Structural Dynamics by Central Difference & New Mark Linear Acceleration

Structural Dynamics by Central Difference & New Mark Linear Acceleration

It is usually the goal of classical dynamic analysis to describe a known system and determine that systems' response to a given excitation. The goal of system identification is to determine the properties of a system from the known response of that system to a given excitation. We have achieved the preceding goal in two different ways in the previous two sections. In this section we will perform the latter procedure (Bathe, 1982).

 There are many different methods of system identification. One method that is familiar in the mechanical and control engineering fields and is relatively simple is the Auto Regressive with exogenous input or ARX approach. This method will be introduced in section 4.4 after some preliminary subject matter is addressed. The assignment at the end of this section involves using the built-in ARX function within Matlab's system identification toolbox. If that toolbox is not available to the students, then this assignment cannot be completed.

 

Fourier Transforms

 The first step in system identification is to take an in depth look at the data one is given and obtain an idea of what to expect. The best way to do this is to take the Fourier transform of the data to express it in frequency domain (Newmark, 1959). This will give you an initial idea of the modal frequencies of the system. The direct Fourier transform of a given function f(t) is given as,

The inverse Fourier transform of the complex-valued function F(iw) is then given as,

 

 This set of two equations is known as the continuous Fourier transform pair. For discrete functions, such as our earthquake ground motion, a discrete Fourier transform (DFT) is employed.

                     &        

 

Where, N = number of data points

           

           

Transfer Function

 When dealing with structural systems, it is convenient to ...