Modal Analysis_Natural frequency

Dear colleague,

 I thing that you should fix your attention in not to the probability of coinciding the frequence of the earthquake and the natural form, but to the great difference between the maximal amplitudes of the natural forms - the higher the form is, the smaller its amplitudes are. Thus the probability of rising of unbearable cracks strongly reduces. That's the reason of not counting the higher forms in modal analysis.

Dear prksh,The correct procedure to analyse your structure against earthquake (or other dynamic loading) is to obtain firstly the (Fast) Fourier spectrum of the earthquake under consideration. Each earthquake time-history is virtually the sum of a specific number of harmonic excitations (usually sines), each of which has selected amplitude and frequency, so that if all these excitations are summed together, they will produce the actual time history of the imposed earthquake. In the Fourier spectrum one can see for a specific frequency, the amplitude that corresponds to the respective harmonic component. Higher amplitude means higher distress for the structure, so you have to select those frequency ranges in which the amplitudes are high and to ignore the remaining spectrum. Assume that the selected frequency spectrum is [a,b].

To proceed, you have to calculate those eigenfrequencies of the structure, which fall into the above range, namely if the inequality a<fn<b is valid, in which fn is the nth eigenfrequency of your structure. Then you have to impose a dynamic loading which consists of only the sines corresponding to eigenfrequencies fn. The final amplitude of the motion of the structure will result from a suitable summing method (for this see Chopra or Clough & Penzien "Dynamics of structures" (two books with the same title...)). You can use modal analysis which is more accurate, or special analysis procedures (such as the static correction method or the mode acceleration superposition method).

Remember, all the above are correct provided that linear elasticity is considered. If this is not true, then the calculation has to be done in different ways. Finally, a major factor is the kind of damping you use.

I hope I helped you a bit, but if you have any question you can contact me via email: gpapazafeiropoulos@yahoo.gr