VM-WB-MECH-014

VM-WB-MECH-014
Harmonic Response of a Single Degree of Freedom System

Overview

Reference:	Any basic Vibration Analysis book
Solver(s):	Ansys Mechanical
Analysis Type(s):	Harmonic Analysis
Element Type(s):	Solid

Test Case

An assembly where four cylinders represent massless springs in series and a point mass simulates a spring mass system. The flat end face of the cylinder (Shaft 1) is fixed. Harmonic force is applied on the end face of another cylinder (Shaft 4) as shown below.

Find the z directional Deformation Frequency Response of the system on the face to which force is applied for the frequency range of 0 to 500 Hz for the following scenarios using Mode-Superposition. Solution intervals = 20.

Scenario 1: Damping ratio = 0
Scenario 2: Damping ratio = 0.05

Figure 14: Schematic

Material Properties
Material	E (Pa)	ν	ρ (kg/m³)
Shaft 1	1.1 x 10¹¹	0.34	1 x 10^-8
Shaft 2	1.1 x 10¹¹	0.34	1 x 10^-8
Shaft 3	4.5 x 10¹⁰	0.35	1 x 10^-8
Shaft 4	4.5 x 10¹⁰	0.35	1 x 10^-8

Geometric Properties

Loading

Each cylinder:

Diameter = 20 mm

Length = 50 mm

Force = 1 x 10⁷ N (Z-direction)

Point Mass = 3.1044 Kg

Results Comparison

Results	Target	Mechanical	Error (%)
Maximum Amplitude without damping (m)	0.14	0.1412	0.5698
Phase angle without damping (degrees)	180	180	0.000
Maximum Amplitude with damping (m)	0.14	0.14078	0.557
Phase angle with damping (degrees)	175.6	175.58	-0.0114