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In this research, we investigate the nonlinear vibration of functionally graded carbon nanotubes (FG-CNTs) for simply supported sandwich cylindrical panels. The sandwich consisting of three layers formed of (FG-CNTs) and isotropic material as (CNT, ALMINUME, CNT). Mechanical properties of the sandwich media are acquired according to a refined rule of blend approach. The governing equations were derived using a first-order deformation theory (FOSDT). Four kinds of carbon nanotubes of sandwich cylindrical panels were analyzed. The volume fraction of CNTs is varied. The properties of nonlinear responses and free vibration are studied. The numerical approach employs the fourth-order Runge-Kutta and Galerkine procedure. Which conducted for the dynamic analysis of the panels to present the natural frequencies and non-linear dynamic response expression. The results show that; the natural frequencies and the nonlinear vibration amplitude decrease with the volume fraction and thickness ratio increase. The nonlinear vibration amplitude response increases when increasing the excitation force. The initial imperfection and the elastic foundation have a minor impact on the nonlinear vibration response of the panel. The Pasternak Foundation has a larger impact than the Winkler foundation. The structure formed of FG-CNT present an excellent choice for high-performance of engineering applications.

Phenolics and fatty acids of some medicinal plants (Juniperus phoenicea and Arbutus pavarii) growing at Al - Jabal Al - Akhder region (Libya) was carried out on the fruits and leaves. The analysis were applied on selected plants. The data showed high content of phenolic compounds in most of the studied leaves comparing with fruits ones, the higher levels were recorded for the compound of 3,5,Di caffeoly guinic acid in the A.pavarii leaves (0.1325 mg/g). The contents of saturated fatty acids recorded high levels in leaves of J. phoenicea (0.157mg/g), while the low levels were recorded in leaves of A.pavarii (0.079 mg/g), for the mono un saturated fatty acids the high concentrations recorded in leaves of A.pavarii (0.065mg/g), on the other side the low concentration was recorded in leaves of J. phoenicea (0.025mg/g). Whereas fruits of A.pavarii don't contain on mono un-saturated fatty acids. While the high contents of poly un-saturated fatty acids were recorded in fruits of J. phoenicea (0.045mg/g) and the low contents recorded in leaves of J. phoenicea (0.014mg/g). Whereas fruits of A.pavarii don't contain on poly un-saturated fatty acids. Generally the olic acid recorded high values of un-saturated fatty acids in leaves of A.pavarii (0.065mg/g).

This study investigates the nonlinear dynamic buckling of the exponentially functionally graded orthotropic toroidal shell segments under constant loading rates under the shear deformation theory with the damping influence. The properties of the shell material are assumed to be graded according to the exponential distribution function through the shell thickness direction. The shear deformation theory with von Karman nonlinearity, Stein and McElman assumption, initial imperfection, and damping effect are adopted to create the theoretical formulations. Nonlinear dynamic stability equation is solved using Galerkin's procedure and the fourth-order Runge–Kutta technique. The dynamic buckling loads are evaluated by using Budiansky–Roth criterion. Moreover, different parameter influences such as geometrical parameters, velocity, imperfections, damping ratios, and nonhomogeneous parameters on the dynamic buckling are examined in detail. The obtained results are validated with the previous publications and the good agreements are shown.

This study offers the elastic response of the variable thickness functionally graded (FG) by single walled carbon nanotubes reinforced composite (CNTRC) moderately thick cylindrical panels under rotating and transverse mechanical loadings. It’s considered that, three kinds of distributions of carbon nanotubes which are uniaxial aligned in the longitudinal direction and two functionally graded in the transverse direction of the cylindrical panels. Depending on first order shear deformation theory (FSDT), the governing equations can be derived. The partial differential equations are solved by utilizing the technique of finite element method (FEM) with a program has been built by using FORTRAN 95. The results are calculated to investigate the influence of the variable thickness, geometric parameters, rotating velocity, carbon nanotubes (CNTs) volume fraction for different boundary conditions on the non-dimensional deflection of the cylindrical panels. A comparison study has been carried out between the results of present study and that available in the open literature and found very good correspondence between the two results.

This study presents an analytical investigation on the effect of stiffener's geometric shape on the nonlinear natural frequencies of eccentrically stiffened functionally graded material cylindrical panels. Based on the classical shell theory with the geometrical shape of nonlinear in von Karman–Donnell means and the smeared stiffeners method (SSM), the governing equations of motion are derived. The properties of nonlinear responses and free vibration are studied. The numerical method utilizing the fourth-order Runge-Kutta are performed for the dynamic analysis of the shells to give expression of nonlinear dynamic responses and the natural frequencies. Effects of stiffener's geometric shape, material properties, and initial geometrical imperfection are presented with obtained results. Some results are presented and compared with the other authors.