08-22-2009, 12:51 PM
(08-22-2009, 10:37 AM)fashion Wrote: essenza, thanks for your answer, the main reason for my question is to know the fund. period of the structure so as to manually calculate the seismic forces (i.e. base shear) so as to hand check the results from etabs. I know i can aproximate the period with the formulas, but eigenmode analysis is kind of precise.
whoa...stop at that, eigen analysis in finite element is approximate..the finite element itself is approximate. Most of the shape function for finite elements is polynomial which only satisfy deformation of the element under static load. In vibration problem, the exact shape function is usually trancendent, that's why if you model a structure using finite element for vibration problem (eigen analysis etc), all structural analysis program requires meshing to capture a "correct" mode shape (even after meshing it is still approximate:P). You may wonder so why we never mesh or divide frame member (beam, column etc) in highrise building structure, well don't get it wrong you actually mesh it with the floor, imagine your structure as a big cantilever tower. People who study fluid, aerodynamics and buckling especially for aerospace industry that i know only use finite element as comparison. They use exact vibration program, one of them called VICONOPT and being used by NASA to analyze exact vibration problem. You may now understand why finite element researchers compete to find the finite element "holy grail" either creating adaptive meshing or increase the polynomial degree in the shape function or number of dof in the element because they need to cope with vibration problem.
The only problem with exact vibration is the goddamn mathematic while with finite element is of course computer speed and storage because the solver for large number of equation is already available. I'm not an expert in either of these two method but i know there are war between this exact and approximate method in journal/paper.