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The dynamic response of the hybrid honeycomb sandwich panel under low-speed impact is studied. According to Hamilton's principle and first-order shear deformation theory, the motion equation of the hybrid honeycomb sandwich panel is deduced. Then the Navier method and Duhamel's integral are used to solve the vibration displacement of panels. Besides, the mass-spring (MS) model is used to calculate the contact force between the honeycomb sandwich panel and the impactor. The results of this model are compared with those of Abaqus and published studies, which verifies the feasibility of the theoretical model in this paper. Based on the developed theoretical model, the influences of the unit cell angle, cell wall length, cell wall thickness, core layer height and impact speed on the dynamic response of sandwich panels have been studied. The results show that under the same low-speed impact, the maximum lateral displacement of hybrid sandwich panels was 11.65% smaller than that of conventional sandwich panels when honeycomb parameter θ = 60°, and was 15.45% when honeycomb parameter β = 0.3. The energy absorption character of the hybrid honeycomb sandwich panel are better than those of the traditional hexagonal honeycomb sandwich panel and the concave hexagonal honeycomb sandwich panel. [ABSTRACT FROM AUTHOR]

In the current research, the dynamic behavior of the spherical nanoshell subjected to a moving harmonic load in hygro-thermo environment is examined for the first time. A size-dependent nonlocal shell theory is dedicated to ponder the nonlocality. The first-order shear deformation theory is dedicated to inquire the shear impacts along with the thickness of the shell. To ponder the effects of the thermal and moisture conditions on the dynamic responses of the nanoshell, we apply the nonlinear relations for temperature and moisture fields. In the current study, it is assumed that the nanoshell is subjected to a moving harmonic load which moves the upper surface of the nanoshell with a certain velocity along the path $ {x_2} = \frac{b}{2} $ x 2 = b 2 . Hamilton's axiom is dedicated to achieve the governing equations of motion. Then, the Navier solution technique is dedicated to derive the dynamic responses of the nanoshell with simply-supported boundary conditions. The impacts of several parameters are examined on the dynamic behavior of the nanoshell. [ABSTRACT FROM AUTHOR]

This research aims to explore the free vibration behavior of functionally graded porous (FGP) plates resting on a Kerr-type elastic foundation. This investigation employs an innovative trigonometric shear deformation (ITSD) theory with five variables. The study encompasses various plate configurations, including homogeneous FGP plates, hard-core FGP sandwich plates, and soft-core FGP sandwich plates with both regular and irregular pore structures. The ITSD theory naturally addresses shear stress concerns at the outer surfaces, while also considering the thickness stretching effect, all without the need for correction factors. To formulate the governing equations for the free vibration of such plates on an elastic foundation, Hamilton’s principle is employed. The Navier double trigonometric series approach is then utilized to solve this problem. To validate the plate theory and methodologies used in this work, a comparative analysis is conducted with existing studies. Additionally, comprehensive parametric simulations are employed to examine the impact of different factors, such as geometric properties, material characteristics, sandwich schemes, and parameters of the Kerr-type foundation, on the dimensionless natural frequencies of simply supported rectangular FGP plates. [ABSTRACT FROM AUTHOR]

Purpose: This article examines the forced vibrations of composite beams that have been reinforced with single-walled carbon nanotubes (SWCNTs) and subjected to a moving charge without considering the effect of mass inertia. Methods: This study investigates three different beams, namely uniform distribution carbon nanotubes (UD-CNT), functionally graded Λ distribution carbon nanotubes (FGΛ-CNT), and functionally graded X distribution carbon nanotubes (FGX-CNT). The SWCNTs exhibit length alignment along the axial direction, while their volume distributions are observed in the thickness direction. The motion equations of beams are derived using Hamilton's principle and mass interaction forces based on a sinusoidal third-order shear deformation theory (TSDT). These equations are then converted into a single equation set and solved using Navier's method. Results: This study presents comprehensive findings on the effects of total volume fraction and distribution types of carbon nanotubes (CNTs) on the forced vibration of a composite beam caused by a moving charge at different mass velocities. The FGX-CNT distribution of the beam has demonstrated increased resistance to the dynamic impact of live load. Conclusion: The study's findings will aid in the development of micro-sensors that carry moving charges. [ABSTRACT FROM AUTHOR]

Deflection of simply supported laminated composite plate under transverse load is found out by semi-analytical method (Classical Lamination Theory) and the results are compared with Finite element method using FEA software ANSYS. The equations developed by classical lamination theory for symmetric angle ply and cross ply laminated plate are solved by Navier and Rayleigh-Ritz method. The efficiency of Navier and Rayleigh-Ritz method in solving the problems of symmetric angle ply and cross ply laminated plate are investigated by comparing their results with ANSYS. Percentage error of the results from finite element method with Navier and Rayleigh-Ritz methods are studied and compared. The model is extended to study the effect of orientation angle, number of lamina and length to thickness ratio on the deflection of simply supported composite plates for symmetric angle ply plates of stacking sequence (orientation angle) of [+θ/− θ]s . From the discussion, it is found that the percentage error depends on the variables: number of lamina, thickness of each lamina, orientation angle and mesh size. The significance of these variables in reducing the percentage error is studied by statistical tool: ANOVA and the relationship between these variables are established by regression equation. Statistical analysis is conducted by testing their significance at the 5% significance level. The comparative study and analysis of the percentage errors of the semi-analytical methods with finite element methods in solving the problem of laminated composite plates is essential to study the degree of approximation in the results.

An analysis is performed in this research to obtain the natural frequencies of a graphene-platelet-reinforced composite plate at nanoscale. To this end, the nonlocal elasticity theory is applied. A composite laminated plate is considered where each layer is reinforced with GPLs. The amount of GPLs may be different between the layers, which results in functionally graded media. To establish the governing equations of the plate, a quasi-3D plate model is used, which takes the non-uniform shear strains as well as normal strain through the thickness into account. With the aid of the Hamilton principle, the governing equations of the plate are established. For the case of a plate that is simply supported all around, natural frequencies are obtained using the well-known Navier solution method. The results of this study are compared with the available data in the open literature, and, after that, novel numerical results are provided to explore the effects of different parameters. It is depicted that, with the introduction of GPLs in the matrix of the composite media, the natural frequencies of the plate enhance. Also, a proper graded pattern in GPL-reinforced composite plates, i.e., an FG-X pattern, results in the maximum frequencies of the plate. In addition, the introduced quasi-3D plate theory is accurate in the estimation of the natural frequencies of thick nanocomposite plates at nanoscale. [ABSTRACT FROM AUTHOR]

This study investigates the size-dependent free vibration analysis of multi-layered graphene sheets based on exponential shear deformation theory (ESDT), which considers the effects of rotary inertia and transverse shear deformations. In order to capture the effects of length scale parameter on the vibrational behavior of the structure, modified strain gradient elasticity theory is utilized. An elastic multiple-plate model is assumed in which the nested plates are coupled with each other through the van der Waals interlayer forces. The governing equations of motion are derived by implementing Hamilton’s principle and then are solved with the Navier approach. To verify the present model, results in specific cases are compared with the available papers in the literature and excellent agreement is seen. Finally, the effects of various parameters such as aspect ratio, thickness ratio, Winkler modulus, shear modulus, and size effects on the natural frequencies of a multi-layered graphene sheet are presented and discussed in detail.

Many investigators have become interested in nanostructures due to their outstanding mechanical, chemical, and electrical properties. Two-dimensional nanoplates with higher mechanical properties compared with traditional structural applications are a common structure of nanosystems. Nanoplates have a wide range of uses in various sectors due to their unique properties. This paper focused on the static analysis of functionally graded (FG) nanoplates with porosities. The nonlocal strain gradient theory is combined with four-variable shear deformation theory to model the nanoplate. The proposed model captures both nonlocal and strain gradient impacts on FG nanoplate structures by incorporating the nonlocal and strain gradient factors into the FG plate's elastic constants. Two different templates of porosity distributions are taken into account. The FG porous nanoplate solutions are compared with previously published ones. The impact of nonlocal and strain gradient parameters, side-to-thickness ratio, aspect ratio, and porosity parameter, are analyzed in detail numerically. This paper presents benchmark solutions for the bending analysis of FG porous nanoplates. Moreover, the current combination of the nonlocal strain gradient theory and the four-variable shear deformation theory can be adapted for various nanostructured materials such as anisotropic, laminated composites, FG carbon nanotube reinforced composites, and so on. [ABSTRACT FROM AUTHOR]

In the present investigation, free vibration and also forced vibration response of a graphene platelet reinforced composite (GPLRC) laminated curved beam is investigated. It is assumed that each layer of the laminated composite curved beam is reinforced with different amount of graphene platelets which results in a piecewise functionally graded media. Using the first order shear deformation theory, linear strain-displacement relations in polar coordinates, linear elastic constitutive law and the Hamilton principle, the basic governing equations of the curved beam subjected to a moving load are obtained. For the case of a beam with both ends simply supported and applying the Galerkin technique, the governing equations of motion are established. In free vibration analysis, an eigenvalue problem is established while for the case of forced vibration, the Newmark time marching scheme is applied to obtain the temporal evolution of displacement field. The obtained results are well-validated with the available data in the open literature. After that, novel numerical results are provided to explore the influences of different parameters. It is shown that geometrical characteristics of the curved beam and also the weight fraction and distribution patterns of GPLs have significant effects on the free and forced vibration responses of the curved beam. In general, as the weight fraction of GPLs enhances, the frequencies of the curved beam increase and also the induced deflections due to moving load decrease. [ABSTRACT FROM AUTHOR]

Free lateral vibration analysis of gyroscope model is studied in this paper. This gyroscope is modeled as a rotating simply-supported beam which is under an initial thermal stress. Thermo-mechanical properties of the beam are mutable with temperature. For the first time beam is supposed to rotate around a fixed axis in which rotational displacement field is expressed as a liner function in terms of combination of axial and lateral displacements. Dynamic-vibration equations of the proposed model are derived based on the Hamilton's principle. Due to the symmetry of the system, Navier approach is adopted as solution approach. For evaluation, current results are compared with the results available at the technical literature showing high level of accuracy. New results emerged from of this paper imply effects of rotation of the beam and thermal stresses simultaneously upon the dynamic response of beams: different values of lateral velocity factor strongly affect the frequencies of the system; however, axial velocity factor does not play any role. In short, rotation of the beam accompanied by thermal stresses are affecting the dynamic behavior of the beam-type gyroscope remarkably. Consideration of thermal stresses and rotation rates are the most vital factors in the design of a gyroscope. [ABSTRACT FROM AUTHOR]

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In this study, free vibration and buckling analyses of functionally graded (FGM) sandwich beams is investigated by Navier's method. Displacement field is defined according to the first order shear deformation theory, and the equations of motion are derived by the Lagrange's principle. Volumetric ceramic ratio is defined by a power-law rule. In the analytical solution, different trigonometric series functions are used for each end conditions considered. Two cases of functionally graded sandwich beams are considered: a) Homogeneous ceramic core and FGM faces (Type A), and b) FGM core and homogeneous faces (Type B). Natural frequencies and buckling loads are obtained for different boundary conditions, power-law indices and slenderness. Numerical results are compared with the available literature, and a good agreement are obtained between the results. [ABSTRACT FROM AUTHOR]

In this research paper, lateral vibration analysis of simply-supported microbeam under thermal stress is investigated. Microbeam model is presented based on the modified couple stress theory and Timoshenko beam theory. Thermo-mechanical properties of the microbeam are assumed variable by temperature shifts. This means that any shift in the temperature leads to different thermo-mechanical properties. Thermal stress is induced to the system due to the temperature difference between the lateral surfaces and the system itself. Major novelty of the current research includes the variable nonclassical length scale parameter. The mentioned parameter derived from the modified couple stress theory is assumed variable based on the power law. Hamilton's approach is taken to derive the system of governing equations of motion. The mentioned coupled system of equations is solved using the Navier method. For verification, current results are compared with those available at benchmark. This research implies the importance of temperature, distribution profile of nonclassical length scale parameter, and slenderness ratio upon dynamic responses of the present model based on both classical and modified couple stress theories. [ABSTRACT FROM AUTHOR]

Abstract: Buckling analysis of isotropic and orthotropic plates using the two variable refined plate theory is presented in this paper. The theory takes account of transverse shear effects and parabolic distribution of the transverse shear strains through the thickness of the plate, hence it is unnecessary to use shear correction factors. Governing equations are derived from the principle of virtual displacements. The closed-form solution of a simply supported rectangular plate subjected to in-plane loading has been obtained by using the Navier method. Numerical results obtained by the present theory are compared with classical plate theory solutions, first-order shear deformable theory solutions, and available exact solutions in the literature. It can be concluded that the present theory, which does not require shear correction factor, is not only simple but also comparable to the first-order shear deformable theory. [Copyright &y& Elsevier]

Cylindrical shell under concentrated force is a fundamental problem, which provides the understanding of general patterns of deformation and allow to consider many other types of loading and geometries. The common idea of existing approaches is expansion of the looking for solutions into Fourier series with respect to n φ , where φ is a circumferential coordinate, and n is the circumferential wave number. This reduces the problem to the 8th order even differential equation as to axial coordinate. Yet the finding of relevant 8 eigenfunctions and exact relations of 8 constants of integration with boundary conditions are still beyond the possibilities of analytical treatment. Most analytical solutions are based on Vlasov-like solution of simplified 4th order equations with unknown ranges of their accuracies. The goal of paper is threefold. First, to give the exact solutions for infinite shell, which are based on: (a) the well-known Navier approach, and (b) the Galerkin methods with application of decaying exponential functions. Second, to modernize the hypotheses of Vlasov's theory (long-wave axial solution) and supplement it with the short solution, and commonly use both in formulation of boundary conditions, i.e., to take into account that their interaction occurs not due to shear force only but other force and displacement parameters may interact too. Third, to perform the tedious comparison of exact Galerkin and Navier solutions with approximate ones for the whole range of circumferential waves n , assess their accuracy and establish the accuracy of plate-like solution for the larger number of n. [Display omitted] • Exact Navier solution is obtained for concentrated radial force in infinite shell. • Application of decaying exponential functions in Galerkin method is proved to be very effective. • Long solution is supplemented by short solution and high accuracy of their coupled application is established. • Simple Plate-like solution is very accurate for bigger number of circumferential waves. [ABSTRACT FROM AUTHOR]