In dynamic response analysis we typically look to the eigenv

In dynamic response analysis, we typically look to the eigenvalues of the system to describe the natural modes of the system. For stable systems, we know that these modes include exponential decay, meaning all of the modes eventually disappear from the system response, and it is based 011 these transient modes that we describe the response characteristics. How is frequency response analysis different from this approach?

Solution

In static studies loads are calculated as constant. Due to this assumption, static studies often overlook damping forces as well as inertial forces. There are several cases where the measurement of loads is not constant or they change with frequency or time.

Dynamic response study method is applied in these situations and the method/result of response dynamics analysis is applied here. In general where frequency of a load is calculated higher than 1/3 of the basic frequency, the method of dynamic response analysis is applied there.

Frequency response is the quantitative measure of the outputspectrum of a system or device in response to a stimulus, and is used to characterize the dynamics of the system. It is a measure of magnitude and phase of the output as a function of frequency, in comparison to the input

Disadvantages:

Requires a transfer function model (poles and zeros); Difficult to infer all performance metrics; Hard to determine response to steady-state (sinusoids) Hard to infer stability margins

when the transfer function fro a component is unknown, the frequency response ca defined experimentally and a approximate expression transfer function can be obtained from the graph of the experimental data

The nyquist stability criterion enables one to investigate both the absolute and relative stabilities of linear time-variant closed-loop systems from their open-loop frequency-response characteristics

For stable systems, the input is a sine wave the steady state output is alsoa sine wave with same frequency but with different amplitude and phase change