# Questions tagged [eigenvalue-analysis]

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### Why do Eigenmodes of a rigid system also diagonalize the Mass and the stiffness matrix seperately?

To set up my question, I will briefly recap the derivation that is usually given for eigenmodes of a system: If there is no force present, and a body is described by a vector $u$, then the equations ...
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### Interpreting eigenvalues of non-normalized covariance matrix in system identification

Cross-posted from physics stackexchange Summary: Eigenvalues of a "non-normalized" covariance matrix of time-series measurements from a linear system have units of Action (energy * time). ...
201 views

### How to add point mass in 3D mass matrix

I have a eigenfrequency simulation $M * \ddot{\vec{x}} + K * \vec{x} = \vec{0}$ and want to add point masses to certain nodes. The only example I have is a 1D matrix where all of the mass at node 1 ...
86 views

### Vibration following an impact

This high-speed video shows a cymbal's response to impact. I'm interested in how the observed vibration relates to the modes and frequencies that an eigenvalue vibration analysis would predict. My ...
73 views

### Large scale nonsymmetric standard and generalized eigenvalue problems in engineering

I apologize if this is not the right forum for my question, but I cannot think of better place to reach a large number of engineers within a short time span. Question: I am a mathematician working in ...
129 views

### Are the modal participation factors bounded for shock response spectrum analysis?

Recently dug myself into the theory of shock response spectrum analysis, but one thing is not clear for me. The theory says that the peak response of the structure can be calculated as the product of ...
37 views

### Construct "Modal Coordinates Time History" from transfer function and test accel-time data

I have a query regarding the calculation of the so called “Modal Participation Factor time signal” from a combination of a) transfer functions (amplitude and phase for each eigenmode) obtained from "...
1 vote
748 views

### Stability with eigenvalues' real part equal to zero

I know, from Lyapunov criteria, that a system is stable (not asymptotically) if the system has eigenvalues with negative real part or it has eigenvalues with real part equals to zero, but in this case ...
378 views

### Elastic (Young's) Modulus relation to the Eigenfrequency

I would like to compare the shape of the frequency spectrum of a plastic and aluminium component. Now if we assume that the plastic and aluminium component only differ in the material, while the mass ...
327 views

### Undamped forced vibration for a multi dof system

I'm trying to determine the amplitude vs the excitation frequency of a multi dof dynamic system. I'm very confused from reading different methods, although I understand there's a very general one, ...
147 views

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### Analytical solution for wall eigenvalue analysis

I have a wall with the bottom end of it fixed to the ground. I want to derive from first principles the frequencies and mode shapes of the structure. I know that I will need to start with the ...