Table 1.

Lumped parameter equations for L-L magnetoelectric (ME) laminate. Adapted from [15].

Lumped Parameter Variable	Constitutive Equation
Characteristic Mechanical Impedance, $Z_0$	$Z_0={\rho }_{avg}v\ast \left(A_1+A_2\right)\left[\frac{\mathrm{kg}}{\mathrm{s}}\right]$
Average Laminate Density, ${\rho }_{avg}$	${\rho }_{avg}=\frac{{\rho }_{ms}{A}_2+{\rho }_{me}{A}_1}{A_1+A_2}\left[\frac{\mathrm{kg}}{{\mathrm{m}}^3}\right]$
Magnetoelectric Wave Speed, $v$	$v=\sqrt{\frac{n}{s_{33}^H}+\frac{\left(1-n\right)}{s_{11}^D}}\left[\frac{\mathrm{m}}{\mathrm{s}}\right]$
Volumetric Layer Ratio, $n$	$n=\frac{A_2}{A_2+A_1}$
Fundamental Frequency, ${\omega }_s$	${\omega }_s=\frac{\pi v}{l}\left[\frac{rad}{s}\right]$
Effective Laminate Quality Factor, $Q_m$	$Q_m={\left(\frac{n}{Q_{ms}}+\frac{1-n}{Q_{me}}\right)}^{-1}$
Magnetostrictive Material Density, ${\rho }_{ms}$	Material property
Piezoelectric Material Density, ${\rho }_{pe}$	Material property
Magnetostrictive Quality Factor, $Q_{ms}$	Material property
Piezoelectric Quality Factor, $Q_{pe}$	Material property