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STRUCTURAL
DYNAMICS
 DISCRETE SYSTEMS  SDOF
Free
Vibration of a SingleDegreeofFreedom System: free.pdf

STRUCTURAL
DYNAMICS
 DISCRETE SYSTEMS  MDOF
Assemble mass and stiffness matrices for a springmass system and solve the corresponding generalized eigenvalue problem.Matlab
scripts:

STRUCTURAL
DYNAMICS
 DISCRETE SYSTEMS  MDOF  Natural Frequencies & Damping
Sample
Lateral Natural Frequency Calculations for a Space Vehicle/Dispenser
Analysis: lateralSV.pdf
Natural
Frequencies of Spring Mass Systems in Series: spring_mass_series.pdf

STRUCTURAL
DYNAMICS
 DISCRETE SYSTEMS  MDOF  Arbitrary Excitation  Force or Base
Excitation
Modal
Transient Response to Arbitrary Base Excitation via Convolution: modal_transient_arbitrary.pdf
Multidegreeoffreedom
System Subjected to an Arbitrary Force: mdof_arbit_force.pdf
Matlab
script: two_dof_arb_force.m

STRUCTURAL DYNAMICS DISCRETE SYSTEMS  MDOF  SteadyState FRF  Base Excitation The
SteadyState Frequency Response Function of a Multidegreeoffreedom
System Subjected to Harmonic Base Excitation: mdof_FRF_base.pdf
Matlab Script: two_dof_frf.mFrequency Response Function for a Multidegreeoffreedom System with Enforced Acceleration: modal_enforced_motion_mdof_fea_frf.pdfThe following script has options for both frequency response functions and base input modal transient. Matlab script: mdof_base_accel_frf_fea.m Supporting functions: mdof_base_th_plot.m mdof_arbit_base_core.m ramp_invariant_filter_coefficients.m enter_time_history.m mdof_half_sine_core.m mdof_base_fea_post.m find_plot_limits.m find_max.m partition_matrices_accel.m partition_matrices_accel_frf.m Generalized_Eigen_fea.m Generalized_Eigen.m Generalized_Eigen_subspace.m progressbar.m 
STRUCTURAL DYNAMICS  DISCRETE SYSTEMS  MDOF  SteadyState FRF  Applied ForceThe SteadyState Reponse of a Twodegreeoffreedomsystem to a Single Harmonic Force: twodof_steady_force.pdfMatlab Script: two_dof_force_steady.mThe
SteadyState Frequency Response Function of a Multidegreeoffreedom
System Subjected to Harmonic Force Excitation: mdof_FRF_force.pdf
Matlab
Script: two_dof_force_frf.m
The
SteadyState Frequency Response Function of a Fourdegreeoffreedom
System Subjected to Harmonic Force Excitation: force_dof_FRF_force.pdf
Matlab
Script: four_dof_force_frf.m

SEMIDEFINITE SYSTEMS
Semidefinite System Examples: semidefinite.pdfNatural
Frequencies of Semidefinite Spring Mass Systems in Series:
Twodegreeoffreedom
Semidefinite System Subjected to an Applied Sinusoidal Force: semidefinite_force.pdf 
SPRING
SURGE
Spring
Surge: spring_surge.pdf
Matlab
Script: spring_surge.m

RODS
 LONGITUDINAL VIBRATION

RODS  LONGITUDINAL VIBRATION  APPLIED FORCE The Longitudinal Vibration Response of a Rod to an Applied Force: long_force.pdfMatlab scripts:Sine vibration: long_force_sine.mFrequency response function: long_force_frf.mModal
transient, abitrary time history: rod_arbit_f.m 

STRINGS,
ROPES, & CABLES
String
Vibration: string.pdf
Stefan
Kaczmarczyk, Resonance Phenomena in Tension Members with TimeVarying
Varying Characteristics: tension_members.pdf

NUMERICAL METHODS

NONLINEAR
VIBRATION
Cornell
University, Lecture Notes: nonlinear_vibration.pdf
Georgia
Tech, nonlinear_oscillator_notes.pdf
Free
Vibration of a Singledegreeoffreedom System with Nonlinear
Stiffness: nonlin_period.pdf

EIGENVALUE
PROBLEM
The
Generalized Eigenvalue Problem: eigen.pdf

MISCELLANEOUS
Chladni
Patterns: Chladni.pdf

Matlab Scripts Matlab 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

_ 
Singledegreeoffreedom
System Natural Frequency.

sdof_fn.exe

_ 
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 via the slicing method, which is
essentially the Sturm Sequence method.

slice_eigenvalues.exe

slice_eigenvalues.cpp

Eigenvalue calculation via the QR algorithm.  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
calculating the roots of the determinant polynomial. The upper limit is
fourth order.

eigen.exe

_ 
Eigenvalues and
eigenvectors of a twodegreeoffreedom system.

twodof.exe

twodof.cpp

Eigenvalues
and eigenvectors of a threedegreeoffreedom system.

threedof.exe

threedof.cpp

Holzer method for
torsional systems.

Holzer.exe

Holzer.cpp

Modal
solution for torsional vibration of freefree shaft with three disks.

three_disks_free_free.exe

three_disks_free_free.cpp

Ring
frequency for a cylindrical structure.

Windows:

ring_mode.cpp

Force
transfer function for a singledegreeoffreedom system.

force_transfer.exe

force_transfer.cpp

Base
excitation transfer function for a singledegreeoffreedom system.

base_transfer.exe

base_transfer.cpp

Transfer
functions for an applied force from natural frequencies, modal damping
and normalized eigenvectors

transfer_modes.exetransfer_function.exe 
transfer_modes.cpptransfer_function.cpp 
Transfer functions for an applied force from natural frequencies, modal damping and normalized eigenvectors with option for omitting rigidbody modes  transfer_function_rb.exe  transfer_function_rb.cpp 
Relative
displacement transfer function for an applied force

transfer_relative_displacement.exe

transfer_relative_displacement.cpp

Free
Vibration of a TwoDegreeofFreedom System Subjected to Initial
Velocity and Displacement

twodof_initial.exe

twodof_initial.cpp

Natural
frequencies of the transverse vibration of a fixedfixed string.

string_fn.exe

string_fn.cpp

Mass
Loading Attenuation Factor for Heavy Equipment and Payloads

mass_attenuation.exe

mass_attenuation.cpp

Unit
conversion program.

units.exe

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