Nonlinear vibration analysis of curvy single-walled boron nitride nanotube using mathematical modeling for dynamic responses

Abstract

This work explores the feasibility of nonlinear behavior of doubly clamped single-walled boron nitride nanotube (SW-BNNT)-based nanoresonator. A nonlinear mathematical model of wavy SW-BNNT has been developed for analyzing the geometrical nonlinearity. Dynamic responses of nonlinear model have been analyzed for different waviness factors varying from 0.01 to 0.06 using various tools like time series, phase space, Poincaré map and Fast Fourier Transforms (FFTs). For the analysis, 20nm length of SW-BNNT has been considered. It has been observed from nonlinear analysis, that for responses with a lower value of waviness (e.g., 0.01) for 20nm long BNNT, the system's nature loses its periodicity and shows onset of chaos with dense spectrum in Poincaré maps and irregular pattern in time response. Thus, it is concluded that chaotic response with a less strange attractor has been observed when waviness is 0.01. It is also concluded that, with increase in waviness factor from 0.02 to 0.06, the system showed the multi-periodic response with 2-T, 3-T and 4-T periods. The dynamic responses with varying waviness showed that the system behavior is changing from chaotic to periodic. This change in periodicity is one of the characteristics of chaotic solution.