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Nonlinear vibration of beams and rectangular plates

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TLDR
In this paper, einfluss von Vorspannungen auf die freien und erzwungenen nichtlinearen Schwingungen von Balken and rechteckigen Platten wird mittels einer einfachen Erweiterung der Losungen fur Falle ohne VorsPannung untersucht.
Abstract
Der Einfluss von Vorspannungen auf die freien und erzwungenen nichtlinearen Schwingungen von Balken und rechteckigen Platten wird mittels einer einfachen Erweiterung der Losungen fur Falle ohne Vorspannung untersucht. Es wird eine einzige Koordinatenfunktion benutzt; es werden einfach aufgelegte und eingespannte Falle betrachtet; und die Diskussion wird auch auf den uberkritischen Bereich ausgedehnt.

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Electrostatically driven vacuum-encapsulated polysilicon resonators part II. theory and performance

TL;DR: In this article, the design, modelling and performance characteristics of electrostatically driven vacuum-encapsulated polysilicon resonators are addressed, and an expression for the pull-in voltage of a beam is given.
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Tuning nonlinearity, dynamic range, and frequency of nanomechanical resonators

TL;DR: In this article, an electrostatic mechanism for tuning the nonlinearity of nanomechanical resonators and increasing their dynamic range for sensor applications is explored, and a theoretical model is developed that qualitatively explains the experimental results and serves as a simple guide for design of tunable nano-chanical devices.
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Dynamic range of nanotube- and nanowire-based electromechanical systems

TL;DR: In this article, the authors derived the equations governing this behavior and found a strong dependence on the aspect ratio on the dynamic range of a nanomechanical resonator with high aspect ratio.
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Micro resonant force gauges

TL;DR: A review of micro resonant force gauges is presented in this article, where a theoretical description is given of gauges operating in a flexural mode of vibration, including a discussion of non-linear effects.
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Initial-boundary value problems for an extensible beam

TL;DR: In this paper, the authors discuss certain initial-boundary value problems for the nonlinear beam equation and present a solution to the first-order value problem for the beam equation.
References
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Journal ArticleDOI

The Effect of an Axial Force on the Vibration of Hinged Bars

TL;DR: In this paper, it was shown that the vibration of an extensible bar, carrying no transverse load and having the ends fixed at the supports, causes an axial tensile force with a period equal to the half-period of the vibration.
Journal ArticleDOI

Influence of Large Amplitudes on Flexural Vibrations of Elastic Plates

TL;DR: In this paper, approximate solutions for the nonlinear bending vibrations of thin plates are presented for the cases of rectangular and circular plates subjected to various boundary conditions, and the effects of large amplitudes on both the free and forced vibrations are clarified.
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