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The free vibration analysis of a perovskite solar cell (PSC) within thermal environments is studied through a quasi-3D plate model. This model is designed to account for the stretching effects and non-uniform shear strains throughout the thickness. The PSC film is represented in the model as a thin laminated plate, comprising five distinct plies: ITO, PEDOT:PSS, perovskite, PCBM, and Au. A graphene platelets reinforced composite (GPLRC) substrate, made of Poly (methyl methacrylate), is assumed to be located under the noted five layers. The GPLRC substrate is conceptualized in the model as a porous foundation with finite depth. The foundation stiffnesses are determined using a modified Vlasov model, and the equivalent Young modulus of the foundation is evaluated using a modified Halpin–Tsai model, introducing the porosity coefficient. It is also considered that the material properties of GPLRC substrates exhibit temperature dependency. For the PSC with all edges simply supported, Navier solution method is applied to obtain the frequencies and associated mode numbers. Based on the results presented in this study, an increase in the porosity and thickness of the substrate can negatively impact the frequencies of the structure. However, natural frequencies experience almost no change if the temperature rises.

In this paper, the free vibration of a sandwich plate with an anisogrid core and two face sheets reinforced with graphene platelets (GPLs) is investigated. A continuous approach is considered for the lattice core and the equivalent properties are calculated. Adopting the Halpin–Tsai micromechanics, the effective Young’s modulus of the nanocomposites/graphene platelets is extracted. Also, mass density and Poisson’s ratio are earned with the simple rule of mixtures. A quasi-3D theory is applied to model the kinematics of the sandwich plate with simply supported boundary conditions. Hamilton’s principle is implemented to obtain the equations of motion that are solved based on the Navier solution. The validity of the results of this study is confirmed by comparing the analytical results with those presented in other researches and also a finite element model. The effect of the parameters of the lattice core such as the width of ribs, the number of helical ribs in one direction, and the ratio of thickness of face sheets to core on the natural frequencies of the sandwich plate was investigated. Additionally, the impact of the pattern of graphene platelets and their weight fraction on the natural frequencies were investigated. The results show that by decreasing the ratio of the thickness of face sheets to the thickness of core and increasing the number of ribs and their width, the natural frequencies will decrease. Moreover, the patterns FG-V and FG-A have the highest and the lowest natural frequencies, respectively, among the other distribution of graphene platelets.

The purpose of this research is to study the free vibration response of composite plates made up of three-phase polymer–glass fiber (FG)–carbon nanotubes (CNTs). Polymer matrix has an important property, i.e. the elastic modulus and Poisson’s ratio decrease over time. In this study, the waviness of the CNTs is also taken into consideration. A three-step hierarchical approach is adopted to estimate the elastic properties of the composite media. The governing equations are derived by quasi-3D plate theory and Hamilton’s principle. The adopted quasi-3D model takes into account the nonuniform shear and normal strain distribution and also satisfies the condition of traction-free on top and bottom surfaces. The natural frequencies of this composite are found using the Navier solution method for simply supported boundary conditions. This work investigates how the dimensionless frequency is affected by time, plate geometry, fiber mass fraction, and CNT mass fraction, all of which have a substantial impact. For example, it is highlighted that for a specific plate, after 60s, the frequency drops by about 14% if one takes the time parameter into account. In addition, increasing the mass fraction of CNTs or FGs results in higher frequencies.

A structure of theoretical models set was suggested to predict the elastic moduli of polyurethane copolymer (PUC)/organic modified montmorillonite (OMMT) nanocomposites (NCs) in terms of length (L) to thickness (t) ratio and volume fraction ($V_f$) of OMMT nanoparticles. The predicted elastic modulus outcomes of PUC/OMMT NCs were compared with experiment data. The outcome demonstrated that the suggested aspect ratio of predicted elastic modulus decreased with increased $V_f$ of OMMT compared to experimental data. The largest value of effective aspect ratio belonged to the Hui–Shia model over all OMMT $V_f$. The modified Halpin–Tsai model incorporated with the factor for decreasing modulus (FFDM) recorded the lowest range of percentage error between theoretical and experimental data around 0.385–0.816% at $V_f<0.125$ (4wt.%) OMMT.