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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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Numerical Simulation of Modal Vibration Response of Wavy Carbon Nanotubes

TL;DR: In this paper, the effect of waviness and aspect ratio on the modal vibration response of CNTs was investigated using the finite element (FE) approach and the benchmarking of the developed models against results from other models and experiments.
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Vibrations of Circular Cylindrical Shells With General Elastic Boundary Restraints

TL;DR: In this article, a general solution method is presented for the vibration analysis of cylindrical shells with elastic boundary supports, and the modal characteristics of elastically restrained shells are discussed against different supporting stiffnesses and configurations.
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Vibration analysis of supported thick-walled cylindrical shell made of functionally graded material under pressure loading

TL;DR: In this article, a study on the vibration of a supported thick-walled cylindrical shell made of functionally graded material (FGM) subjected to pressure loading is presented.
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Efficient modal dynamic analysis of flexible beam–fluid systems

TL;DR: In this article, an efficient simplified method to determine the modal dynamic and earthquake response of coupled flexible beam-fluid systems and to evaluate their natural vibration frequencies is proposed, which can be easily implemented in day-to-day engineering practice, as it constitutes an efficient alternative solution considering the fluid-structure modeling complexities and related high expertise generally involved when using advanced finite elements.
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Determination of the optimal span length to minimize resonance effects in bridges on high-speed lines

TL;DR: In this paper, the authors revisited the creation and cancellation of the dynamic resonance phenomenon that occurs in bridge structures on high-speed lines when crossed by wheel loads and derived the dependency of the cancellation phenomenon on the mode shape.