Free Vibrations of Nanoscale Beam Under Two-Temperature Green and Naghdi Model

Abstract

The influence of the coupling between strain rate and temperature becomes domineering in the nanoscale beam. In this work, the free vibration of nanoscale beam resonators is analysed using Green and Naghdis theorem under the two-temperature model (2TGNIII). The influence of two-temperature parameters in a nanoscale beam is studied for beams under simply supported conditions. Exact expressions for frequency shift and the thermoelastic damping have been derived in the resonator, and calculation outcomes have been presented graphically with respect to frequency shift, natural frequency, and thermoelastic damping. The scale of length and thickness for a nanobeam equal to 15 × 10−9 m and equal to 1.3 × 10−12 s for time.

Investigation on the thermo‐piezo‐flexoelectric energy harvesting performance of self‐powered microbeam devices considering strain gradient and dual‐phase‐lag effects

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“…Zenkour [11] studied the thermomechanical response of microbeams with Refined two-temperature MPL theory and the modified couple stress analysis. Also, some other researchers worked on the nanobeam with other theories of thermoelasticity as Sharma and Kaur [12], Abouelregal and Zenkour [13], Elaziz et al [14], Wu et al [15], Reddy and Cheng [16], Bhatti et al [17], Singh et al [18], Craciun et al [19], Sharma and Marin [20], Khisaeva and Ostoja-Starzewski [21], Singh et al [22], Sharma and Grover [23], Vlase et al [24], Groza et al [25], Nicolescu & Bobe [26], Golewski [27][28][29], Abbas [30], Lata and Kaur [31][32][33][34][35][36], Bhatti and Michaelides [37].…”

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“…Zenkour & Abouelregal [14] studied axially moving microbeam due to sinusoidal pulse heating. Moreover, other several researchers such as, Povstenko [15,16], Marin [17][18][19], Abbas et al [20], Sharma & Grover [21], Abd-Alla & Abbas [22], Othman & Abbas [23], Abbas & Othman [24], Abbas & Youssef [25], Kumar & Abbas [26], Abbas [27][28][29], Ezzat et al [30], Othman & Marin [31], Aldawody et al [32], Lata & Kaur [33][34][35][36], Abbas [29], Sharma & Marin [37] worked on the different theories of thermoelasticity.…”

“…Moreover, other several researchers such as, Povstenko [15, 16], Marin [17–19], Abbas et al. [20], Sharma & Grover [21], Abd‐Alla & Abbas [22], Othman & Abbas [23], Abbas & Othman [24], Abbas & Youssef [25], Kumar & Abbas [26], Abbas [27–29], Ezzat et al. [30], Othman & Marin [31], Aldawody et al.…”

“…[30], Othman & Marin [31], Aldawody et al. [32], Lata & Kaur [33–36], Abbas [29], Sharma & Marin [37] worked on the different theories of thermoelasticity.…”