Functional dependence of resonant harmonics on nanomechanical parameters in dynamic mode atomic force microscopy

• Federico Gramazio,
• Matteo Lorenzoni,
• Francesc Pérez-Murano,
• Enrique Rull Trinidad,
• Urs Staufer and
• Jordi Fraxedas

Beilstein J. Nanotechnol. 2017, 8, 883–891, doi:10.3762/bjnano.8.90

• frequencies fn = nf [2][3]: where a is a constant amplitude value. The An coefficients can be analytically calculated, in the limit of weak tip–sample interaction (A1 >> An for n > 1), by integrating the force field Fts that is modulated by weighted Chebyshev polynomials of the first kind, Tn(u) [4][5]. The

Free vibration of functionally graded carbon-nanotube-reinforced composite plates with cutout

• Mostafa Mirzaei and
• Yaser Kiani

Beilstein J. Nanotechnol. 2016, 7, 511–523, doi:10.3762/bjnano.7.45

• frequency of a rectangular plate with or without a cutout may be enhanced. Furthermore, the frequencies are highly dependent on the volume fraction of carbon nanotubes and may be increased upon using more carbon nanotubes as reinforcement. Keywords: Chebyshev polynomials; cutout; functionally graded carbon

• -CNTRC rectangular plate containing a central, rectangular cutout. The distribution of CNTs across the plate thickness are assumed to be either uniform or nonuniform. A modified rule of mixtures approach is used to obtain the properties of the composite media. Chebyshev polynomials are used as the basic

• this study, the approximation of the displacement field is carried out using the Ritz method whose shape functions are written in terms of the Chebyshev polynomials. As a result, the essential variables may be written as In Equation 15, the i-th Chebyshev polynomial of the first kind is denoted by Pi