Questions tagged [eigenvalue-analysis]

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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 "...
2
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1answer
30 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 ...
0
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0answers
25 views

H infinity control problem - changing eigenvalues of plant

I'm applying $H_\infty$ approach to control a system with a given input $u$, and I can measure and feedback position and velocity errors. The plant is described by the following transfer function $$...
6
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1answer
112 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
159 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
80 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
118 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
606 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
45 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
2k 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
618 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 ...