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4 votes
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Strategies for cable vibration: eigenvalues are suitable?

Mathematically, an eigenvalue analysis assumes the modal displacements are infinitesimally small, so the change in stiffness in the cable caused by the vibration is a second order effect which can be ...
alephzero's user avatar
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3 votes
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How do I represent equations of motion of a dynamic system in State Space?

Karlo mentioned to use the state space of $[q,\dot{q}]^T$ this allows you to write the system as a first order differential equation of state space. If $X$ were the state space, you could write $\dot{...
Orion Yeung's user avatar
2 votes
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What's the difference of using different state-space forms for solving eigenvalue problem?

Regarding the different state space formulations. First, M might not be invertible. In many cases it will be invertible, but sometimes it will not be. In your specific case, this would correspond ...
Daniel K's user avatar
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2 votes

What's the difference of using different state-space forms for solving eigenvalue problem?

For any sinusoidal motion, the $\mathbf{q}$ really represents the motion $\Re(\mathbf{q}\,e^{i \omega t})$ in the time domain. $\mathbf{q}$ is complex because in general, the different elements of the ...
alephzero's user avatar
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2 votes
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Are the modal participation factors bounded for shock response spectrum analysis?

In the section "The Multiple DOF System" the Comsol document says It has been assumed that the mass matrix normalization of the eigenmodes is used and that the damping matrix can be ...
alephzero's user avatar
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2 votes

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

I assume you will be doing this in a software, matlab or Abaqus for example, it’s not particularly easy thing to do with your given info, but. Perhaps this example method will help Abaqus Infos at ...
DrMrstheMonarch's user avatar
2 votes

Stability with eigenvalues' real part equal to zero

If the algebraic multiplicity of an eigenvalue is greater than the geometric multiplicity, then the system matrix is not diagonalizable and there are vectors which are not linear combinations of the ...
alephzero's user avatar
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1 vote

Vibration following an impact

Regarding your first question IMHO eigenvalue analysis is appropriate and valid as long as the material is within the elastic range. Also another misconception is that, the application of eigenvalue ...
NMech's user avatar
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1 vote

What's the difference of using different state-space forms for solving eigenvalue problem?

You basically want to solve for the homogeneous solutions of the system $$ \textbf{M}\, \ddot{\textbf{q}} + \textbf{D}\, \dot{\textbf{q}} + \textbf{K}\, \textbf{q} = \textbf{0}. $$ It can be shown ...
fibonatic's user avatar
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1 vote
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Undamped forced vibration for a multi dof system

The code in your OP seems to be for a 2 DOF system not a 24 DOF system. You could check that by printing the "frequencies" variable from your eigensolution. The reason you are not getting anti-...
alephzero's user avatar
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1 vote

Strategies for cable vibration: eigenvalues are suitable?

The equation you showed is an ordinary differential equation. It works for solving natural frequencies of discrete systems (ie lumped rigid masses connected by massless springs). Here you have a ...
Daniel K's user avatar
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1 vote
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Analytical solution for wall eigenvalue analysis

Your "wall" would be referred as a "plate" in the technical literature. The eigenvalue problem for a plate is significantly more complicated than a beam, but similar ideas. I would suggest that you ...
Daniel K's user avatar
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1 vote

The distinction between lateral mass participation and vertical mass participation

From my understanding, mass participation for each mode is determined by the general mass and the eigenvector of the mode, and eigenvector of the mode usually consists of contribution from all the ...
alephzero's user avatar
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