The dynamics of a three-component nonlinear delocalized vibrational mode in graphene is studied with molecular dynamics. This mode, being a superposition of a root and two one-component modes, is an exact and symmetrically determined solution of nonlinear equations of motion of carbon atoms. The dependences of a frequency, energy per atom, and average stresses over a period that appeared in graphene are calculated as a function of amplitude of a root mode. We showed that the vibrations become periodic with certain amplitudes of three component modes, and the vibrations of one-component modes are close to periodic one and have a frequency twice the frequency of a root mode, which is noticeably higher than the upper boundary of a spectrum of low-amplitude vibrations of a graphene lattice. The data obtained expand our understanding of nonlinear vibrations of graphene lattice.

The paper proposes a new method for studying nonlinear processes in ferroelectric ceramics under external influences, based on the measurement and analysis of piezoelectric resonance spectra. The method provides high accuracy in determining complex elastic, dielectric and piezoelectric constants of piezoelectric materials, as well as their changes under external influences. To study nonlinear processes, we measured the dependences of complex electromechanical parameters of ferroelectrically «soft» piezoceramics based on PZT system on dc electric field. A physical interpretation of the results is proposed.