VM-WB-MECH-024

VM-WB-MECH-024
Harmonic Response of a Single Degree of Freedom System for Beams

Overview

Reference:Any basic Vibration Analysis book
Solver(s):

Ansys Mechanical

Analysis Type(s):Harmonic Analysis
Element Type(s):Beam

Test Case

Two collinear beams form a spring-mass system. The density of the longer beam is kept very low so that it acts as a massless spring and the smaller beam acts as a mass. The end vertex of the longer beam (acting as a spring) is fixed. A Harmonic force F is applied on the free vertex of the shorter beam in z direction. Both beams have hollow circular cross-sections, as indicated below.

  • Scenario 1: Damping ratio = 0

  • Scenario 2: Damping ratio = 0.05

Find the z directional deformation of the vertex where force is applied at frequency F = 500 Hz for the above scenarios with solution intervals = 25 and a frequency range of 0 to 2000 Hz. Use both Mode Superposition and Full Method.

Figure 27: Schematic

Schematic

Material Properties
MaterialE (Pa)νρ (kg/m3)
Spring1.1e110.341e-8
Mass2e1107.85e5
Geometric PropertiesLoading
Cross-section of each beam:
Outer radius = 10 mm
Inner radius = 5 mm
Length of longer beam = 100 mm
Length of shorter beam = 5 mm
Harmonic force F = 1 e6 N (z-direction)

Results Comparison

ResultsTargetMechanicalError (%)
Mode-SuperpositionMaximum z directional deformation without damping (m)4.11332 x 10-34.078 x 10-3-0.859
Maximum z directional deformation with damping (m)4.11252 x 10-34.0765 x 10-3-0.876
Full MethodMaximum z directional deformation without damping (m)4.11332 x 10-34.1132 x 10-3-0.003
Maximum z directional deformation with damping (m)4.11252 x 10-34.1022 x 10-3-0.251