验证例题33.pdf

1Example 33 Title Eigenvalue analysis of the cantilever Description Compare the natural frequencies of a cantilever modeled with plate elements and beam elements separately.Structural geometry and analysis model 2MODEL Analysis Type 3-D eigenvalue analysis Unit System m,N Dimension Length 1.0 m Depth 0.05 m Thickness 0.1 m Gravitational acceleration g=1.0 m/sec2 Element Plate element(Thick type)and beam element Material Beam Elements Modulus of elasticity E=2.0 1011 N/m2 Poissons ratio =0.3 Weight density =7800.0 N/m3 Plate Elements Modulus of elasticity E =2.0 1011 N/m2 Poissons ratio =0.3 Weight density =7800.0 N/m3 Section Property Beam Elements Area A=0.005 m2 Effective shear area Az=4.1667 10-3 m2 Moment of inertia Iyy =4.166 10-6 m2 Plate Elements Size a b =0.1 m 0.05m Thickness t=0.1 m Example 60 3Boundary Condition Fixed end ;Constrain all DOFs The remaining nodes;Constrain Dy and Rz Analysis Case Self weight is converted to nodal masses automatically.Number of natural frequencies to be computed =5 Results Eigenvalue Analysis Results(Beam elements)Eigenvalue Analysis Results(Plate elements)4Comparison of Results Unit:Hz Natural frequency of the first mode(f1)Frequency Theoretical ADINA NISA II MIDAS/GenPlate elements 81.80 81.33 82.30 81.87 Beam elements 81.80 80.94 81.15 80.94 References Blevins,R.D.,“Formulas for Natural Frequency and Mode Shape”,Van Nostrand Reinhold Company,1979.“ADINA,Verification Manual-Linear Problems”,Version 6.1,ADINA R&D,Inc,1992,Example A.47&A.66.“NISA II,Verification Manual”,Version 91.0,Engineering Mechanics Research Corporation,1991.