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# Modal Analysis of a Rectangular Plate - PPT

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### Modal Analysis of a Rectangular Plate - PPT

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