Nonlinear modal coupling in a high-stress doubly-clamped nanomechanical   resonator
  We present results from a study of the nonlinear intermodal coupling between different flexural vibrational modes of a single high-stress, doubly-clamped silicon nitride nanomechanical beam. The measurements were carried out at 100 mK and the beam was actuated using the magnetomotive technique. We observed the nonlinear behavior of the modes individually and also measured the coupling between them by driving the beam at multiple frequencies. We demonstrate that the different modes of the resonator are coupled to each other by the displacement induced tension in the beam, which also leads to the well known Duffing nonlinearity in doubly-clamped beams. 
K. J. Lulla, R. B. Cousins, A. Venkatesan, M. J. Patton, A. D. Armour,   C. J. Mellor, and J. R. Owers-Bradley
cond-mat.mes-hall