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.