Modal Analysis of a Rectangular Plate - PPT

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  • 1. MAE 501 INDEPENDENT STUDYModal Analysis of a Rectangular Plate
    By
    Sasi BhushanBeera
    #35763829
  • 2. Problem Details
    Problem statement:
    To determine the lowest six non-zero frequencies and associated mode shapes for a rectangular plate for three different thickness of the plate.
    Geometry of the plate:
    Rectangular Plate with length 2a, width 2b and thickness h.
    γ = a/b=2
    ξ = h/b = 1/4, 1/16, 1/64
    a = 20m, b = 10 mm, h = 2.5mm, 0.625mm, 0.15625m
    Thus, the dimensions of the plate are as follows:
    Length of the plate = 40mm
    Width of the plate = 20mm
    Thickness of the plate = 2.5mm, 0.625mm, 0.15625mm
  • 3. Problem Details
    Material Properties of the plate:
    • ν = Poisson’s ratio = 0.05
    • 4. Material of the plate : Cast Iron
    • 5. E = Modulus of Elasticity = 139.7GPa
    • 6. ρ = Density = 7300 kg/m3
    Boundary Conditions:
    • The two adjacent edges of the rectangular plate are fixed while the other two are free.
    Element Details:
    • The modal analysis is performed using two types of elements i.e. solid and shell.
  • Meshing:
    • A 3-D model of the plate was created and the plate was meshed using SOLID45 element.
    Solver used for Modal Analysis:
    The modal analysis was performed using the PCG Lanczos solver.
    Applying boundary conditions:
    The two adjacent sides of the plate are fixed in x and y directions and all the four sides are constrained in z direction.
    C0nvergence Criteria:
    Natural Frequency: For the problem to converge, the variation of all the six natural frequencies between two iterations should be less that 1%.
    Modal Analysis using Solid45
  • 7. Case 1: h = 2.5 mm
    Results
    Case 2: h = 0.625 mm
  • 8. Results
    • As the thickness of the plate decreases the frequency values go on decreasing as the mass and the dimensions of the plate are decreased.
    • 9. The lower frequencies converge quickly as compared to the higher frequencies.
    • 10. The convergence details of each case are plotted graphically below:
    • 11. As the thickness of the plate decreases the frequency values go on decreasing as the mass and the dimensions of the plate are decreased.
    • 12. The lower frequencies converge quickly as compared to the higher frequencies.
    • 13. The convergence details of each case are plotted graphically below:
    Case 3: h = 0.15625 mm
    -As the thickness of the plate decreases the frequency values go on decreasing as the mass and the dimensions of the plate are decreased.
    -The lower frequencies converge quickly as compared to the higher
    frequencies.
  • 14. Case 1: h = 2.5 mm Case 2: h = 0.625 mm Case 3: h = 0.15625 mm
    Convergence
  • 15. Meshing:
    • A 2D-model of the plate was created and the plate was meshed using SHELL63 element.
    • 16. The thickness of the plate was entered as a real constant of the SHELL63 element.
    Solver used for Modal Analysis:
    The modal analysis was performed using the PCG Lanczos solver.
    Applying boundary conditions:
    The two adjacent sides of the plate are fixed in x and y directions and all the four sides are constrained in z direction.
    C0nvergence Criteria:
    Natural Frequency: For the problem to converge, the variation of all the six natural frequencies between two iterations should be less that 0.03%.
    Modal Analysis using Shell63
  • 17. Case 1: h = 2.5 mm
    Results
    Case 2: h = 0.625 mm
  • 18. Results
    • As the thickness of the plate decreases the frequency values go on decreasing as the mass and the dimensions of the plate are decreased.
    • 19. The lower frequencies converge quickly as compared to the higher frequencies.
    • 20. The convergence details of each case are plotted graphically below:
    • 21. As the thickness of the plate decreases the frequency values go on decreasing as the mass and the dimensions of the plate are decreased.
    • 22. The lower frequencies converge quickly as compared to the higher frequencies.
    • 23. The convergence details of each case are plotted graphically below:
    Case 3: h = 0.15625 mm
    -As the thickness of the plate decreases the frequency values go on decreasing.
    -Lower frequencies converge quickly as compared to higher frequencies.
  • 24. Convergence
    Case 1: h = 2.5 mm Case 2: h = 0.625 mm Case 3: h = 0.15625 mm
  • 25. Case 1: h = 2.5 mmCase 2: h = 0.625 mm Case 2: h = 0.15625 mm
    Comparison of Results
  • 26. Comparison of Modal Shapes
    • The mode shape obtained here is the same for both SOLID45 and SHELL63.
    • 27. The mode shape obtained here is the same for both SOLID45 and SHELL63.
    Case 3: h = 0.15625 mm
    Mode Shape for the 1st Natural Frequency:
    Solid Elements Shell Elements
    The mode shape obtained here is the same for both SOLID45 and SHELL63.
  • 28. Mode Shape for the 2nd Natural Frequency:
    Solid Elements Shell Elements
    Comparison of Modal Shapes
    The mode shape obtained here is the same for both SOLID45 and SHELL63.
  • 29. Mode Shape for the 3rd Natural Frequency:
    Solid Elements Shell Elements
    Comparison of Modal Shapes
    The mode shape obtained here is the same for both SOLID45 and SHELL63.
  • 30. Mode Shape for the 4th Natural Frequency:
    Solid Elements Shell Elements
    Comparison of Modal Shapes
    The mode shape obtained here is the same with deformations in different directions
  • 31. Mode Shape for the 5th Natural Frequency:
    Solid Elements Shell Elements
    Comparison of Modal Shapes
    Different mode shapes are obtained
  • 32. Mode Shape for the 6th Natural Frequency:
    Solid Elements Shell Elements
    Comparison of Modal Shapes
    Different mode shapes are obtained
  • 33.
    • The natural frequency values of any structure depend on its dimensions and boundary conditions. In this case, the frequency values decrease with decrease in thickness of the plate.
    • 34. Meshing with SHELL elements is easier as compared to SOLID mesh in case of complex structures.
    • 35. SHELL elements give better performance as the shell thickness go on decreasing.
    Conclusion