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The multidisciplinary nature of piezoelectric (PZ) structures necessitates precise and efficient methods to express their behavior under different conditions. This article extends the general usage of PZ materials by introducing acoustic and fluid loading effects in a way that an unfilled multilayer cylindrical nanoshell with a functionally graded (FG) material core and PZ layers is subjected to preliminary external electric load, acoustic waves and external flow motion. As the properties of a functionally graded material changes along the shell thickness, a power law model is assumed to be governing such variations of desired characteristics. Evidently, this system includes different types of couplings and a comprehensive approach is required to describe the structural response. To this aim, the first-order shear deformation theory (FSDT) is used to define different displacement components. Next, the coupled size-dependent vibroacoustic equations are derived based on in conjunction with nonlocal strain gradient theory (NSGT) with the aid of Hamilton’s variational principle and fluid/structure compatibility conditions. NSGT is complemented with hardening and softening material effects which can greatly enhance the precision of results. It is expected to use the findings of this paper in the optimization of similar systems by selecting suitable FG index, incident angle of sound waves, flow Mach number, nonlocal and strain gradient parameters, starting electric potential and geometric features. One of the important findings of this study is that increasing the electric voltage can obtain better sound insulation at small frequencies, specially prior to the ring frequency.

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In this article, a numerical efficient method for fractional mobile/immobile equation is developed. The presented numerical technique is based on the compact finite difference method. The spatial and temporal derivatives are approximated based on two difference schemes of orders O(t 2Àa ) and O(h 4 ), respectively. The proposed method is unconditionally stable and the convergence is analyzed within Fourier analysis. Furthermore, the solvability of the compact finite difference approach is proved. The obtained results show the ability of the compact finite difference.

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