Analysis Type:

Modal

Model Type:

2D Plane Strain

Comparison:

Theoretical Results

Reference:

Roark, R.J. and Young, W.C. Formulas for Stress and Strain. NY: McGrawHill Book Co. 1982. pp.576578.

Description:

Find the fundamental frequency of a cantilever plate modeled as a plane strain model.

Element Type:  2D shell (1)  
Units:  MKS  
Dimensions:  width: 2 thickness: 0.01  
Material Properties:  Mass Density: 7850 Cost Per Unit Mass: 0 Young's Modulus: 2e11  Poisson's Ratio: 0.3 Thermal Expansion: 0 Conductivity: 0 
Constraint:  placed on point A: fixed in all DOF 
Theory  Structure  % Difference  
Fundamental Frequency (Hz) (mode=1)  2.1393  2.1374  0.08% 
Convergence %: 0.4% on Frequency  Max P: 4  No. Equations: 12 
Analysis Type:  Modal 
Model Type:  2D Plane Stress 
Comparison:  Theoretical Results 
Reference:  Roark, R.J. and Young, W.C. Formulas for Stress and Strain. NY: McGrawHill Book Co. 1982. pp.576578. 
Description:  Find the fundamental frequency for the lateral vibration of a cantilever plate. 
Element Type:  2D plate (1)  
Units:  IPS  
Dimensions:  length: 36 width: 4 thickness: 0.1  
Material Properties:  Mass Density: 7.28e4 Cost Per Unit Mass: 0 Young's Modulus: 3e7  Poisson's Ratio: 0.3 Thermal Expansion: 0 Conductivity: 0 
Constraint:  placed on edge AB: fixed in TransX and TransY 
Theory  Structure  % Difference  
Fundamental Frequency (Hz) (mode=1)  101.326  100.988  0.33% 
Convergence %: 0.4% on Frequency  Max P: 6  No. Equations: 42 
Analysis Type:  Modal 
Model Type:  2D Plane Strain 
Comparison:  Theoretical Results 
Reference:  Roark, R.J., and Young, W.C. Formulas for Stress and Strain, NY: McGrawHill Book Co. 1982. pp.576578. 
Description:  Find the fundamental frequency of a cantilever plate modeled as a plane strain model. 
Element Type:  2D solid (2)  
Units:  IPS  
Dimensions:  length: 36 width: 4  
Material Properties:  Mass Density: 7.28e4 Cost Per Unit Mass: 0 Young's Modulus: 3e7  Poisson's Ratio: 0.3 Thermal Expansion: 0 Conductivity: 0 
Constraint:  placed on edge AB: fixed in TransX, TransY, and RotZ 
Theory  Structure  % Difference  
Fundamental Frequency (Hz) (mode=1)  106.219  106.604  0.36% 
Convergence %: 0.8% on Frequency  Max P: 6  No. Equations: 42 
Analysis Type:  Modal 
Model Type:  2D Axisymmetric 
Comparison:  ANSYS No. 67 
Reference:  Timoshenko, S., and Young, D.H. Vibration Problems in Engineering. 3rd ed. NY: D. Van Nostrand Co., Inc. 1955. p. 425, Art. 68. 
Description:  Find the fundamental frequency for the radial vibration of an annulus modeled axisymmetrically. 
Element Type:  2D solid (1)  
Units:  IPS  
Dimensions:  inner radius: 99.975 outer radius: 100.025 height: 0.05  
Material Properties:  Mass Density: 7.3e4 Cost Per Unit Mass: 0 Young's Modulus: 3e7  Poisson's Ratio: 0 Thermal Expansion: 0 Conductivity: 0 
Constraints:  placed on edge AB: fixed in TransY and RotZ placed on edge CD: fixed in TransY and Rot Z 
Theory  ANSYS  Structure  % Difference  
Radial Frequency (Hz) (mode=1)  322.64  322.64  322.64  0.0% 
Convergence %: 0.0% on Frequency  Max P: 2  No. Equations: 10 
Analysis Type:  Modal 
Model Type:  3D 
Comparison:  Theoretical Results 
Reference:  Love, A.E.H. A Treatise on the Mathematical Theory of Elasticity. 4th ed. NY: Dover Publications. 1944. p. 452, Art. 293b. 
Description:  Determine the first and second modal frequencies for the radial vibration of a ring modeled as a onequarter model. 
Element Type:  beam (1)  
Units:  IPS  
Dimensions:  radius: 2  
Beam Properties:  Area: 0.01 IYY: 1e3 Shear FY: 0.83333 CY: 1  J: 1.008e3 IZZ: 8.33e6 Shear FZ: 0.83333 CZ: 1 
Material Properties:  Mass Density: 7.28e4 Cost Per Unit Mass: 0 Young's Modulus: 3e7  Poisson's Ratio: 0.3 Thermal Expansion: 0 Conductivity: 0 
Constraints:  placed on point A: fixed in all DOF except TransX placed on point B: fixed in all DOF except TransY 
Theory  Structure  % Difference  
Mode 1 Frequency (Hz)  625.65  624.43  0.19% 
Mode 2 Frequency (Hz)  3393.06  3369.13  0.70% 
Convergence %: 0.0% on Frequency  Max P: 9  No. Equations: 50 
Analysis Type:  Modal 
Model Type:  3D 
Comparison:  ANSYS No. 62 
Reference:  Timoshenko, S., and Young, D.H. Vibration Problems in Engineering. 3rd ed. NY: D. Van Nostrand Co., Inc. 1955. p. 392, Art. 62. 
Description:  Find the fundamental frequency for the lateral vibration of a cantilever, wedgeshaped plate. 
Element Type:  shell (1)  
Units:  IPS  
Dimensions:  length: 16 width: 4 thickness: 1  
Material Properties:  Mass Density: 7.28e4 Cost Per Unit Mass: 0 Young's Modulus: 3e7  Poisson's Ratio: 0 Thermal Expansion: 0 Conductivity: 0 
Constraint:  placed on edge AB: fixed in all DOF 
Theory  ANSYS  Structure  % Difference  
Frequency (Hz) (mode=1)  259.16  260.99  259.15  0.004% 
Convergence %: 0.0% on Frequency  Max P: 4  No. Equations: 60 
Analysis Type:  Modal 
Model Type:  3D 
Comparison:  Theoretical results 
Reference:  Roark, R.J., and Young, W.C. Formula for Stress and Strain. NY: McGrawHill Co. 1982. p.576. 
Description:  A cantilever cylindrical shell is modeled as a half cylinder using symmetry. Find the fundamental frequency. 
Element Type:  shell (3)  
Units:  IPS  
Dimensions:  length: 36 radius: 1 thickness: 0.1  
Material Properties:  Mass Density: 7.28e4 Cost Per Unit Mass: 0 Young's Modulus: 3e7  Poisson's Ratio: 0.3 Thermal Expansion: 0 Conductivity: 0 
Constraint:  placed on edge AB: fixed in all DOF placed on edge AC, BD: fixed in TransX, RotY, and RotZ 
Theory  Structure  % Difference  
Frequency (Hz) (mode=1)  62.05  62.125  0.12% 
Convergence %: 0.4% on Frequency  Max P: 6  No. Equations: 180 
Analysis Type:  Modal 
Model Type:  3D 
Comparison:  ANSYS No. 62 
Reference:  Timoshenko, S., and Young, D.H. Vibration Problems in Engineering. 3rd ed. NY: D. Van Nostrand Co., Inc. 1955. p. 392, Art. 62. 
Description:  Find the fundamental frequency for the lateral vibration of a cantilever, wedgeshaped plate. 
Element Type:  solid (1)  
Units:  IPS  
Dimensions:  length: 16 width: 4 depth: 1  
Material Properties:  Mass Density: 7.28e–4 Cost Per Unit Mass: 0 Young's Modulus: 3e7  Poisson's Ratio: 0 Thermal Expansion: 0 Conductivity: 0 
Constraint:  placed on face ABCD: fixed in all DOF 
Theory  ANSYS  Structure  % Difference  
Fundamental Frequency (Hz) (mode=1)  259.16  260.99  259.24  0.03% 
Convergence %: 0.0% on Frequency  Max P: 4  No. Equations: 72 
Analysis Type:  Modal 
Model Type:  3D 
Reference:  NAFEMS, SBNFA (November 1987), Test 1. 
Description:  Determine the first to eighth modal frequencies for the inplane vibration of a cross with a pin joint at points A, B, C, & D. 
Element Type:  beam (4)  
Units:  NMS  
Dimensions:  length: 5  
Beam Properties:  Area: 0.015625 IYY: 2.0345e–5 Shear FY: 0.83333 CY: 0.0625  J: 4.069e–5 IZZ: 2.0345e–5 Shear FZ: 0.83333 CZ: 0.0625 
Material Properties:  Mass Density: 8000 Cost Per Unit Mass: 0 Young's Modulus: 2e11  Poisson's Ratio: 0.3 Thermal Expansion: 0 Conductivity: 0 
Constraints:  placed on points A, B, C, D: fixed TransX, TransY, TransZ placed on beams AO, BO, CO, DO: fixed in TransZ 
Theory  Structure  % Difference  
Mode 1 Frequency (Hz)  11.336  11.312  0.211% 
Mode 2 & 3 Frequency (Hz)  17.709  17.636  0.412% 
Mode 4 Frequency (Hz)  17.709  17.636  0.412% 
Mode 5 Frequency (Hz)  45.345  45.155  0.419% 
Mode 6 & 7 Frequency (Hz)  57.390  56.692  1.216% 
Mode 8 Frequency (Hz)  57.390  57.001  0.677% 
Convergence %: 3.4% on Frequency  Max P: 8  No. Equations: 157 
Analysis Type:  Modal 
Model Type:  3D 
Reference:  NAFEMS, SBNFA (November 1987), Test 53. 
Description:  Determine the first to fifth modal frequencies for the axisymmetric vibration of an annular plate. 
Element Type:  solid (3)  
Units:  NMS  
Dimensions:  inner radius: 1.8 outer radius: 6 height: 0.6  
Material Properties:  Mass Density: 8000 Cost Per Unit Mass: 0 Young's Modulus: 2e11  Poisson's Ratio: 0.3 Thermal Expansion: 0 Conductivity: 0 
Constraints:  Location  Degrees of Freedom 
constraint1  placed on surfaces ABCD, BCNO, ADMP, ABMN, CDPO, MNOP  fixed in TransT, RotR, and RotZ 
placed on curve MP  fixed in TransZ 
Theory  Structure  % Difference  
Modal 1 Frequency (Hz)  18.583  18.550  0.17% 
Modal 2 Frequency (Hz)  140.15  138.22  1.37% 
Modal 3 Frequency (Hz)  224.16  224.16  0% 
Modal 4 Frequency (Hz)  358.29  355.80  0.7% 
Modal 5 Frequency (Hz)  629.19  620.43  1.4% 
Convergence %: 1.3 on Frequency  Max P: 9  No. Equations: 1094 