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This study investigates the size-dependent wave propagation behaviors under the thermoelectric loads of porous functionally graded piezoelectric (FGP) nanoplates deposited in a viscoelastic foundation. It is assumed that (i) the material parameters of the nanoplates obey a power-law variation in thickness and (ii) the uniform porosity exists in the nanoplates. The combined effects of viscoelasticity and shear deformation are considered by using the Kelvin-Voigt viscoelastic model and the refined higher-order shear deformation theory. The scale effects of the nanoplates are captured by employing nonlocal strain gradient theory (NSGT). The motion equations are calculated in accordance with Hamilton's principle. Finally, the dispersion characteristics of the nanoplates are numerically determined by using a harmonic solution. The results indicate that the nonlocal parameters (NLPs) and length scale parameters (LSPs) have exactly the opposite effects on the wave frequency. In addition, it is found that the effect of porosity volume fractions (PVFs) on the wave frequency depends on the gradient indices and damping coefficients. When these two values are small, the wave frequency increases with the volume fraction. By contrast, at larger gradient index and damping coefficient values, the wave frequency decreases as the volume fraction increases. [ABSTRACT FROM AUTHOR]

The wave propagation characteristics of a porous functionally graded piezoelectric material (FGPM), that is, FGPM nanoshells, resting on a viscoelastic foundation are analyzed. First, the governing equations are developed based on the first-order shear deformation theory by employing Hamilton's principle. Then, the motion equations are obtained by exploiting the nonlocal strain gradient theory. Finally, an extensive parametric investigation is carried out to explore the influences of various parameters, namely, scale parameters, pore distribution, porosity coefficient, FG index, and viscoelastic foundation, on the wave propagation characteristics of the FGPM nanoshells. The degree of influence of different parameters on the frequency of waves in the FGPM is significantly thickness-dependent. The porosity and Pasternak parameters considerably influence the frequency at small thickness, while the FG index and Winkler parameters significantly influence it at large thickness. The findings of this study provide insights for the optimal design of FGPM nanoshells and for further research on nanomaterials. • The frequency of uniform porous is lower than that of uneven porous. • The influence of viscoelastic effects on frequency is thickness-dependent. • Influences of thickness on frequency are more notable than that of radius. • The effect of negative voltage on frequency is greater than positive voltage. [ABSTRACT FROM AUTHOR]