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STRUCTURAL DYNAMICS - DISCRETE SYSTEMS - SDOF
Free Vibration of a Single-Degree-of-Freedom System: free.pdf
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
 STRUCTURAL DYNAMICS - DISCRETE SYSTEMS - MDOF
Free Vibration of a Two-Degree-of-Freedom System Subjected to Initial Velocity and Displacement: twodof_initial.pdf
The Generalized Coordinate Method for Discrete Systems: gencoord.pdf

The Generalized Coordinate Method for Discrete Systems Subjected to Base Excitation: genbase.pdf
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
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
Shock Response of Multi-degree-of-freedom Systems:  mdof_srs.pdf
Effective Modal Mass & Modal Participation Factors: ModalMass.pdf
Sample Lateral Natural Frequency Calculations for a Space Vehicle/Dispenser Analysis: lateralSV.pdf
Mass Loading Effects for Heavy Equipment and Payloads: mass_loading.pdf
Matlab script: mass_loading.m
SPRING SURGE
Spring Surge: spring_surge.pdf
Matlab Script: spring_surge.m

 STRUCTURAL DYNAMICS - BEAMS & RODS

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  
Natural Frequencies of Multispan Beams: mspan.pdf
Natural Frequencies of Beams Subjected to a Uniform Axial Load: beam_axial_load.pdf
Steady-State Vibration Response of a Cantilever Beam Subjected to Base Excitation: steady_cant.pdf

Longitudinal Natural Frequencies of Rods: long.pdf  

Longitudinal Vibration of a Tapered Rod: taper_long.pdf 
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
PLATES
Natural Frequencies of Rectangular Plate Bending Modes: plate.pdf

Natural Frequencies of Circular Plate Bending Modes: circular.pdf

Natural Frequencies of Honeycomb Plates: honeycomb.pdf
FEA Model: annular_bulkhead.nas
The Fundamental Frequency of an Isolated Circular Plate: circular_elastic.pdf
The Fundamental Frequency of an Isolated Annular Plate: annular_elastic.pdf
The Fundamental Bending Frequency of a Square Plate with Fixed Corners and Otherwise Free Edges (Point-Supported at Each Corner): square_plate_corners.pdf
The Natural Frequency of a Rectangular Plate Point-Supported at Each Corner: plate_point_corner.pdf
Corresponding Matlab scripts:  plate_corners.m & pfunction.m
The Fundamental Bending Frequency of a Plate with Fixed-Free-Free-Free Boundary Conditions: cantilever_plate.pdf
Samuel Levy, Square Plate with Clamped Edges Under Normal Pressure Producing Large Deflections: NACA-TN-847.pdf
Samuel Levy & Samuel Geenman, Bending with Large Deflection of a Clamped Rectangular Plate with Length Width Ratio of 1.5 under Normal Pressure: NACA-TN-853.pdf
Kang, Huang & Knowles, Torsional Vibrations of Circular Elastic Plates with Thickness Steps: circular_torsion.pdf
Eric Reissner & Manuel Stein, Torsion and Transverse Bending of Cantilever Plates: naca-tn-2369.pdf
Launch Vehicle Bulkhead Flight Accelerometer Data: flight_bulkhead.pdf
LEISSA PLATES
Arthur W. Leissa, NASA SP-160, Vibration of Plates. Note that these are large files. The total file size is approximately 250 Mb. The format is MS Word with scanned images.
Lplates1.doc
Lplates2.doc
Lplates3.doc
Lplates4.doc
Lplates5.doc
Lplates6.doc
Lplates7.doc
Lplates8.doc
Lplates9.doc
Alternate:
Leissa_vibration_plates.pdf
RINGS, CYLINDERS & SHELLS
Ring Vibration Modes: ringmode.pdf
Nastran Model: ring_modes.nas
Natural Frequencies of an Infinite Cylinder with Plain Strain: infinite_cylinder.pdf
Matlab Script: infinite_cylinder.m
Vibroacoustic Response of a Cylinder: cylinder_vibroacoustic.pdf
Natural Frequencies of a Finite, Thin-Walled Cylindrical Shell: cylindrical_shell.pdf
FEA file: fixed_fixed_cylinder3.nas
Matlab Scripts: cylinder_wave.m and progressbar.m
Bing-ru, et al, Study on applicability of modal analysis of thin finite length cylindrical shells using wave propagation approach: cylinder_wave.pdf
Pellicano, Linear and Nonlinear Vibration of Shells: LNV_Shells.pdf
Arthur W. Leissa, NASA SP-288, Vibration of Shells: Leissa_vibration_shells.pdf
CONES
Murphy, Transverse Vibration of a Simply Supported Frustum of a Right Circular Cone: transverse_cone.pdf
Platus, Conical Shell Vibrations: NASA_Conical_Shell.pdf
Backlund, Jesper, Free Vibration Analysis of Rocket Nozzles Using Energy Methods: rocket_nozzle_vibration.pdf
Sewall and Catherines, Analytical Vibration Study of a Ring-Stiffened Conical Shell and Comparison with Experiment, NASA TN D-5663: ring_stiffened_conical_shell.pdf
Derivation of the Volume of a Cone and of a Conical Shell: volume_cone.pdf
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
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 )

 Software Description

 Executable

  Source
Natural frequencies of beam modes, both lateral  and longitudinal.
 beam.exe
 _
Beam mode animation via setup file.
 setup_b.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
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
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
Book Recommendations
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