VM-WB-MECH-080

VM-WB-MECH-080
Transient Response of a Spring-Mass System

Overview

Reference:	Vierck, R. K. (1979). Vibration Analysis (2nd ed.). New York, NY: Harper & Row Publishers. (sec. 5-8)
Solver(s):	Ansys Mechanical
Analysis Type(s):	Transient Dynamic Mode-Superposition Analysis
Element Type(s):

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 105: Schematic

Material Properties	Geometric Properties	Loading
k₁ = 6 N/m k₂ = 16 N/m m₁ = 2 Kg m₂ = 2 Kg	--	F₀ = 50 N t_d = 1.8 sec

Material Properties

Geometric Properties

k₁ = 6 N/m

k₂ = 16 N/m

m₁ = 2 Kg

m₂ = 2 Kg

F₀ = 50 N

t_d = 1.8 sec

Results Comparison

Results	Target	Mechanical	Error (%)
Y₁ , m (@ t = 1.3s)	14.48	14.442	-0.2624
Y₂ , m (@ t = 1.3s)	3.99	3.9618	-0.7067
Y₁ , m (@ t = 2.4s)	18.32	18.638	1.736
Y₂ , m (@ t = 2.4s)	6.14	6.2524	1.8306