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Following previous study about AdS-Schwarzschild black holes minimally coupled to a cloud of strings in the context of massive gravity [1] and inspired by strong connection between Gauss-Bonnet Gravity and heterotic string theory, in this paper, we first take into account the Gauss-Bonnet term and we study thermodynamics and critical behavior of these black holes in the extended phase space. The effects of Gauss-Bonnet, massive, and string cloud parameters on the criticality of these black holes has been investigated. It can be seen that the Gauss-Bonnet and massive parameters have opposite effects on the criticality and phase transition of the solutions. We also observe that the increase in the value of the string cloud parameter above a critical value, eliminates the van der Waals like behavior of these solutions. Also, the Joule-Thomson effect is not observed. Then we examine thermal stability of these black holes in canonical ensemble by calculating the heat capacity. In addition, we explore critical behavior in extended phase space by employing heat capacity and consequently, we observe that the results are in agreement with the previous results from the usual method in section 3.

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In this paper, we analytically study vibration of functionally graded piezoelectric (FGP) nanoplates based on the nonlocal strain gradient theory. The top and bottom surfaces of the nanoplate are made of PZT-5H and PZT-4, respectively. We employ Hamilton's principle and derive the governing differential equations. Then, we use Navier's solution to obtain the natural frequencies of the FGP nanoplate. In the first step, we compare our results with the obtained results for the piezoelectric nanoplates in the previous studies. In the second step, we neglect the piezoelectric effect and compare our results with those obtained for the functionally graded (FG) nanoplates. Finally, the effects of the FG power index, the nonlocal parameter, the aspect ratio, and the lengthto-thickness ratio, and the nanoplate shape on natural frequencies are investigated.

The structural, electronic, magnetic, and vibrational properties of full-Heusler compounds Ir2CrSi and Ir2CrGe based on the density functional theory are investigated. Ir2CrSi is half-metallic ferromagnet at equilibrium lattice constant and preserves its half-metallic behavior under stress. Ir2CrGe just represents half-metallicity under stress. For this reason, we changed the equilibrium lattice constant from −4%a0 to +4%a0 in a range of a = (a0 ± x%a0), where x = 1, 2, 3, 4, and calculations were done for these new lattice parameters. In all of this interval Ir2CrSi holds its half-metallic property. The dynamical stability at equilibrium lattice constant and under stress have been investigated. The Ir2CrSi compound has dynamical stability at lattice constant a = a0 − 3%a0 and a = a0 − 4%a0.