E01: Eigenvalue analysis of a two DOF system

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 DOFs

Nodes 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 = 2

Tested Features

App

Library

Sources

Donald 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)	Percent Difference (OpenBrIM vs Independent1)	Percent Difference (OpenBrIM vs Independent2)	Percent Difference (OpenBrIM vs Independent3)
Mode1	Frequency (rad/sec)	10.8267	10.8267	10.8267	10.8267	10.8267	0%	0%	0%	0%	0%	0%
	Frequency (cycle/sec)	1.7231	1.7231	1.7231	1.7231	1.7231	0%	0%	0%	0%	0%	0%
	Period (sec)	0.5803	0.5803	0.5803	0.5803	0.5803	0%	0%	0%	0%	0%	0%
	X1	1.0000	1.0000	1.0000	1.0000
	X2	0.531	0.531	0.531	0.531
Mode2	Frequency (rad/sec)	46.1821	46.1821	46.1821	46.1821	46.1821	0%	0%	0%	0%	0%	0%
	Frequency (cycle/sec)	7.3501	7.3501	7.3501	7.3501	7.3501	0%	0%	0%	0%	0%	0%
	Period (sec)	0.1361	0.1361	0.1361	0.1361	0.1361	0%	0%	0%	0%	0%	0%
	X1	-0.133	-0.133	-0.133	-0.133
	X2	1.0000	1.0000	1.0000	1.0000