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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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Improved Method for In-situ Elastic Constants of Isotropic and Orthotropic Composite Materials Using Plate Modal Data With Trimodal and Hexamodal Rayleigh Formulations

TL;DR: In this paper, the authors presented a method for deriving the four independent elastic constants (longitudinal and transverse Young's moduli, in-plane shear modulus and major Poisson's ratio) of an orthotropic material from resonance data obtained in a modal analysis of a freely-supported plate made out of the material.
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Energy Dissipation Pathways in Few-Layer MoS 2 Nanoelectromechanical Systems

TL;DR: The dominant energy dissipation pathways in few-layer MoS2 nanoelectromechanical systems are identified, and a room temperature thermomechanical-noise-limited force sensitivity of ~8 fN/Hz1/2 is demonstrated that remains effectively constant over the course of more than four years.
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Toward Higher-Order Mass Detection: Influence of an Adsorbate's Rotational Inertia and Eccentricity on the Resonant Response of a Bernoulli-Euler Cantilever Beam.

TL;DR: A new theoretical model is derived that permits a detailed examination of how the resonant characteristics of a cantilever are influenced by a particle (adsorbate) attached at an arbitrary position along the beam’s length, suggesting the potential for “higher-order” nanobeam-based mass detection methods by which the multi-mode frequency response reflects not only the adsorbate”s mass but also important geometric data related to its size, shape, or orientation.
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A nonlinear state-dependent model for vibrations excited by roughness in rolling contacts

TL;DR: In this article, a state-dependent method to model contact nonlinearities in rolling contacts is proposed by pre-calculation of contact stiffness and contact filters as functions of vertical relative displacement, a computationally efficient modelling approach based on a moving point force description is developed.
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The effect of pinhole defect on vibrational characteristics of single walled carbon nanotube

TL;DR: In this article, the effect of pinhole defects on the dynamic characteristics of carbon nanotubes is investigated using continuum mechanics and the molecular structural mechanics approach, and the shift of the principal frequency of the nanotube with number of pinholes on the length is observed and analyzed.