scholarly journals A Detailed Analysis of the Resonant Frequency and Sensitivity of Flexural Modes of Atomic Force Microscope Cantilevers with a Sidewall Probe Based on a Nonlocal Elasticity Theory

2014 ◽  
Vol 60 (3) ◽  
pp. 179-186 ◽  
Author(s):  
Mohammad Abbasi ◽  
Ardeshir Karami Mohammadi
Keyword(s):  
Resonant Frequency ◽  
Atomic Force Microscope ◽  
Detailed Analysis ◽  
Elasticity Theory ◽  
Nonlocal Elasticity ◽  
Nonlocal Elasticity Theory ◽  
Atomic Force

scholarly journals Double mode model of size-dependent chaotic vibrations of nanoplates based on the nonlocal elasticity theory

2021 ◽  
Author(s):  
Jan Awrejcewicz ◽  
Grzegorz Kudra ◽  
Olga Mazur
Keyword(s):  
Elasticity Theory ◽  
Nonlocal Elasticity ◽  
Scale Effects ◽  
Plate Theory ◽  
Nonlocal Parameter ◽  
Nonlocal Elasticity Theory ◽  
Phase Portraits ◽  
Small Scale ◽  
Governing System ◽  
Account Due

AbstractIn this paper vibrations of the isotropic micro/nanoplates subjected to transverse and in-plane excitation are investigated. The governing equations of the problem are based on the von Kármán plate theory and Kirchhoff–Love hypothesis. The small-size effect is taken into account due to the nonlocal elasticity theory. The formulation of the problem is mixed and employs the Airy stress function. The two-mode approximation of the deflection and application of the Bubnov–Galerkin method reduces the governing system of equations to the system of ordinary differential equations. Varying the load parameters and the nonlocal parameter, the bifurcation analysis is performed. The bifurcations diagrams, the maximum Lyapunov exponents, phase portraits as well as Poincare maps are constructed based on the numerical simulations. It is shown that for some excitation conditions the chaotic motion may occur in the system. Also, the small-scale effects on the character of vibrating regimes are illustrated and discussed.

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