Questions tagged [eigenvalue-analysis]
16 questions
6
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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 and stiffness stay the same (I know, large…
mcluka
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4
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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
$\mathbf{M}\mathbf{\ddot{u}} + \mathbf{K}\mathbf{u} =…
marcoresk
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2
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1 answer
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 interest is not specific to cymbals, the video just…
ik2
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2
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1 answer
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 the participation factor and the pertaining point…
G.David
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2
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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 response is measured for this system. I would…
Chaitanya Krishna
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1 answer
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 of motion can be given (with $M$ the mass matrix,…
Quantumwhisp
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1
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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 the algebraic multiplicity must be equal to the…
th3gr3yman
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3 answers
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:
$$\mathbf{M{\ddot q}+{\Omega_c}G{\dot q}+{Kq}=F(t)}$$
$K$: stiffness symmetrical matrix
$M$: Mass…
spe4ker
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1
vote
1 answer
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{\dot…
spe4ker
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0
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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 mass participation for a frame structure.
I don't…
Graviton
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0
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Why does the state transition matrix of a Discrete-PI controller have a real eigenvalue at 1 when $K_I = 0$?
I am working with the state-space representation of a PI controller for a system with a 1-step delay. When the integral gain $K_I$ is set to zero, the controller effectively becomes proportional-only. Under these conditions, I notice that the state…
M lab
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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 is added to the x1/x1 element in the…
Joe
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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 the field of high performance scientific…
Carl Christian
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0
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1 answer
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, which is not giving me the results that I think…
spe4ker
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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 following formula:
$K-\omega^2M=0$
And I know how to do…
Graviton
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