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Modal Analysis of a Rectangular Plate - PPT
 

Modal Analysis of a Rectangular Plate - PPT

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    Modal Analysis of a Rectangular Plate - PPT Modal Analysis of a Rectangular Plate - PPT Presentation Transcript

    • MAE 501 INDEPENDENT STUDYModal Analysis of a Rectangular Plate
      By
      Sasi BhushanBeera
      #35763829
    • 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
    • Problem Details
      Material Properties of the plate:
      • ν = Poisson’s ratio = 0.05
      • Material of the plate : Cast Iron
      • E = Modulus of Elasticity = 139.7GPa
      • 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
    • Case 1: h = 2.5 mm
      Results
      Case 2: h = 0.625 mm
    • 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.
      • The lower frequencies converge quickly as compared to the higher frequencies.
      • The convergence details of each case are plotted graphically below:
      • 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.
      • 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.
    • Case 1: h = 2.5 mm Case 2: h = 0.625 mm Case 3: h = 0.15625 mm
      Convergence
    • Meshing:
      • A 2D-model of the plate was created and the plate was meshed using SHELL63 element.
      • 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
    • Case 1: h = 2.5 mm
      Results
      Case 2: h = 0.625 mm
    • 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.
      • The lower frequencies converge quickly as compared to the higher frequencies.
      • The convergence details of each case are plotted graphically below:
      • 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.
      • 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.
    • Convergence
      Case 1: h = 2.5 mm Case 2: h = 0.625 mm Case 3: h = 0.15625 mm
    • Case 1: h = 2.5 mmCase 2: h = 0.625 mm Case 2: h = 0.15625 mm
      Comparison of Results
    • Comparison of Modal Shapes
      • The mode shape obtained here is the same for both SOLID45 and SHELL63.
      • 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.
    • 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.
    • 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.
    • 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
    • Mode Shape for the 5th Natural Frequency:
      Solid Elements Shell Elements
      Comparison of Modal Shapes
      Different mode shapes are obtained
    • Mode Shape for the 6th Natural Frequency:
      Solid Elements Shell Elements
      Comparison of Modal Shapes
      Different mode shapes are obtained
      • 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.
      • Meshing with SHELL elements is easier as compared to SOLID mesh in case of complex structures.
      • SHELL elements give better performance as the shell thickness go on decreasing.
      Conclusion