Love wave transference in piezomagnetic layered structure guided by an imperfect interface

Abstract

The problem presents an analytical study of the wave transference in piezo-composite layer lying over an elastic substrate. The interface of the geometry is assumed to be imperfect. The imperfection is characterized by Linear Spring Model. Dynamics of the media taken are framed in form of direct Sturm–Liouville problem. Dispersion relations are found for both magnetically open and magnetically short case. Velocity profile of Love wave has been delineated through graphs for different affecting parameters (i.e., imperfection at the interface, layer thickness and heterogeneity in the substrate). It has been shown that the increase in these parameters increases the phase velocity of the Love wave. Further, layer thickness is noted to have a less effect on the velocity profile of the wave as compared to heterogeneity in the substrate. Moreover, a comparative study has been shown between the aforementioned cases with the variation in imperfect parameter. The velocity in open case is found to be higher than that of short case. The obtained results may provide guidance towards optimization of Surface Acoustic Wave devices and measurement of imperfections.

Appendices

Appendix A

$$ a_{11} = q_{1} \overline{c}_{44} \,,\,\,\,a_{13} = - h_{15}^{m} k\,,\,\,\,a_{14} = h_{15}^{m} k $$

$$ a_{23} = - \mu_{11} k\,\,,\,\,a_{24} = \mu_{11} k $$

$$ \begin{gathered} a_{31} = q_{1} \overline{c}_{44} cos(q_{1} h)\,,\,\,a_{32} = - q_{1} \overline{c}_{44} sin(q_{1} h)\,\,,\,\,a_{33} = - ke^{ - kh} ,\,\,a_{34} = ke^{kh} \,,\, \hfill \\ a_{35} = \mu^{e} me^{ - mh} \hfill \\ \end{gathered} $$

$$ \begin{gathered} a_{41} = \overline{c}_{44} q_{1} cos(q_{1} h) - s\frac{{\overline{c}_{44} }}{h}sin(q_{1} h)\,\,,\,\,a_{42} = - \left( {q_{1} sin(q_{1} h)\overline{c}_{44} + s\frac{{\overline{c}_{44} }}{h}cos(q_{1} h)} \right)\,,\,\,a_{43} = - h_{15}^{m} ke^{ - kh} \,\,, \hfill \\ a_{44} = h_{15}^{m} ke^{kh} ,\,\,a_{45} = s\frac{{\overline{c}_{44} }}{h}e^{ - mh} \hfill \\ \end{gathered} $$

$$ a_{51} = \frac{{h_{15}^{m} }}{{\mu_{11} }}sin(q_{1} h)\,,\,\,\,a_{52} = \frac{{h_{15}^{m} }}{{\mu_{11} }}cos(q_{1} h)\,,\,\,\,a_{53} = e^{ - kh} \,,\,\,\,a_{54} = e^{kh} $$

Appendix B

$$ b_{11} = q_{1} \overline{c}_{44} \,,\,\,\,b_{13} = - h_{15}^{m} k\,,\,\,\,b_{14} = h_{15}^{m} k $$

$$ b_{12} = \frac{{h_{15}^{m} }}{{\mu_{11} }}\,,\,\,\,b_{13} = 1\,,\,\,\,b_{14} = 1 $$

$$ \begin{gathered} b_{31} = q_{1} \overline{c}_{44} cos(q_{1} h)\,,\,\,b_{32} = - q_{1} \overline{c}_{44} sin(q_{1} h)\,\,,\,\,b_{33} = - ke^{ - kh} ,\,\,b_{34} = ke^{kh} \,,\, \hfill \\ b_{35} = \mu^{e} me^{ - mh} \hfill \\ \end{gathered} $$

$$ \begin{gathered} b_{41} = \overline{c}_{44} b_{1} cos(q_{1} h) - s\frac{{\overline{c}_{44} }}{h}sin(q_{1} h)\,\,,\,\,b_{42} = - \left( {q_{1} sin(q_{1} h)\overline{c}_{44} + s\frac{{\overline{c}_{44} }}{h}cos(q_{1} h)} \right)\,,\,\,b_{43} = - h_{15}^{m} ke^{ - kh} \,\,, \hfill \\ b_{44} = h_{15}^{m} ke^{kh} ,\,\,b_{45} = s\frac{{\overline{c}_{44} }}{h}e^{ - mh} \hfill \\ \end{gathered} $$

$$ b_{51} = \frac{{h_{15}^{m} }}{{\mu_{11} }}sin(q_{1} h)\,,\,\,\,b_{52} = \frac{{h_{15}^{m} }}{{\mu_{11} }}cos(q_{1} h)\,,\,\,\,b_{53} = e^{ - kh} \,,\,\,\,b_{54} = e^{kh} $$