4 Dynamic Analysis |
4 Introduction
The analysis of dynamic systems difers from the static systems in theat inertia forces have to be considered in addition to other forces.
There are 3 main types of dynamic analysis which are of interest:
i) Modal analysis giving the modal shapes and frequencies of a component or structure. These frequencies must be avoided by machinery.
ii) Sinusoidal response. This is the steaddy state response of the system to a regulary fluctuating forcing function.
ii) Transient response. This is the response of a asystem to a short term forcing function such as an impact or an earthquake.
For many mechanical systems the damping is fairly low (often only 2 - 3% of critical) and has little effect on the accuracy of many of the important results. For most of this analysis the damping is ignored.
4.1 Modal Analysis |
4.1.1 Considering the two degree of freedom configuration shown below:
4.1.2 Eigenvalues
if
4.1.5 Modal Matrix
For previous example:
The transformation used is:
Lumped Mass:
10th September 2012.