VM52

VM52
Automobile Suspension System Vibration

Overview

Reference:

W. T. Thomson, Vibration Theory and Applications, 2nd Printing, Prentice-Hall, Inc., Englewood Cliffs, NJ, 1965, pg. 181, ex. 6.7-1

Analysis Type(s):

Mode-frequency Analysis (ANTYPE = 2)

Element Type(s):

3D 2 Node Beam (BEAM188)

Spring-Damper Elements (COMBIN14)

Structural Mass Element (MASS21)

Input Listing:

vm52.dat

Test Case

An automobile suspension system is simplified to consider only two major motions of the system:

up and down linear motion of the body
pitching angular motion of the body

If the body is idealized as a lumped mass with weight W and radius of gyration r, determine the corresponding coupled frequencies f₁ and f₂.

Figure 76: Automobile Suspension Problem Sketch

Material Properties

Geometric Properties

E = 4 x 10⁹ psf

w = 3220 lb

m = W/g = 100 lb-sec²/ft

k₁ = 2400 lb/ft

k₂ = 2600 lb/ft

₁ = 4.5 ft

₂ = 5.5ft

r = 4 ft

g = 32.2 ft/sec²

Analysis Assumptions and Modeling Notes

The beam geometric properties are input (all as unity) but not used for this solution. The torsional moment of inertia I_T is calculated as I_T = Wr²/g = 1600 lb-sec²-ft. The spring length is used only to define the spring direction.

Results Comparison

	Target	Mechanical APDL	Ratio
f₁ , Hz	1.0981	1.0979	1.000
f₂ , Hz	1.4406	1.4403	1.000