Modal and Harmonic Analysis of a Single Degree of Freedom

Isometric view of the Single Degree of Freedom Spring Mass system.

Boundary conditions of the spring mass system in Modal analysis.

This is an assignment for my ME-441 Computer Simulation and Analysis class. In the Computer Simulation and Analysis class ANSYS Workbench and Discovery AIM were used extensively to simulate. Instructions were provided, and sometimes the models, either from Creo Parametric or SolidWorks, were provided as well. Some assignments however need the objects to be modelled from scratch or modified before hand.

The assignment

In this assignment, a harmonic analysis is conducted on a single degree of freedom spring mass system using ANSYS Modal and Harmonic Response. The assignment is to find the natural frequency and the harmonic response from 0 -100 Hz.

The mass (m) of the block is 10 Kg, the spring constant (k) (or longitudinal stiffness in ANSYS) is 400,000 N/m, the damping ratio is 0.02 (c), and the force (F_o) being applied at the top of the block is 1,000 N.

The theoretical calculations goes:

Natural frequency

w_n = (k/m)^(1/2) = (400,000/10)^(1/2) = 200 rad/s

f = w_n/2*pi = 200 rad/s / 2*pi = 31.831 Hz

When excitation frequency (w) is equal to the natural frequency (w_n), then resonance occurs.

Amplitude

Y = (F_o/k)*(1/([1 - (w/w_n)^2]^2 + [2*c*(w/w_n)]^2)^(1/2)) = (1,000/400,000)*(1/([1 - (200/200)^2]^2 + [2*0.02*(200/200)]^2)^(1/2)) = 0.0625 m

When using Modal analysis, the mass block was set as a frictionless support and the base plate was set as a fixed support. During the Harmonic Response analysis, a force of -1000 N in the y-direction is applied at the top of the mass block.

Results