VM-WB-MECH-083

VM-WB-MECH-083
Transient Response to a Step Excitation

Overview

Reference:

Thomson, W.T. (1965). Vibration Theory and Applications (2nd Printing, p. 102, article 4.3). Englewood Cliffs, NJ: Prentice-Hall, Inc.

Solver(s):

Ansys Mechanical

Analysis Type(s):

Mode-Superposition Transient Dynamic Analysis

Element Type(s):  

Test Case

A spring-mass-damping system that is initially at rest is subjected to a step force change F acting on the mass. Determine the displacement u at time t for damping ratio, ξ = 0.5.

This problem is also presented in

VM75

in the Mechanical APDL Verification Manual.

Figure 108: Schematic

Schematic
Schematic

Material PropertiesLoading

m = 0.5 lb-sec2/in

k = 200 lb/in

F = 200 lb

Analysis Assumptions and Modeling Notes

The damping coefficient c is calculated as lb-sec/in for .

Results Comparison

ResultsTargetMechanicalError (%)
Total Def Max (ξ = 0.5) Time = 0.20 sec1.15311.15440.113

Figure 109: Maximum Deformation vs. Time (damped)

Maximum Deformation vs. Time (damped)