Hi,
I have some problems with mode shapes. First of all, I have eigenvectors and eigenvalues of the structure (state space solution) which has 4 elements and 18 DOF. Now, I want to create animations for every mode freqencies.
How can I set up X, Y, Z free response functions with my complex eigenvectors?
Dear Yalcin
first, the absolute of the complex function must be calculated. then, MATLAB can consider infinite arguments for a parameter. for example u(x,y,z,t,.....). Therefore, you can calculate free response in each mode for animation purpose.
best regards
Panji
You should have complex-valued eigenmodes, which show the modal displacements and phase shifts regarding a reference. You basically need a geometry in 3D space, to which add the scaled motion vector, then run the animation and you'll appreciate the complex-valued pairs you have. In my website you can see something made in that way, but not with MATLAB, just with algebra and C-Language + OpenGL libraries.
Hope this helps,
my regards,
Alessandro.
Dear Yalcin
first, the absolute of the complex function must be calculated. then, MATLAB can consider infinite arguments for a parameter. for example u(x,y,z,t,.....). Therefore, you can calculate free response in each mode for animation purpose.
best regards
Panji
Dear Yalcin,
According to modal analysis theory, every eigenmode of your structure corresponds to an equivalent single degree of freedom system (SDOF), the eigenfrequency of which is equal to the eigenfrequency of the corresponding eigenmode.
So, all you have to do is a dynamic time-integration analysis of the equivalent SDOF system, take its dynamic response, and multiply the displacements of all the degrees of freedom of the eigenmode (18 dof) with the calculated response. Thus, you obtain the dynamic response of the specific eigenmode in this way and then you can easily make an animation of it by plotting its shape with respect to time.
The superposition of the dynamic histories of all the eigenmodes will give you the overall system response, provided that it remains elastic.
I hope this helps,
George
Try to obtain the eigensolution from matrix A of state equation ($\dot{X} = \bar{A} X + \bar{B} U$, where $X^T = \left[ x \dot{x} \right]$. Using eig (MatLab), you will obtain the eigenfrequencies and eigenmode of a MDoF Damped Structure.
Thank you for all response. However, I have unsymmetrical space state matrix which leads to complex eigenvectors. Therefore, its not easy to set up mode shapes. My target is to see the orbit or the rotor while it's rotating.
Alessandro Zanarini, i couldn't find your document. Can you share a link?
Mehdi Panji Do you mean?
X(t)= (C0)*(e^(Sigma*t))*(abs(Eigenvectors))*cos (wdt-O)
and set Y(t) and Z(t) --> plot3 (x,y,z) in loop which depends on time
I am really not sure about abs(Eigenvectors) parts
Marcus V. G. de Morais I couldn't understand your respond.
I am still open to more responds.
Dear Yalcin,
here is my research page at Bologna University (http://diem1.ing.unibo.it/personale/zanarini/Zanarini_ricerca_EN.htm), in which you can find examples of full field operational deflection shapes as complex-valued vectors, the same form of data you get out of an eigenproblem solution in state space.
See also my profile here in RG, where I added 2 mp4 videos of mode shape animation, one from Experimental Full Field Modal Analysis and the other from Model Updating by means of Full Field modal datasets.
You can download all of them, please refer to them with the DOI code.
Have a nice day,
Alessandro
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