Pentamode metamaterials are a class of extremal materials exhibiting fluid-like mechanical behavior. The mechanical properties of pentamode metamaterials arise from their unique micro-architecture, ...rather than their constituent material. In this research, we present closed-form analytical relationships for the elastic modulus and Poisson’s ratio of pentamode lattice structures with double-cone struts based on cubic diamond morphology. To validate our analytical solutions, we performed numerical simulations and experimental tests, which confirmed the accuracy of the derived relationships. Our findings indicate that increasing the smaller diameter (d) and the larger-to-smaller diameter ratio (α) of the double-cones increases the elastic modulus of pentamode metamaterials. However, within the considered range of d and α, the Poisson’s ratio is nearly constant and lies within the range of approximately 0.5. These analytical relationships provide valuable insight into the mechanical behavior of pentamode metamaterials, which can aid in the design and optimization of new materials with unique properties.
The linear and nonlinear forced vibration response of axially functionally graded (AFG) cylindrical truncated conical and imperfect microbeam subjected to the dynamic harmonically load carried out in ...the presented research. Based on a couple of modified couple stress theory, the Euler-Bernoulli beam theory and von-Kármán theory, the linear and nonlinear governing equations and related boundary conditions for dynamic response of micro-size tubes are derived employing the Hamilton principle. We considered the uniform and nonuniform functions for the cross-section, in which the convex, linear and exponential functions are the nonuniform sections, and the porosity is regarded as an imperfection. The generalized differential quadrature method (GDQM) is used to prepare the initial conditions for homotopy perturbation (HP) techniques as the semi-analytical approach to calculate the linear and nonlinear results of dynamic responses. The obtained linear and nonlinear results of the free and forced vibration response show the negative and positive effects of some parameters such as the porosity parameter, the nonlinear amplitude, the small-scale parameter, AFG parameter, and different cross-section impact on the dynamic deflection and natural frequency of micro-scale tube and beams with both clamped and simply-supported boundary conditions.
In the context of nonclassical continuum mechanics, the nonlocal strain gradient theory is employed to develop a nonclassical size dependent model to investigate the dynamic behavior of a CNTs ...reinforced composite beam resting on two parameters elastic foundations under a moving load. The governing dynamic equations of motion are derived based on third-order shear deformation theory using Hamilton's principle. An analytical solution methodology is developed using Navier's procedure is developed to derive the analytical solution for the equations of motion. The developed methodology is checked and compared. Parametric studies are conducted to demonstrate the applicability of the developed procedure to investigate the dynamic behavior of CNTs beams under moving load. Effects of the elastic foundation parameters, volume fraction, CNTs configuration, the nonclassical parameters, and the moving load velocity parameter on the dynamic behavior of CNTs beams under moving load are investigated and analyzed. The obtained results are supportive for design and manufacturing of composite CNTs beams.
New generalized Schrödinger equations with polynomial nonlinearities are considered. The Cauchy problem for these equations cannot be solved by the inverse scattering transform and optical solitons ...of these equations are looked for taking into account the traveling wave solutions.
Application of the well-known auxiliary equations as the Riccati equation and equations for elliptic functions for construction of solutions of new generalized Schrödinger equations is impossible right away. Therefore solutions of nonlinear ordinary differential equations are found using the transformations of dependent and independent variables. This extended approach allows us to obtain some new auxiliary nonlinear ordinary equations.
New auxiliary differential equations allow to look for optical solitons of the other generalized Schrödinger equations. We demonstrate that by using new auxiliary equations, we can find the optical solitons of the generalized nonlinear Schrödinger equations of the fourth degree with a polynomial of the eighteenth power.
In this paper, the free vibration analysis of rectangular plates composed of functionally graded materials with porosities is investigated based on a simple first-order shear deformation plate ...theory. The network of pores in assumed to be empty or filled by low pressure air and the material properties of the plate varies through the thickness. Using Hamilton's principle and utilizing the variational method, the governing equations of motion of FG plates with porosities are derived. Considering two boundary layer functions, the governing equations of the system are rewritten and decoupled. Finally, two decoupled equations are solved analytically for Lévy-type boundary conditions so as to obtain the eigenfrequencies of the plate. The effects of porosity parameter, power law index, thickness-side ratio, aspect ratio, porosity distribution and boundary conditions on natural frequencies of the plate are investigated in detail.
•An analytical solution for free vibration analysis of porous FG plates is presented.•The variation of natural frequency with respect to e depends upon the value of n.•Opposite trends for variation of ϖ against, is seen as gets larger.•The variation of natural frequency is more sensitive to n for FGM-I plates.
In this paper, a new integral transform operator, which is similar to Fourier transform, is proposed for the first time. As a testing example, an application to the one-dimensional heat-diffusion ...problem is discussed. The result demonstrates accuracy and efficiency of the present technology to find the analytical solution for the heat-transfer problem.
•The symplectic methodology is extended to line-hinged plate problems.•Analytical free vibration solutions of non-Lévy-type line-hinged plates are reported.•No predetermination of solution forms is ...needed in the solution procedure.•The effects of size parameters and boundary conditions are quantitatively revealed.
The free vibration behavior of non-Lévy-type line-hinged plates is common in engineering, but it is intractable to deal with such an issue by analytical methods for the difficulties in solving the fourth-order partial differential equations under hinge conditions. This paper aims to extend the symplectic methodology to the free vibration of non-Lévy-type line-hinged plates. The solution procedure involves dividing a line-hinged plate into subplates, processing boundary and hinge conditions, formulating the corresponding subproblems which can be solved with an analytical symplectic superposition method, determining the imposed mechanical quantities, and integrating the solutions of subproblems. Compared to previous studies on line-hinged plates, the present analytical free vibration solutions are obtained with no need for predetermination of solution forms. The comprehensive results under six non-Lévy-type boundaries are all well validated and utilized for a parametric study, providing guidance for the structural design of hinged plates.
A theoretical study of two-phase non-Newtonian fluid with heat transfer is presented in this article. Jeffrey fluid model is used as the base liquid to form a multiphase suspension with the help of ...gold particles. Heating effects have also been applied on an electro-osmotic two-phase flow through a divergent channel. The lubrication effects have been applied to dampen the skin friction of the opposite walls. An analytical solution is obtained for the nonlinear multiphase fluid flow with heat transfer. Separate expressions for the volumetric flow rate of two-phase flow and pressure gradient are determined via a complex mathematical manipulation. A concise parametric study reveals that slippery walls of the channel have a prominent influence on the momentum of both phases.
•3D thermo-elastic bending solutions are obtained for functionally graded circular and annular plates reinforced with GPLs.•Thinner GPLs are preferred to achieve better enhancement in bending ...stiffness hence reduced bending deflection.•The parabolic GPL distribution offers the best reinforcing effect, followed by uniform then linear distribution patterns.•For plates reinforced by uniformly distributed GPLs, the temperature field and radial stress distribution are not affected by GPL's total content.
Within the framework of three-dimensional elasticity theory, this paper investigates the axisymmetric bending of novel functionally graded polymer nanocomposite circular and annular plates reinforced with graphene nanoplatelets (GPLs) whose weight fraction varies continuously and smoothly along the thickness direction. The generalized Mian and Spencer method is utilized to obtain the analytical solutions of nanocomposite circular and annular plates under a combined action of a uniformly distributed transverse load and a through-thickness steady temperature field. Three different distribution patterns of GPLs within the polymer matrix are considered. The present analytical solutions are validated through comparisons against those available in open literature for the reduced cases. A parametric study is conducted to examine the effects of GPL weight fraction, distribution pattern, plate thickness to radius ratio, and boundary conditions on the stress and deformation fields of the plate. The results show that GPL nanofillers with a low content can have a significant reinforcing effect on the bending behavior of the thermo-mechanically loaded plate.
This paper presents an anisotropically elasto-plastic solution to the undrained expansion of a cylindrical cavity in K0-consolidated clay. The elasto-plastic constitutive relationship following the ...soil yielding process is described by the K0-based modified Cam-clay (K0-MCC) model, which can properly reflect the anisotropic effects on the soil behaviour. Following the large strain deformation theory, the problem is reduced to solving a system of first-order ordinary differential equations in the plastic region. The semi-analytical solutions to the radial, tangential and vertical effective stresses are obtained using the Lagrangian method and the elastic–plastic (EP) boundary conditions. In addition, based on the semi-analytical results, an approximate closed-form solution is presented for practical purposes. Extensive comparisons with the isotropic constitutive model-based solutions have been performed to illustrate the effects of the initial stress anisotropy and initial stress-induced anisotropy on the cavity expansion and the stress distributions. The present solution incorporates the anisotropic properties of the natural K0-consolidated clay, thereby providing a more realistic theoretical basis for the practical engineering problems such as the pile installation and the pressuremeter tests.
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