Frequency Domain Anaalysis

Seismic Analysis Of Structures
                             

THEORY
Civil engineering is known to be the mother of all engineering branches. Since the era of Indus valley civilization, civil engineering techniques have been burgeoning.
In the 21st century world, we get to see perfect examples of the limit of civil engineering. In fact there is no limit, there is no end to these innovations. Today what we call civil engineering marvels, are actually the result of spotless construction skills hybridized with the knowledge of safeguarding the structures from natural calamities(earthquake, tsunami, tornado, floods, etc).
Of all the natural calamities, earthquakes tend to be the most devastating. In order to protect our structures from the rage of earthquakes, we need to design them in such a way that our structures can take the horizontal ground acceleration and the combination of several irregular excitations caused by it without any damage.
This situation calls for a Frequency Domain Analysis of structures. Here we take into account the ground acceleration produced by any earthquake and analyze the reaction of the structure to it.
The above problem can be easily solved if we convert we analyze the ground acceleration obtained in frequency domain. So we convert the data from time domain to frequency domain. This procedure can be simplified with the help of a tool in MATLAB known as ‘fft’. it corresponds to Fast Fourier Transform. This command converts the (ground acceleration vs time) i.e.,[input] to (real no. vs frequency) + (complex no. vs frequency).
After the above operation we can obtain the plots of (phase angle vs frequency) & (magnitude of ‘fft’ vs frequency). Now in order to get the desired output (preferably displacement), we have to multiply a factor (frequency response factor or transfer function) with the input.

The equation of motion for the system can be written as:
mx + cx + kx = p(t)

p(t) is Fourier synthesized using FFT. If...