Surface and thermal effects of the flexural wave propagation of piezoelectric functionally graded nanobeam using nonlocal elasticity

•Thermal effects should be investigated for piezoelectric functionally graded nanobeam (PFGN).•Dispersion relationship of the flexural wave of PFGN weakens with scale and thermal effect.•Flexural wave of PFGN exhibits an abnormal dispersion without thermal and scale effect.•The temperature effects on the phase velocity and group velocity are remarkable for wave number.

This study investigates the propagation peculiarities of the flexural wave of piezoelectric functionally graded nanobeam with surface and thermal effects. The equation of the flexural wave of the piezoelectric functionally graded nanobeam was expressed using nonlocal elastic theory because of the thermal and surface effects. The phase and group velocities were derived. The dispersion relation was analyzed using different wave numbers and temperatures and scale coefficient. The dispersion degree was weakened by scale coefficient and temperature and an increase in wave numbers. Changing the scale coefficient and temperatures are two of the main approaches in investigating the propagation characteristics of piezoelectric functionally graded nanobeam with surface effects and identifying new characteristics were found.

Graphical abstractUnder the conditions of T = 20 K, the ratio of group velocity and phase velocity vs. wave number.Figure optionsDownload full-size imageDownload as PowerPoint slide