Nonlocal Aspect of Piezoelectric Composite on Transmission of Mechanical Wave

Abstract

This research article aims to conduct a more thorough examination of the effects of size on piezoelectric composites when subjected to Love-type mechanical wave propagation. The objective is to take into account the structural size influences by employing Eringen’s nonlocal theory. By utilizing Maxwell’s relation and electric boundary conditions, the distribution of electric potentials along the piezoelectric composite is derived. Through exact analysis, the dispersion relations for the piezoelectric composite are obtained. Specific outcomes are acquired and validated by comparing them to existing results. Subsequently, a detailed investigation of various influential parameters such as the nonlocal parameter and material parameters on the wave dispersion characteristics of the nanoscaled structure is conducted. These findings demonstrate that the nonlocality parameter within the medium significantly affects wave propagation.

Appendix

$G_{11}^o=G_{11}^c=\alpha _0\overline{c_{44}^L}\sin (k\alpha _0d)$,    $G_{12}^o=G_{12}^c=\alpha _0\overline{c_{44}^L}\cos (k\alpha _0d)$,    $G_{13}^o=G_{13}^c={e_{15}^Le^{-kd}},$ $G_{14}^o=G_{14}^c=-e_{15}^Le^{kd},$    $G_{32}^o=G_{32}^c=\alpha _0\overline{c_{44}^L},$    $G_{33}^o=G_{33}^c=-G_{34}^o=-G_{34}^c=e_{15}^L,$    $G_{35}^o=G_{35}^c=\alpha _1\overline{c_{44}^H},$ $G_{36}^o=G_{36}^c=e_{15}^H,$    $G_{41}^o=G_{41}^c=\frac{e_{15}^L}{\kappa _{11}^L},$    $G_{45}^o=G_{45}^c=-\frac{e_{15}^H}{\kappa _{11}^H},$    $G_{53}^o=G_{53}^c=-G_{54}^o=-G_{54}^c=\kappa _{11}^L,$    $G_{56}^o=G_{56}^c=-\kappa _{11}^H,$    $-G_{63}^o=G_{63}^c=e^{-kd},$    $G_{64}^o=G_{64}^c=e^{kd},$    $G_{61}^c=\frac{e_{15}^L}{\kappa _{11}^L}\cos {k\alpha _0d},$  $G_{62}^c=-\frac{e_{15}^L}{\kappa _{11}^L}\sin {k\alpha _0d},$    $G_{21}^o=G_{21}^c=-G_{25}^o=-G_{25}^c=G_{43}^o=G_{43}^c=G_{44}^o=G_{44}^c=-G_{46}^o=-G_{46}^c=1$

$\chi _1=\left( \frac{e_{15}^L}{\kappa _{11}^L}-\frac{e_{15}^H}{\kappa _{11}^H}\right)$,   $\chi _2=\kappa _{11}^He_{15}^L-\kappa _{11}^Le_{15}^H,$   $\chi _3=\alpha _0\overline{c_{44}^L}\tan (k\alpha _0d)-\alpha _1\overline{c_{44}^H}$,   $\chi _4=\tanh (kd)\kappa _{11}^L+\kappa _{11}^H$, $\chi _5=\left( \alpha _0\overline{c_{44}^L}-(\frac{{e_{15}^L}^2}{\kappa _{11}^L})\tan (k\alpha _0d)\tanh (kh)\right) (\kappa _{11}^He_{15}^L-\kappa _{11}^Le_{15}^H)+2\alpha _1\overline{c_{44}^L}e_{15}^L\kappa _{11}^H sec(k\alpha _0d)sech(kd),$ $\chi _6=\alpha _0\overline{c_{44}^L}\tan (k\alpha _0d)-\alpha _1\overline{c_{44}^H},$    $\chi _7=\kappa _{11}^H\tanh (kd)+\kappa _{11}^L,$   $\chi _8=\left( \frac{{e_{15}^L}^2}{\kappa _{11}^L}\right) (\alpha _0\overline{c_{44}^L}+\alpha _1\overline{c_{44}^H}\tan (k\alpha _0d)),$    $\chi _9=\kappa _{11}^L\tanh (kd)+\kappa _{11}^H$