Questions tagged [eigenvalue-analysis]

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1answer
58 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 ...
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0answers
45 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 ...
0
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0answers
31 views

Modal analysis in Abaqus AMS solver

I have a huge model for which I am performing modal analysis. Abaqus fails to solve with Lanczos solver and hence I use AMS solver, which successfully computes the solution. But since AMS solver ...
2
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1answer
36 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 ...
-1
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1answer
16 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 "...
2
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1answer
145 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 ...
6
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1answer
194 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 ...
0
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1answer
198 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, ...
4
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2answers
103 views

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 $\...
1
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3answers
168 views

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: $$\mathbf{M{\ddot q}+{\Omega_c}G{\dot q}+{Kq}=F(t)}$$...
1
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1answer
985 views

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{\...
0
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1answer
46 views

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 ...
1
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0answers
3k views

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 ...
0
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1answer
961 views

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 ...