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Magneto-Electro-Thermo nanobeam resting on a nonlinear elastic foundation is presented. This beam is subjected to the external electric voltage and magnetic potential, mechanical potential and temperature change. Also, we added the new material PTZ-5H-COFe2O4. The governing equations and boundary conditions are derived using Hamilton principle. These equations are discretized by using three differential quadrature methods and iterative quadrature technique to determine the natural frequencies and mode shapes. Numerical analysis is introduced to explain the influence of computational characteristics of the proposed schemes on convergence, accuracy and efficiency of the obtained results. The obtained results agreed with the previous analytical and numerical ones. A detailed parametric study is conducted to investigate the influences of different boundary conditions, various composite materials, nonlinear elastic foundation, nonlocal parameter, the length-to-thickness ratio, external electric and magnetic potentials, axial forces, temperature and their effects on the vibration characteristics of Magneto-Electro-Thermo-Elastic nanobeam.

This work introduces a numerical scheme for free vibration analysis of elastically supported piezoelectric nanobeam. Based on Hamilton principle, governing equations of the problem are derived. The problem is formulated for linear and nonlinear Winkler–Pasternak foundation type. Three differential quadrature techniques are employed to reduce the problem to an Eigen-value problem. The reduced system is solved iteratively. The natural frequencies of the beam are obtained. Numerical analysis is implemented to investigate computational characteristics affecting convergence, accuracy and efficiency of the proposed scheme. The obtained results agreed with the previous analytical and numerical ones. Furthermore, a parametric study is introduced to show influence of supporting conditions, two different electrical boundary conditions, material characteristics, foundation parameters, temperature change, external electric voltage, nonlocal parameter and beam length-to-thickness ratio on the values of natural frequencies and mode shapes of the problem.

Summary This work presents different numerical methods that are used for the first time in solving Perovskite solar cells (PSCs). Classical differential quadrature, sinc, and discrete singular convolution (Regularized Shannon and Delta Lagrange kernels) methods are employed for studying this problem. The governing equations are derived based on Poisson's and continuity equations. The different quadrature techniques are introduced to convert the system of nonlinear partial differential equations to nonlinear algebraic system. Then, an iterative method is used to solve this system. Convergence and efficiency of the obtained results with error ≤10−8 depend on various computational characteristics for each technique. The computed results match with previous experiment, exact, finite difference, SCAPS 1‐D simulation software, and finite element scheme. Then, the comprehensive parametric study is explored to show the effects of density states, gap energy, thickness, temperatures, lifetimes, wavelength, absorption coefficient, recombination prefactor, and recombination mechanisms whether direct or indirect on power conversion efficiency (PCE) and charge transport of solar cells with and without interface material. After all that have been studied on PSCs, it was found that the best value of PCEs was 32%. Thus, the computed results of the present schemes may be useful for improving the performance level of PSCs.

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