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STRUCTURAL DYNAMICS - DISCRETE SYSTEMS - SDOF
Free Vibration of a Single-Degree-of-Freedom System: free.pdf
Matlab script: free.m
The Response of a Single-Degree-of-Freedom System to Excitation from Random Surface Irregularities. (The input function may be a spatial power spectral density). random_surface.pdf
The Total Response of a Single-degree-of-freedom System to a Harmonic Excitation Force: fsine.pdf  &  fsine_phase.pdf
Matlab script:  sdof_sine_force.m
The Steady-state Response of Single-degree-of-freedom System to a Harmonic Excitation Force:  sforce.pdf
The Steady-state Response of Single-degree-of-freedom System to a Harmonic Base Excitation: base_sine.pdf
The Steady-state Relative Displacement Response to Base Excitation: relative_disp.pdf
The Vibration Response of Some Spring-Damper Systems with and without Masses:  spring_damper.pdf
STRUCTURAL DYNAMICS - DISCRETE SYSTEMS - MDOF
Assemble mass and stiffness matrices for a spring-mass system and solve the corresponding generalized eigenvalue problem.
Matlab scripts:
spring_mass_system.m
Generalized_Eigen.m
Free Vibration of a Two-Degree-of-Freedom System Subjected to Initial Velocity and Displacement: twodof_initial.pdf
Matlab scripts: 
mdof_free.m

Generalized_Eigen.m
plot_legend.m
line_colors.m
The Generalized Coordinate Method for Discrete Systems: gencoord.pdf
Matlab scripts:
twodof_sine_force.m
Generalized_Eigen.m

The Generalized Coordinate Method for Discrete Systems Subjected to Base Excitation: genbase.pdf
Response of a Two-degree-of-freedom System Subject to a Half-Sine Applied Force: two_dof_half_sine.pdf

Matlab script:
Matlab script:  twodof_half_sine_force.m
Shock Response of Multi-degree-of-freedom Systems:  mdof_srs.pdf
Effective Modal Mass & Modal Participation Factors: ModalMass.pdf
Mass Loading Effects for Heavy Equipment and Payloads: mass_loading.pdf
Matlab script: mass_loading.m
Notes on Internal and Transmitted Forces in Vibrating Multi-degree-of-freedom Systems: mdof_transmitted.pdf
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
Matlab scripts:

spring_mass_series.m
Generalized_Eigen.m

Damping Coefficient Matrix from Modal Damping for All Modes: damping_matrix.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
Multi-degree-of-freedom System Subjected to an Arbitrary Force: mdof_arbit_force.pdf
Matlab script: two_dof_arb_force.m

STRUCTURAL DYNAMICS- DISCRETE SYSTEMS - MDOF - Steady-State FRF - Base Excitation

The Steady-State Frequency Response Function of a Multi-degree-of-freedom System Subjected to Harmonic Base Excitation: mdof_FRF_base.pdf
Matlab Script: two_dof_frf.m
 Frequency Response Function for a Multi-degree-of-freedom System with Enforced Acceleration: modal_enforced_motion_mdof_fea_frf.pdf

The 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 - Steady-State FRF - Applied Force
The Steady-State Reponse of a Two-degree-of-freedom-system to a Single Harmonic Force: twodof_steady_force.pdf
Matlab Script: two_dof_force_steady.m
The Steady-State Frequency Response Function of a Multi-degree-of-freedom System Subjected to Harmonic Force Excitation: mdof_FRF_force.pdf
Matlab Script: two_dof_force_frf.m
The Steady-State Frequency Response Function of a Four-degree-of-freedom System Subjected to Harmonic Force Excitation: force_dof_FRF_force.pdf
Matlab Script: four_dof_force_frf.m
SEMIDEFINITE SYSTEMS
Semidefinite System Examples: semidefinite.pdf
Natural Frequencies of Semidefinite Spring Mass Systems in Series:

Matlab scripts:
spring_mass_semidefinite_series.m
Generalized_Eigen_semidefinite.m

Free Vibration of a Semidefinite System Subjected to Initial Conditions: semi_initial.pdf
Two-degree-of-freedom Semidefinite System Subjected to an Applied Sinusoidal Force:  semidefinite_force.pdf

Matlab scripts:
semidefinite_force.m
mdof_plot.m
 Generalized_Eigen_semidefinite.m
SPRING SURGE
Spring Surge: spring_surge.pdf
Matlab Script: spring_surge.m
RODS - LONGITUDINAL VIBRATION

Longitudinal Natural Frequencies of Rods and Response to Initial Conditions: long.pdf  

Longitudinal Vibration of a Tapered Rod: taper_long.pdf
Initial Velocity Excitation of the Longitudinal Modes in a Beam for Pyrotechnic Shock Simulation: iv_rod.pdf
Matlab script: beamvs.m
Rod Response to Longitudinal Base Excitation, Steady-State and Transient: long_base.pdf
Matlab script: fixed_free_rod.m & materials.m

RODS - LONGITUDINAL VIBRATION - APPLIED FORCE

The Longitudinal Vibration Response of a Rod to an Applied Force:  long_force.pdf
Matlab scripts:
Sine vibration: long_force_sine.m 
Frequency response function: long_force_frf.m
Modal transient, abitrary time history: rod_arbit_f.m
Supporting functions: 
geometry_materials.m
geometry_materials_units.m
materials.m

 

 

BEAMS  Moved to: beams
CIRCULAR & ANNULAR PLATES     Moved to:  circular_annular
RECTANGULAR PLATES  Moved to:  rectangular_plates
RINGS, CYLINDERS, SHELLS & CONES  Moved to:  rings_cylinder
TRANSFER FUNCTIONS  Moved to:  Transfer_Functions
STRINGS, ROPES, & CABLES
String Vibration: string.pdf  
Stefan Kaczmarczyk, Resonance Phenomena in Tension Members with Time--Varying Varying Characteristics: tension_members.pdf
 NUMERICAL METHODS

Newton-Raphson Method Applied to Vibration Problems: Newrap.pdf
Matlab Script: NewtonRaphson.m
NONLINEAR VIBRATION
Cornell University, Lecture Notes: nonlinear_vibration.pdf
Georgia Tech, nonlinear_oscillator_notes.pdf
Free Vibration of a Single-degree-of-freedom System with Nonlinear Stiffness: nonlin_period.pdf

Corresponding Matlab Scripts: sdof_stiff2_ode45.m  and sdof_stiff2_free_function.m
See also: nonlinear page
EIGENVALUE PROBLEM
The Generalized Eigenvalue Problem:  eigen.pdf  

Dr. Edward L. Wilson, The Eigenvalue Problem (Berkeley Link )
MISCELLANEOUS
Chladni Patterns: Chladni.pdf

Buckling and Vibration Analysis of a Simply Supported Column With A Piecewise Constant Cross Section By Mark S. Lake and Martin M. Mikulas, Jr.: sscol.pdf
Strain Energy Formulas: strain_energy.pdf
Electrical-Mechanical Analogy for Dynamic Systems: electrical_mechanical.pdf
Assembly of subsystem matrices: assembly_subsystem_matrices.pdf

Jacobian Matrix & Determinant:  Jacobian.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

  _
Single-degree-of-freedom 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 two-degree-of-freedom system.
 twodof.exe
  twodof.cpp
Eigenvalues and eigenvectors of a three-degree-of-freedom system.
 threedof.exe
 threedof.cpp
 Holzer method for torsional systems.
 Holzer.exe
  Holzer.cpp
Modal solution for torsional vibration of free-free shaft with three disks.
 three_disks_free_free.exe
 three_disks_free_free.cpp
Ring frequency for a cylindrical structure.
Windows:
ring.exe
DOS: 
ring_mode.exe
 ring_mode.cpp
Force transfer function for a single-degree-of-freedom system. 
 force_transfer.exe
 force_transfer.cpp
Base excitation transfer function for a single-degree-of-freedom system.
 base_transfer.exe
 base_transfer.cpp
Transfer functions for an applied force from natural frequencies, modal damping and normalized eigenvectors
transfer_modes.exe

transfer_function.exe
transfer_modes.cpp

transfer_function.cpp
Transfer functions for an applied force from natural frequencies, modal damping and normalized eigenvectors with option for omitting rigid-body modes
transfer_function_rb.exetransfer_function_rb.cpp
Relative displacement transfer function for an applied force
transfer_relative_displacement.exe
transfer_relative_displacement.cpp
Free Vibration of a Two-Degree-of-Freedom System Subjected to Initial Velocity and Displacement
twodof_initial.exe
twodof_initial.cpp
Natural frequencies of the transverse vibration of a fixed-fixed 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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