> > Modal Analysis Problems

Modal Analysis Problems
This chapter contains modal analysis problems and Creo Simulate's results. In a modal analysis, Structure calculates the natural frequencies and mode shapes of your model. Structure also automatically calculates all predefined measures. This list of measures differs based on the analysis type.
This chapter contains the following modal problems:
mvsm001: 2D Plane Strain Shell Cantilever Plate
mvsm002: 2D Plane Stress Cantilever Plate
mvsm003: 2D Plane Strain Solid Cantilever Plate
mvms004: 2D Axisymmetric Radial Vibration of an Annulus
mvsm005: 3D Radial Vibration of a Ring
mvsm006: 3D Cantilever Wedge-Shaped Plate
mvsm007: 3D Cantilever Cylindrical Shell
mvsm008: 3D Solid Wedge-Shaped Plate
mvsm009: 3D In-Plane Vibration of a Pin-Ended Cross
mvsm010: 3D Annular Plate Axisymmetric Vibration
mvsm001: 2D Plane Strain Shell Cantilever Plate
 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: McGraw-Hill Book Co. 1982. pp.576578. Description: Find the fundamental frequency of a cantilever plate modeled as a plane strain model.
Specifications
 Element Type: 2D shell (1) Units: MKS Dimensions: width: 2thickness: 0.01 Material Properties: Mass Density: 7850Cost Per Unit Mass: 0Young's Modulus: 2e11 Poisson's Ratio: 0.3Thermal Expansion: 0Conductivity: 0 Constraint: placed on point A: fixed in all DOF
Comparison of Results Data
 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
mvsm002: 2D Plane Stress Cantilever Plate
 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: McGraw-Hill Book Co. 1982. pp.576578. Description: Find the fundamental frequency for the lateral vibration of a cantilever plate.
Specifications
 Element Type: 2D plate (1) Units: IPS Dimensions: length: 36width: 4thickness: 0.1 Material Properties: Mass Density: 7.28e4Cost Per Unit Mass: 0Young's Modulus: 3e7 Poisson's Ratio: 0.3Thermal Expansion: 0Conductivity: 0 Constraint: placed on edge A-B: fixed in TransX and TransY
Comparison of Results Data
 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
mvsm003: 2D Plane Strain Solid Cantilever Plate
 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: McGraw-Hill Book Co. 1982. pp.576578. Description: Find the fundamental frequency of a cantilever plate modeled as a plane strain model.
Specifications
 Element Type: 2D solid (2) Units: IPS Dimensions: length: 36width: 4 Material Properties: Mass Density: 7.28e4Cost Per Unit Mass: 0Young's Modulus: 3e7 Poisson's Ratio: 0.3Thermal Expansion: 0Conductivity: 0 Constraint: placed on edge A-B: fixed in TransX, TransY, and RotZ
Comparison of Results Data
 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
mvsm004: 2D Axisymmetric Radial Vibration of an Annulus
 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.
Specifications
 Element Type: 2D solid (1) Units: IPS Dimensions: inner radius: 99.975outer radius: 100.025height: 0.05 Material Properties: Mass Density: 7.3e4Cost Per Unit Mass: 0Young's Modulus: 3e7 Poisson's Ratio: 0Thermal Expansion: 0Conductivity: 0 Constraints: placed on edge A-B: fixed in TransY and RotZplaced on edge C-D: fixed in TransY and Rot Z
Comparison of Results Data
 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
mvsm005: 3D Radial Vibration of a Ring
 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 one-quarter model.
Specifications
 Element Type: beam (1) Units: IPS Dimensions: radius: 2 Beam Properties: Area: 0.01IYY: 1e3Shear FY: 0.83333CY: 1 J: 1.008e3IZZ: 8.33e6Shear FZ: 0.83333CZ: 1 Material Properties: Mass Density: 7.28e4Cost Per Unit Mass: 0Young's Modulus: 3e7 Poisson's Ratio: 0.3Thermal Expansion: 0Conductivity: 0 Constraints: placed on point A: fixed in all DOF except TransXplaced on point B: fixed in all DOF except TransY
Comparison of Results Data
 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
mvsm006: 3D Cantilever Wedge-Shaped Plate
 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, wedge-shaped plate.
Specifications
 Element Type: shell (1) Units: IPS Dimensions: length: 16width: 4thickness: 1 Material Properties: Mass Density: 7.28e4Cost Per Unit Mass: 0Young's Modulus: 3e7 Poisson's Ratio: 0Thermal Expansion: 0Conductivity: 0 Constraint: placed on edge A-B: fixed in all DOF
Comparison of Results Data
 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
mvsm007: 3D Cantilever Cylindrical Shell
 Analysis Type: Modal Model Type: 3D Comparison: Theoretical results Reference: Roark, R.J., and Young, W.C. Formula for Stress and Strain. NY: McGraw-Hill Co. 1982. p.576. Description: A cantilever cylindrical shell is modeled as a half cylinder using symmetry. Find the fundamental frequency.
Specifications
 Element Type: shell (3) Units: IPS Dimensions: length: 36radius: 1thickness: 0.1 Material Properties: Mass Density: 7.28e4Cost Per Unit Mass: 0Young's Modulus: 3e7 Poisson's Ratio: 0.3Thermal Expansion: 0Conductivity: 0 Constraint: placed on edge A-B: fixed in all DOFplaced on edge A-C, B-D: fixed in TransX, RotY, and RotZ
Comparison of Results Data
 Theory Structure % Difference Frequency (Hz)(mode=1) 62.05 62.125 0.12% Convergence %: 0.4% on Frequency Max P: 6 No. Equations: 180
mvsm008: 3D Solid Wedge-Shaped Plate
 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, wedge-shaped plate.
Specifications
 Element Type: solid (1) Units: IPS Dimensions: length: 16width: 4depth: 1 Material Properties: Mass Density: 7.28e–4Cost Per Unit Mass: 0Young's Modulus: 3e7 Poisson's Ratio: 0Thermal Expansion: 0Conductivity: 0 Constraint: placed on face A-B-C-D: fixed in all DOF
Comparison of Results Data
 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
mvsm009: 3D In-Plane Vibration of a Pin-Ended Cross
 Analysis Type: Modal Model Type: 3D Reference: NAFEMS, SBNFA (November 1987), Test 1. Description: Determine the first to eighth modal frequencies for the in-plane vibration of a cross with a pin joint at points A, B, C, & D.
Specifications
 Element Type: beam (4) Units: NMS Dimensions: length: 5 Beam Properties: Area: 0.015625IYY: 2.0345e–5Shear FY: 0.83333CY: 0.0625 J: 4.069e–5IZZ: 2.0345e–5Shear FZ: 0.83333CZ: 0.0625 Material Properties: Mass Density: 8000Cost Per Unit Mass: 0Young's Modulus: 2e11 Poisson's Ratio: 0.3Thermal Expansion: 0Conductivity: 0 Constraints: placed on points A, B, C, D: fixed TransX, TransY, TransZplaced on beams A-O, B-O, C-O, D-O: fixed in TransZ
Comparison of Results Data
 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
mvsm010: 3D Annular Plate Axisymmetric Vibration
 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.
Specifications
 Element Type: solid (3) Units: NMS Dimensions: inner radius: 1.8outer radius: 6height: 0.6 Material Properties: Mass Density: 8000Cost Per Unit Mass: 0Young's Modulus: 2e11 Poisson's Ratio: 0.3Thermal Expansion: 0Conductivity: 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
Comparison of Results Data
 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