Theory and Methods for Studying the Nonlinear Dynamics of a Beam-Plate Nano Resonator Taking into Account the Temperature and Strain Fields Connection in Additive Color Noise

A theory of geometrically nonlinear dynamics of nanoplates has been constructed with allowance for the temperature and strain fields connection on the basis of the modified moment theory taking into account the transverse load and additive color noise. A research method based on the qualitative theory of differential equations has been developed. An example of the additive color noise influence on nonlinear vibrations for an elastic Euler-Bernoulli beam is given.