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Formulas for natural frequency and mode shape

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The article was published on 1979-01-01 and is currently open access. It has received 2002 citations till now. The article focuses on the topics: Natural frequency & Normal mode.

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Vibrational analysis of single-walled carbon nanotubes using beam element

TL;DR: In this article, the vibrational analysis of single-walled carbon nanotubes (SWCNTs) is performed using a finite element method (FEM) using three-dimensional elastic beams and point masses and the beam element elastic properties are calculated by considering mechanical characteristics of the covalent bonds between the carbon atoms in the hexagonal lattice.
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Transverse vibration of single-layer graphene sheets

TL;DR: In this paper, the vibrational properties of zigzag and armchair single-layer graphene sheets (SLGSs) using the molecular mechanics (MM) approach have been investigated and the natural frequencies of vibration and their associated intrinsic vibration modes are obtained.
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Vibration characteristics of FGM circular cylindrical shells using wave propagation approach

TL;DR: In this article, the wave propagation approach is employed to study the vibration characteristics of functionally graded material circular cylindrical shells, and a theoretical analysis of shell natural frequencies are conducted for various boundary conditions.
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Modal analysis of pile-supported structures during seismic liquefaction

TL;DR: In this article, the effects of liquefaction on modal parameters (frequency and damping) of pile-supported structures were investigated in a shaking table where the soil surrounding the pile liquefied because of seismic shaking.
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Effect of ignition position on vented hydrogen–air explosions

TL;DR: In this article, the authors investigated the effect of the ignition position on explosion venting of hydrogen-air mixtures with equivalence ratios ranging from 0.6 to 5.0.