VM69

VM69
Seismic Response

Overview

Reference:	W. T. Thomson, Vibration Theory and Applications, 2nd Printing, Prentice-Hall, Inc., Englewood Cliffs, NJ, 1965, pg. 78, ex. 3.11-1
Analysis Type(s):	Mode-frequency, Seismic Analysis (ANTYPE = 2)
Element Type(s):	Combination Elements (COMBIN40)
Input Listing:	vm69.dat

Test Case

The spring-mass system shown below represents a vibrometer. Determine its natural frequency f. The displacement response spectrum for the vibrometer is shown for 3 points, based on an input of u_i = A cos ωt, where u_i is the excitation at the support (node 1). Show that the vibrometer response Δ is 2% in error when operated at frequency ω.

Figure 94: Seismic Response Problem Sketch

Material Properties

m = 1 lb-sec²/in

k = 9.8696 lb/in

ω = 22.43537 rad/sec

A = 1 in

Analysis Assumptions and Modeling Notes

The node locations are arbitrarily selected. The spring is arbitrarily assumed to vibrate in the X direction.

Results Comparison

	Target	Mechanical APDL	Ratio
f, Hz	0.5000	0.5000	1.000
A_e, in[1]	1.0200	1.0200	1.000

A_e = expanded mode shape amplitude. Vibrometer accuracy is equal to 100 x (A_e - A)/A = 2%