验证例题43.pdf

1Example 43 Title Transient response to a step excitation Description A spring-mass-damping system,initially at rest,is subjected to a step force.Perform a time history analysis and compare the maximum displacements of the structure between the cases of damping and undamping.Verification Example 2 Structural geometry and analysis model Example 43 3Model Analysis Type 2-D time history analysis Unit System in,lbf Dimension Length L =100.0 in Mass M =0.5 lbf sec2/in(Y axis)Analysis time t =0.25 sec Time step t =0.0025 sec Damping ratio =0.0(0%)=0.5(50%)Element Truss Element Material Modulus of elasticity E=20000 psi Section Property Area A=1.0 in2 Boundary Condition Node 1 ;Constrain all DOFs.Node 2 ;Constrain Dx and Ry Analysis Case Step force acts in the Y direction.The time step force data are as follows;Time(sec)Force(lbf)0.0025 200 0.2050 200 Verification Example 4Results Displacements at the nodes 2(Damping ratio is 0.0)In the case of damping ratio is 0.5 Example 43 5Comparison of Results Unit:in Result Theoretical MIDAS/Gen Maximum displacement Damping ratio=0.0 2.000 2.000 Damping ratio=0.0 1.654 1.672 Displacement(t=0.2 sec)Damping ratio=0.5 1.1531 1.1543 References Thomson,W.T.,“Vibration Theory and Applications”,Prentice-Hall,Inc.,Englewood Cliffs,N.Y.,2nd Printing,1965,p.102,Article 4.3.Verification Example 6 Step force data