E11: 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

		Independent	MSC/NASTRAN	NISA II	MIDAS	OpenBrIM	Percent Difference (MIDAS vs Independent)	Percent Difference (MSC/NASTRAN vs Independent)	Percent Difference (NISA II vs Independent)	Percent Difference (OpenBrIM vs Independent)
Mode1	Frequency (rad/sec)	10.8267	10.8267	10.8267	10.8267	10.8267	0%	0%	0%	0%
	Frequency (cycle/sec)	1.7231	1.7231	1.7231	1.7231	1.7231	0%	0%	0%	0%
	Period (sec)	0.5803	0.5803	0.5803	0.5803	0.5803	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%
	Frequency (cycle/sec)	7.3501	7.3501	7.3501	7.3501	7.3501	0%	0%	0%	0%
	Period (sec)	0.1361	0.1361	0.1361	0.1361	0.1361	0%	0%	0%	0%
	X1	-0.133	-0.133	-0.133	-0.133
	X2	1.0000	1.0000	1.0000	1.0000