A simple frictionless two DOF system is constructed with two springs and two lumped
masses.
Find the two natural frequencies and the corresponding mode shapes.
-Analysis Type
2-D eigenvalue analysis (X-Y plane)
-Unit System
in, lbf
-Dimension
Length: 20.0 in
Mass: M1=4.0 lbf.sec2/in
M2=1.0 lbf.sec2/in
Stiffness: K=EA/L
-Element
Truss element
-Material
Modulus of elasticity E=1.0 x 105
psi-Section Property
Area A=0.1 in2
-Boundary Condition
Node 3 ;Constrain all DOFsNodes 1 and 2 ;Constrain Dy and Rz (Only Dx allowed)-Analysis Case
Messes M1 and M2 exist at the nodes 1 and 2 in the X direction respectively.
Number of eigenvalues to be computed = 2Tested FeaturesApp
Object Link: https://openbrim.org/objidpgfg1tbcrad6drzwcxp5cd.project
Library
Object Link: https://openbrim.org/objidiq0x8tggiub6ud8t6gz7qs.libobj
SourcesDonald T. Greenwood, "Principles of Dynamics", Englewood Cliff, Prentice-Hall, Inc.,1965 .p.459, EX.9-1."MSC/NASTRAN, Verification Problem Manual", V.64, The MacNeal-Schwendler Corporation, 1986, Problem No.V0301."NISA II, Verification Manual", Version 91.0, Engineering Mechanics Research Corporation,1991.
Results| Independent1 (Theoretical) | Independent2 (MSC/NASTRAN) | Independent3 (NISA II) | MIDAS | OpenBrIM | Percent Difference (MIDAS vs Independent1) | Percent Difference (MIDAS vs Independent2) | Percent Difference (MIDAS vs Independent3) | |||||
|---|---|---|---|---|---|---|---|---|---|---|---|---|
| Mode1 | Frequency (rad/sec) | |||||||||||
| Frequency (cycle/sec) | ||||||||||||
| Period (sec) | ||||||||||||
| Angular velocity, w1 (rad/sec) | ||||||||||||
| X1 | ||||||||||||
| X2 | ||||||||||||
| Mode2 | Frequency (rad/sec) | |||||||||||
| Frequency (cycle/sec) | ||||||||||||
| Period (sec) | ||||||||||||
| Angular velocity, w1 (rad/sec) | ||||||||||||
| X1 | ||||||||||||
| X2 |