Foundations of nanomechanics

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High-sensitivity monitoring of micromechanical vibration using optical whispering gallery mode resonators (2008, background): “The fundamental frequencies of a cantilever of length L can in general be expressed as Ωi/2π = C · √ ki/2π, where C is a material constant and the ki are given by the solutions of [60]”
Nanophononics: state of the art and perspectives (2016, background): “Substrate-borne electrodes are for dielectric transduction. properties are conveniently described by elasticity theory [188,190].”
Mechanical systems in the quantum regime (2011, background): “For a rectangular beam the second moment of inertia is I = h3w/12; for a (solid) cylinder with radius r it is I = πr4/4 [15].”
Toward single-molecule nanomechanical mass spectrometry (2005, background): “The algebra of the proof can be found in references like [22] .”
Qubit-induced phonon blockade as a signature of quantum behavior in nanomechanical resonators (2009, background): “30 66 v2 [ qu an tph ] 18 J un 2 01 0 Qubit-induced phonon blockade as a signature of quantum behavior in nanomechanical resonators Yu-xi Liu,1, 2, 3 Adam Miranowicz,1, 4 Y. B. Gao,5 Jiřı́ Bajer,6 C. P. Sun,7 and Franco Nori1, 8 1Advanced Science Institute, RIKEN, Wako-shi, Saitama 351-0198, Japan ”
Quantum electromechanical systems (2004, background): “[22] for a comprehensive review of device fabrication).”