Hello,I'm trying to find frequences and mode shapes of a cantilever beam with a tip mass!!!!! I used DQM but can't solve the system of equation because of boundry conditions can't reach the (F-omega^2*I)*phi=0 two solve the eigenvalue problem
thank you.
see the following reference
Evaluation of the bound states of a quantum system via the differential quadrature method: Extended to coupled differential equations
A. Zerarka, H. Saidi, S. Hassouni, N. Bensalah
https://booksc.xyz/book/3381165/63b2dd\
ON THE EIGENFREQUENCIES OF A CANTILEVER BEAM WITH ATTACHED TIP MASS AND A SPRING-MASS SYSTEM
M. Gürgöze
https://booksc.xyz/book/1952626/f01b27
Maged Gumaan Bin-Saad
thank you for your kindness and the help
I have a problem in details, My eqs. should be in this form (F-omega^2*Identity matrix)*phi=0 to find "omega" and "phi" . all the eqs are exactly in this form exept
this one:
-6.5*phi(3)-5.0*phi(4)-6.1*phi(5)-1.2*phi(6)-It*omega^2*(295.8*phi(3)+22674.1*phi(4)+2.7*phi(5)+5.8*phi(6))
Hi .
You have to discretize both motion equations and boundary equations to domain and boundary matrix. I don't have any information about your geometry and its dimension. I strongly recommend "Differential Quadrature and Its Application in Engineering" by Shu especially chapter 7.
Good luck
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