cant_beam_sine_force.m
geometry_materials.m
fix_size.m
progressbar.m


The Response of a Cantilever Beam Subjected to an Applied Concentrated Arbitrary Force:  cant_beam_arbitrary_force.pdf

Matlab scripts:

cant_beam_arbit_force.m
enter_time_history.m
geometry_materials.m
progressbar.m

The Response of a Cantilever Beam Subjected to an Applied Concentrated Impulse Force:
cant_beam_impulse_force.pdf

BEAMS - BENDING VIBRATION - BERNOULLI-EULER BEAMS -
UNIFORMLY DISTRIBUTED APPLIED FORCE 

Vibration Response of a Fixed-Fixed Beam Subjected to an Applied Uniform Distributed Force:  steady_fixed_beam_force.pdf

Matlab script: fixed_fixed_beam_frf.m

Vibration Response of a Simply-Supported Beam Subjected to an Applied Uniform Distributed Force:  steady_ss_beam_force.pdf

Matlab Scripts:  ss_ss_beam_frf.m

Common Supporing Functions:

fixed_fixed_beam_modes.m
ss_beam_modes.m
beam_frf.m
fix_size.m

materials.m
damping_entry.m
geometry_entry.m

BEAMS - BENDING VIBRATION - BERNOULLI-EULER BEAMS -
- APPLIED FORCE WITH SPATIAL VARIATION 
Steady-State Vibration Response of a Simply-Supported Beam Subjected to an Applied Force with Spatial Variation:  steady_ss_beam_force_spatial.pdf

Matlab script:
ss_ss_beam_spatial_frf.m

Steady-State Vibration Response of a Fixed-Fixed Beam Subjected to an Applied Force with Spatial Variation:  steady_fixed_fixed_beam_force_spatial.pdf

Matlab script: fixed_fixed_beam_spatial_frf.m

Supporing Functions:materials.m
damping_entry.m
geometry_entry.m

MULTISPAN BEAMS - BENDING VIBRATION 
Natural Frequencies of Multispan Beams: mspan.pdf
Matlab script for Clamped-Pinned-Free Beam:

clamped_pinned_free.m

Supporting Functions:
find_root_mbeam.m
cpf_C.m
cpf_C_coefficients.m


Matlab script for Clamped-Pinned-Clamped Beam:

clamped_pinned_clamped.m

Supporting Functions:
find_root_mbeam.m
cpc_C.m
cpc_C_coefficients.m
Matlab script (FEA implementation):   beam_multispan.m
Supporting Functions: 
beam_data_entry_ms.m
local_stiffness.m

local_mass.m
assembly_ms.m
plot_modes_ms.m
Generalized_Eigen.m

BEAMS WITH AXIAL LOAD - BENDING VIBRATION - BERNOULLI-EULER BEAMS

Natural Frequencies of Beams Subjected to a Uniform Axial Load: beam_axial_load.pdf

F. Shaker, Effect of Axial Load on Mode Shapes and Frequencies of Beams, NASA TN D-8109: NASA_TN_8109.pdf

BEAMS - BENDING & SHEAR VIBRATION - TIMOSHENKO BEAMS
Transverse Vibration of a Beam Simply-Supported at Each End with Bending, Shear, and Rotary Inertia: bending_shear _beam.pdf
Transverse Vibration of a Fixed-Free Timoshenko Beam: bending_Timoshenko_fixed_free.pdf
Matlab Script: beam_shear_inertia.m
Natural Frequencies of a Shear Beam: shear_beam.pdf

BEAM VIBRATION - FINITE ELEMENT METHOD - Natural Frequencies
Transverse Vibration of a Beam via the Finite Element Method: beam_FEM.pdf
Transverse Vibration of a Rotating Beam via the Finite Element Method:  Beam_FEM_rotating.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
BEAM VIBRATION - FINITE ELEMENT METHOD - Enforced Motion
Frequency Response Function for Beam Bending with Enforced Acceleration via Finite Element Analysis:  modal_enforced_motion_beam_fea_frf.pdf

Modal Transient Analysis of a Beam with Enforced Motion via a Ramp Invariant Digital Recursive Filtering Relationship: modal_enforced_motion_beam_transient.pdf

 

 
  Matlab Scripts

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 two 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
This script calculates the natural frequencies of a beam via the finite element method. It also calculates the frequency response functions for base excitation. beam_base_accel_fea.zip

Natural Frequencies and Mode Shapes of a Rotating Beam (like a helicopter blade)  via the Finite Element Method with two 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_rotating.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

 Software Description

 Executable

  Source

Natural frequencies of beam modes, both lateral and longitudinal.
 beam.exe
 _
Natural frequencies of rectangular plates.
 plate.exe

 _

Natural frequencies of circular plates.
 circular.exe

  _

Single-degree-of-freedom System Natural Frequency.
 sdof_fn.exe

 _

 Holzer method for torsional systems.
 Holzer.exe
  Holzer.cpp
Unit conversion  program.
units.exe

 

Please recommend this site by clicking on the Google +1 Button.
__________________________________________________________________________________

Other Vibrationdata Pages:    Home | Structural Dynamics - Classical MethodsTutorials