VM182

VM182
Transient Response of a Spring-mass System

Overview

Reference:R. K. Vierck, Vibration Analysis, 2nd Edition, Harper & Row Publishers, New York, NY, 1979, sec. 5-8.
Analysis Type(s):
Mode-frequency Analysis (ANTYPE = 2)
Transient Dynamic Mode-Superposition Analysis (ANTYPE = 4)
Element Type(s):Combination Elements (COMBIN40)
Input Listing:vm182.dat

Test Case

A system containing two masses, m1 and m2, and two springs of stiffness k1 and k2 is subjected to a pulse load F(t) on mass 1. Determine the displacement response of the system for the load history shown.

Figure 273: Spring-mass System Problem Sketch

Spring-mass System Problem Sketch

Material PropertiesLoading
k1 = 6 N/m
k2 = 16 N/m
m1 = 2 Kg
m2 = 2 Kg
F0 = 50 N
td = 1.8 sec

Analysis Assumptions and Modeling Notes

COMBIN40 combination elements are used to represent the springs and masses. Node locations are arbitrary. The response of the system is examined for an additional 0.6 seconds after the load is removed.

Results Comparison

TargetMechanical APDLRatio
Y1 , m (@ t = 1.3s)14.4814.400.995
Y2 , m (@ t = 1.3s)3.993.950.990
Y1 , m (@ t = 2.4s)18.3218.401.004
Y2 , m (@ t = 2.4s)6.146.161.004

Figure 274: POST26 Displacement Display

POST26 Displacement Display