验证例题32.pdf

1Example 32 Title Eigenvalue analysis of a simply supported shaft Description Calculate the natural frequencies of a simply supported shaft.Structural geometry and analysis model Verification Example 2MODEL Analysis Type 2-D eigenvalue analysis (X-Y plane)Unit System in,lbf Dimension Length L=100 in Weight density =7.764 10-4 lbfsec2/in4 Gravitational acceleration g=1.0 in/sec2 Element Beam element Material Modulus of elasticity E =30 106 psi Section Property Area A=0.31416 in2 Moment of inertia Iyy=0.15708 in4 Radius R=1.00 in Thickness t =0.05 in Boundary Condition Nodes 1 and 21;Constrain Dx and Dz.Analysis Case Self weight is converted to nodal masses automatically.Number of natural frequencies to be computed=6 Example 32 3Results Eigenvalue Analysis Results Eigenvalue Analysis Results Verification Example 4Comparison of Results Unit:Hz Natural frequency Ref.1 MSC/NASTRAN MIDAS/Gen f1 21.8335 21.8335 21.8335 f2 87.3339 87.3333 87.3333 f3 196.501 196.494 196.494 f4 349.335 349.294 349.294 f5 545.837 545.670 545.670 f6 786.005 785.476 785.476 References J.P.Den Hartog,“Mechanical Vibrations”,4th Edition,McGraw-Hill,New York,1956,p.432.“MSC/NASTRAN,Verification Problem Manual”,V.64,The MacNeal-Schwendler Corporation,1986,Problem No.V0306.