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Structural Dynamics - Circular & Annular Plates Page

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CIRCULAR PLATES

Natural Frequencies of Circular Plate Bending Modes: circular.pdf
Matlab script: circular_plate.m
Supporting function: circular_plate_materials.m

Response of a Circular Plate to Base Exciation:  circular_base.pdf

Simply-supported Circular Plate, Matlab script with Participation Factor Calculation. This script also calculates the transfer function for base excitation and has an option for a half-sine base input:
circular_SS.m
Supporting functions:

circular_plate_materials.m
circular_ss_bessel_function.m
circular_ss_bessel_function_PF.m
circular_ss_base_sine.m

circular_SS_base_half_sine.m

progressbar.m
Bessel_SS.m
Fixed Circular Plate, Matlab script with Participation Factor Calculation:
circular_fixed.m
The Fundamental Frequency of an Isolated Circular Plate: circular_elastic.pdf
Matlab script: circular_elastic.m
The natural frequency of a Circular Plate with Four Fixed Point Supports:  circular_plate_four.pdf  

Matlab script: circular_point_four.m

Supporting functions: polarplot3d.m   &   parse_pv_pairs.m

Nastran file: circular_plate_four_points.nas  
Kang, Huang & Knowles, Torsional Vibrations of Circular Elastic Plates with Thickness Steps: circular_torsion.pdf
R.S. Weiner,  Transient Motion of Circular Elastic Plates Subjected to Impulsive and Moving Loads:  Weiner_circular_plate.pdf
Launch Vehicle Bulkhead Flight Accelerometer Data: flight_bulkhead.pdf
CIRCULAR PLATES - Finite Element Method - via Triangular Elements

Plate Bending Frequencies via the Finite Element Method with Triangular Elements: triangular_plate_bending_specht.pdf

Matlab Script
triangular_specht.m

Supporting functions:
triangular_plate_specht_integrated_terms.m
triangular_plate_local.m
triangular_specht_cbar.m
materials.m

Generalized_Eigen_fea.m
Generalized_Eigen.m
Generalized_Eigen_subspace.m

 progressbar.m
honeycomb_materials.m

pf_emm_fea_post1.m
mode_shape_correction.m

triangular_elements_plot_modes.m

plate_materials_mass.m

Sample Data Files for a 24 inch Diameter Circular Plate that is Fixed along its Circumference:

Grid coordinates:  circular_grids.txt
Element Connectivity: circular_elements.txt
Constraints:  circular_bc.txt

CIRCULAR PLATES - Finite Element Method - via Triangular Elements using a Scalable Reference Plate

Common Functions

triangular_plate_local.m
triangular_specht_cbar.m

circular_plate_elements_reference.m
circular_plate_grid_reference.m
circular_plate_bc_reference.m
find_contraints_circular.m
circular_plate_bc_apply.m

Generalized_Eigen_fea.m
Generalized_Eigen.m
Generalized_Eigen_subspace.m

progressbar.m

materials.m
honeycomb_materials.m
plate_materials_mass.m

________________________________________________________________________________

Normal Modes Analysis:

circular_plate_bending_fea.m

Supporting functions:

pf_emm_fea_post1.m
mode_shape_correction.m

triangular_elements_plot_modes.m

________________________________________________________________________________

Base Excitation - Frequency Response & Modal Transient

circular_plate_base_accel_fea.m

Supporting functions:

mdof_half_sine_core.m
mdof_arbit_base_core.m
enter_time_history.m

ramp_invariant_filter_coefficients.m　

circular_plate_th_plot.m
find_circular_plot_node.m

circular_plate_constraint_nodes.m
partition_matrices_accel_frf.m
circular_plate_base_fea_post.m

ANNULAR PLATES - Finite Element Method - via Triangular Elements

Matlab Script
annular_plate_specht.m

Supporting functions:
annular_plate_bc_apply.m
triangular_plate_specht_integrated_terms.m
triangular_plate_local.m
triangular_specht_cbar.m
materials.m

Generalized_Eigen_fea.m
Generalized_Eigen.m
Generalized_Eigen_subspace.m

 progressbar.m
honeycomb_materials.m

pf_emm_fea_post1.m
mode_shape_correction.m

triangular_elements_plot_modes.m

plate_materials_mass.m

ANNULAR PLATES
The Fundamental Frequency of an Isolated Annular Plate: annular_elastic.pdf
Matlab script: annular_elastic.m
HONEYCOMB SANDWICH PLATES
Natural Frequencies of Honeycomb Plates, includes Bending-Shear Transition: honeycomb.pdf

FEA Model 1: annular_bulkhead.nas
FEA Model 2: bending_shear.nas
See also:  Honeycomb Material Page
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

  

 Software Description

 Executable

  Source
Natural frequencies of circular plates.
 circular.exe

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

 _
Unit conversion  program.
units.exe
  _

 

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