VM-WB-MECH-075

VM-WB-MECH-075
Harmonic Response of Two-Story Building under Transverse Loading

Overview

Reference:

Thomson, W. T. (1999). Theory of Vibration with Applications (3rd ed.). Example 6.4-1. (pp. 166).

Solver(s):

Ansys Mechanical

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

Test Case

A two-story building has two columns (2K and K) constituting stiffness elements and two slabs (2M and M) constituting mass elements. Find the y directional deformation frequency response of the system at 70 Hz on each of the vertices for the frequency range of 0 to 500 Hz using mode-superposition as the solution method.

Figure 101: Schematic

Schematic

Material Properties
MaterialE (Pa)νρ (kg/m3)
Block 22 x 10180.37850
Shaft 24.5 x 10100.351 x 10-8
Block 12 x 10180.315700
Shaft 19 x 10100.351 x 10-8
Geometric Properties
Block 1 and 2:
40 mm x 40 mm x 40 mm
Shaft 1 and 2:
20 mm x 20 mm x 200 mm
Loading
Force = -1 x 105 N (y direction)

Analysis Assumptions and Modeling Notes

The material of the columns is assigned negligible density to make them as massless springs. The slabs are allowed to move only in the y-direction by applying frictionless supports on all the faces of the slabs in the y direction. The end face of the column (2K) is fixed and a harmonic force is applied on the face of the slab (M) as shown in Figure 101: Schematic.

Set the solution intervals to 50. Add the frictionless support and fixed support in a modal system, and then link the modal system to a harmonic response system.

Note:  There are frictionless supports on eight faces of the geometry shown.

Results Comparison

ResultsTargetMechanicalError (%)
Maximum Amplitude for Vertex A (m)0.208530.211351.3523
Maximum Amplitude for Vertex B (m)0.0749020.0757211.0934