Journal ArticleDOI
On the non-linear vibrations of a circular membrane☆
David H. Y. Yen,T.W. Lee +1 more
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In this paper, free axisymmetric vibrations of a stretched circular membrane are studied using a membrane theory consisting of a pair of non-linear partial differential equations coupled between the transverse and radial displacements of the membrane.Abstract:
Free axisymmetric vibrations of a stretched circular membrane are studied using a membrane theory consisting of a pair of non-linear partial differential equations coupled between the transverse and radial displacements of the membrane. A systematic perturbation method, in which the amplitude of the transverse displacement is taken as the perturbation parameter, is used to obtain periodic solutions of the non-linear equations. The initial membrane strain enters the problem as a parameter which is allowed to vary over a range of values. A case of self-resonance is encountered when the initial membrane strain approaches some critical values. This self-resonance case is also treated through an appropriate modification of the perturbation method.read more
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Frequency tuning, nonlinearities and mode coupling in circular mechanical graphene resonators.
TL;DR: Using perturbation theory, it is shown that it is necessary to include the effects of the non-uniform stress distribution for finite deflections, which correctly reproduces the spectrum and frequency tuning of the resonator, including frequency crossings.
Journal ArticleDOI
Frequency tuning, nonlinearities and mode coupling in circular graphene resonators
TL;DR: In this paper, the authors derived dynamic equations for the flexural mode amplitudes of circular nanomechanical graphene resonators by means of continuum elasticity theory, treating them as membranes.
Journal ArticleDOI
Very large scale characterization of graphene mechanical devices using a colorimetry technique
Santiago J. Cartamil-Bueno,Alba Centeno,Amaia Zurutuza,Peter G. Steeneken,Herre S. J. van der Zant,Samer Houri +5 more
TL;DR: The survival probability is correlated with a structural mechanics scaling parameter given by D4/g3 and the median adhesion energy of Γ = 0.9 J m-2 between the membrane and the native SiO2 at the bottom of the cavities is extracted.
Graphene Based Pressure Sensors: Resonant Pressure Transduction using Atomically Thin Materials
TL;DR: In this article, an absolute (atmospheric) pressure sensor and pressure difference (gage) sensor were developed and compared to existing measurements of similar devices or to numerical simulations, and it was concluded that these devices will not only be smaller and cheaper, but also have a larger bandwidth and less sensitivity to mechanical disturbances.
References
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Book
Theory of plates and shells
TL;DR: In this article, the authors describe the bending of long RECTANGULAR PLATES to a cycloidal surface, and the resulting deformation of shels without bending the plates.
Journal ArticleDOI
Periodic vibrations of systems governed by nonlinear partial differential equations
Joseph B. Keller,Lu Ting +1 more
Journal ArticleDOI
Nonlinear Response of a Circular Membrane to Sinusoidal Acoustic Excitation
V. A. Chobotov,R. C. Binder +1 more
TL;DR: In this article, the exact nonlinear differential equations of motion for free symmetric vibration of a circular membrane have been derived and solved, approximately, by a perturbation procedure and the Ritz-Galerkin technique.
Journal ArticleDOI
Oscillations of a Circular Membrane on a Nonlinear Elastic Foundation
TL;DR: In this paper, the solution for periodic axisymmetric oscillations of a taut circular membrane on a Duffing-type nonlinear elastic foundation is obtained through the second order, the zeroth order being the linearized solution.