VM-WB-MECH-039

VM-WB-MECH-039
Transient Response of a Spring-Mass System

Overview

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

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 51: Schematic

Material Properties

Geometric Properties

E = 2 x 10¹¹ Pa

γ = 0.3

ρ = 0.25 kg/m³

k₁ = 6 N/m

k₂ = 16 N/m

m₁ = 2 kg

m₂ = 2kg

2 Blocks = 2 m x 2 m x 2 m

Length of L1 spring = 6 m

Length of L2 spring = 7 m

F₀ = 50 N

t_d = 1.8 sec

Analysis Assumptions and Modeling Notes

The step drop is modeled as F₀ = 50 N @ t = 1.8 sec and F₀ = 0 N @ t = 1.80001 sec.

Results Comparison

Results	Target	Mechanical	Error (%)
Y₁, m (@ t = 1.3s)	14.48	14.335	-1.0014
Y₂, m (@ t = 1.3s)	3.99	3.9148	-1.8847
Y₁, m (@ t = 2.4s)	18.32	18.51	1.0347
Y₂, m (@ t = 2.4s)	6.14	6.1942	0.8827