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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). ...
user3716267's user avatar
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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 ...
Quantumwhisp's user avatar
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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 ...
Joe's user avatar
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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 ...
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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 ...
Carl Christian's user avatar
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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 ...
G.David's user avatar
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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 "...
shoggananna's user avatar
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1 answer
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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 ...
th3gr3yman's user avatar
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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 ...
mcluka's user avatar
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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, ...
spe4ker's user avatar
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4 votes
2 answers
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Strategies for cable vibration: eigenvalues are suitable?

This is a theoretical question. It is known that in "classic" vibration analysis natural frequencies can be found by solving an eigenvalue problem, from the undampened vibration equation like $\...
marcoresk's user avatar
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What's the difference of using different state-space forms for solving eigenvalue problem?

I have a set of equations of motion describing a planetary gear train of 18 DoF (sun, 3 planets, carrier and ring), they have the general form of: $$\mathbf{M{\ddot q}+{\Omega_c}G{\dot q}+{Kq}=F(t)}$$...
spe4ker's user avatar
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How do I represent equations of motion of a dynamic system in State Space?

I'm going through some vibration theory and I need to represent the equations in state space for vibration control. The main forced general equation of motion is: $$\mathbf{M{\ddot q}+{\Omega_c}G{\...
spe4ker's user avatar
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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 ...
Graviton's user avatar
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How to get mass normalized mode shapes?

I have an MDOF system with 4 degrees of freedom with forced input at one of the dof (4th dof)(it is a sinusoidal wave with a particular frequency expected to be generated using a shaker); displacement ...
Chaitanya Krishna's user avatar
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The distinction between lateral mass participation and vertical mass participation

Refer to the chapter 14 of the Wilson book "Dynamic Analysis of structures": calculation of stiffness and mass orthogonal vectors. The table 14.6 shows the lateral mass participation and vertical ...
Graviton's user avatar
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