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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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Vibration characteristics of functionally graded cylindrical shells under various boundary conditions

TL;DR: In this article, the vibration of a functionally graded cylindrical shell made up of stainless steel and zirconia is studied and its properties are graded in the thickness direction of the shell according to volume fraction power law distribution.
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Modal identification of simple structures with high-speed video using motion magnification

TL;DR: In this article, motion magnification has been developed for visualizing exaggerated versions of small displacements with an extension of the methodology to obtain the optical flow to measure displacements, which can be extended to modal identification in structures and the measurement of structural vibrations.
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The design, fabrication and evaluation of a MEMS PZT cantilever with an integrated Si proof mass for vibration energy harvesting

TL;DR: In this article, a unimorph PZT cantilever with an integrated Si proof mass, designed for low vibration frequency and high vibration amplitude environment, was designed for MEMS power generators, with an optimal resistive load of 6 kΩ from 2g (g = 9.81 m s−2) acceleration at its resonant frequency of 461.15 Hz.
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Piezoelectric buckled beams for random vibration energy harvesting

TL;DR: In this paper, a thin piezoelectric axially loaded beam is theoretically modelled and experimentally investigated under wideband random vibrations, and the results show that the device exhibits superior power generation over a large interval of resistive load, with gains up to more than a factor of ten compared to the unbuckled state.
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Bottom-up assembly of large-area nanowire resonator arrays

TL;DR: Bottom-up nanowire assembly can offer a practical alternative to top-down fabrication for sensitive chip-based detection and is introduced to fabricate large-area nanoelectromechanical arrays each having over 2,000 single-nanowire resonators.