Frequency & Eigenvalue from dynamic eqn

AI Thread Summary
To find the natural period of a vertical cantilever beam, the user has formulated the equation [M]-w^2[K] = 0 using global mass (M) and stiffness (K) matrices, which are square symmetric but not diagonal. A numerical eigensolution is necessary for solving this characteristic polynomial, with various numerical analysis packages available, including MatLab. The user has identified that transforming the matrix into diagonal form simplifies the solution process. This approach is essential for determining the cyclic frequency (w). The discussion emphasizes the importance of numerical methods in structural dynamics analysis.
rk81
Messages
2
Reaction score
0
Hi, i am trying to find the natural period of a vertical cantilever beam which is fixed at bottom and free at other end., i worked out the global M & K matrices and i have the eqn in the form [M]-w^2[K] = 0, the M & K are not diagonal matrices, but square symetric matrices of rank 6. i understand that w2 is the cyclic frequency, how do i solve this characteristic polynomial the matrix way.. thanks in advance,
 
Engineering news on Phys.org
You need a numerical eigensolution, such as is available in many numerical analysis packages (NAG, EisPack, etc.). I think MatLab probably has one as well, and there are many other sources as well.
 
thanks, i think i found the answer.. i need to make the matrix to diagonal form, and then the soln is simple.
 

Thread 'A practical way to vaporize fuel for high MPG?'

Here's a video by “driving 4 answers” who seems to me to be well versed on the details of Internal Combustion engines. The video does cover something that's a bit shrouded in 'conspiracy theory', and he touches on that, but of course for phys.org, I'm only interested in the actual science involved. He analyzes the claim of achieving 100 mpg with a 427 cubic inch V8 1970 Ford Galaxy in 1977. Only the fuel supply system was modified. I was surprised that he feels the claim could have been...
View full post »
Thread 'Turbocharging carbureted petrol 2 stroke engines'

Thread 'Turbocharging carbureted petrol 2 stroke engines'

Hi everyone, online I ve seen some images about 2 stroke carbureted turbo (motorcycle derivation engine). Now.. In the past in this forum some members spoke about turbocharging 2 stroke but not in sufficient detail. The intake and the exhaust are open at the same time and there are no valves like a 4 stroke. But if you search online you can find carbureted 2stroke turbo sled or the Am6 turbo. The question is: Is really possible turbocharge a 2 stroke carburated(NOT EFI)petrol engine and...
View full post »

Similar threads

4DOF Spur Gear System - Eigenvalues not corresponding with the Eqns?
Replies
4
Views
3K
A First eigenvalue not matching, but all others are
Replies
8
Views
2K
I Find Practical Resonance Frequencies in Linear Differential Equations
Replies
1
Views
3K
Modal mass and kinetic energy in FEM modal analysis
Replies
3
Views
4K
A Eigenvalue problem: locating complex eigenvalues via frequency scan
Replies
13
Views
2K
Why are the natural frequencies of a clamped-clamped beam smaller than usual?
Replies
2
Views
2K
I Is a symmetric matrix with positive eigenvalues always real?
Replies
8
Views
2K
Challenge Math Challenge - July 2023
2
Replies
69
Views
8K
Dot diagrams and Jordan canonical forms
Replies
3
Views
1K
Help finding the vibrational frequencies and normal modes
Replies
11
Views
2K

Hot Threads

Recent Insights

Back
Top