Vibration analysis of non-uniform and non-homogeneous boron nitride nanorods embedded in an elastic medium under combined loadings using DQM

Electro-thermo-mechanical vibration analysis of non-uniform and non-homogeneous boron nitride nanorod (BNNR) embedded in elastic medium is presented. The steady state heat transfer equation without external heat source for non-homogeneous rod is developed and temperature distribution is derived. Using Maxwell׳s equation and nonlocal elasticity theory the coupled displacement and electrical potential equations are presented. Differential quadrature method (DQM) is implemented to evaluate the natural frequencies. The effects of attached mass, lower and higher vibrational mode, elastic medium, piezoelectric coefficient, dielectric coefficient, cross section coefficient, non-homogeneity parameter and small scale parameter on the natural frequency are investigated. The appropriate values for Winkler and Pasternak modulus in axial vibration of boron nitride nanorod are reported. The mass sensitivity limit of 10−1 (zg) is derived for BNNR-based nano-electro-mechanical sensors. The results show that the C-F boundary condition of BNNRs are more sensitive to attached mass than the C-C boundary condition and also the sensitivity range for BNNRs. It is concluded that frequency ratio decreases considering electro-thermal loadings and electrical loadings are more effective in non-uniform nanorods, in comparison with uniform nanorod. The natural frequency of BNNRs can be varied using different cross section coefficient and non-homogeneity parameter. This fact can be employed for practical tools to design and control nano-devices and nano-electro-mechanical systems (NEMS) to prevent resonance phenomenon.