The problem of the analytical construction of the optimal regulator of oscillatory systems with liquid ‎dampers on the complex plane is considered. Since the fractional derivative is included in the differential ‎equation describing the oscillatory systems with liquid dampers movement, the corresponding input-output ‎transfer function also contains fractional rational orders, the general Larin parameterization scheme is ‎modifying for this case. The results are illustrated by numerical examples and it is shown that they coincide ‎with Letov’s А.М. analytical construction of the optimal regulator.

In this paper, the Elzaki transform method is used for solving two-dimensional (2D) elasticity problems in plane polar coordinates. Airy stress function was used to express the stress compatibility equation as a biharmonic equation. Elzaki transform was applied with respect to the radial coordinate to a modified form of the stress compatibility equation, and the biharmonic equation simplified to a fourth order ordinary differential equation (ODE). The general solution for the Airy stress potential function in the Elzaki transform space was obtained by solving the ODE. By inversion, the general solution for the Airy stress potential function was obtained in the physical domain space variables in terms of four unknown integration constants. Normal stresses and shear stress fields were also determined for the general case of 2D elasticity problems. The Flamant problem was solved as a particular illustration of 2D elasticity problems. The stress boundary conditions and the requirement of equilibrium of the internal stress resultants and the external forces were used simultaneously to determine the four constants of integration. The Airy stress potential function and the normal and shear stress fields were thus completely determined. The principle of superposition was used to obtain the elasticity solutions for the stress fields in the elastic half plane due to strip load of infinite extent, and solutions for horizontal stresses on smooth rigid retaining walls due to strip loads and parallel line load of infinite extent acting on the elastic half plane.

The parametric resonance of the axial vibrations of a cantilever pipe conveying harmonically perturbed two-phase flow is investigated using the method of multiple scale perturbation. The nonlinear coupled and uncoupled planar dynamics of the pipe are examined for a scenario when the axial vibration is parametrically excited by the pulsating frequencies of the two phases conveyed by the pipe. Away from the internal resonance condition, the stability regions are determined analytically. The stability boundaries are found to reduce as the void fraction is increasing. With the amplitude of the harmonic velocity fluctuations of the phases taken as the control parameters, the presence of internal resonance condition results in the occurrence of both axial and transverse resonance peaks due to the transfer of energy between the planar directions. However, an increase in the void fraction is observed to reduce the amplitude of oscillations due to the increase in mass content in the pipe and which further dampens the motions of the pipe.

The aim of this paper is to compare the static deflections and stress results of layered and functionally graded composite beams under static load. In the comparison study, the results obtained for a cantilever beam under point load. The Timoshenko beam and the Euler-Bernoulli beam theories are used in the beam model. The energy based Ritz method is used for the solution of the problem and algebraic polynomials are used with the trivial functions for the Ritz method. Two different materials are considered as layered and functionally graded distribution in a cantilever beam and their static deflections, stress distributions are compared under a point load at free end of the beam. For two different distributions, the formulations of Ritz method are obtained and solved numerically. In the numerical results, the effects of material distribution parameter, aspect ratio on the static deflections and stress distribution of functionally graded beams are obtained and compared with the results of the layered composite beam. Difference among of beam theories are compared for functionally graded and layered beams. Also, some comparison studies are performed in order to validate the using formulations.

In this study, a static and free vibration analysis of single layer FG and sandwich FG plates is carried out using a fifth order shear and normal deformation theory. The displacement field of the present theory includes the terms considering the effect of transverse shear and normal deformation. Also, the terms of the thickness co-ordinate are expanded upto fifth order to predict the accurate bending behavior of the plates. The equations of motion are derived based on Hamilton’s principle, and further solved using Navier’s solution scheme. The present results of displacement, stresses and natural frequencies in sandwich FG plates are obtained and compared with other higher order theories available in literature to check the validity and efficacy of the theory.

This article concentrates on the effect of MHD heat mass transfer on the stagnation point nanofluid flow over a stretching or shrinking sheet with homogeneous-heterogeneous reactions. The flow analysis is disclosed in the neighborhood of stagnation point. Features of heat transport are characterized with Newtonian heating. The homogeneous-heterogeneous chemical reaction between the fluid and diffusing species is included in the mass diffusion equation. The MHD stagnation boundary layer flow is explored in the presence of heat generation/absorption. Numerical convergent solutions are computed via the spectral quasi-linearization method (SQLM). The physical aspects of different parameters are discussed through graphs.

A comprehensive set of ten artificial neural networks <strong>i</strong>s developed to suggest optimal dimensions of type ‘C’ Bi-lobe tanks used in the shipping of liquefied natural gas. Multi-objective optimization technique considering the maximum capacity and minimum cost of vessels <strong>a</strong>re implemented for determining optimum vessel dimensions. Generated populations from a genetic algorithm <strong>a</strong>re used by Finite Element Analysis to develop new models and find primary membrane and local stresses to compare with their permissible ranges using PYTHON coding. The optimum design space <strong>i</strong>s mathematically modeled by training ten artificial neural networks with design variables generated by the Taguchi method. The results <strong>a</strong>re compared with actual design data and the 93% achieved accuracy shows the precision of the developed design system.

Human beings have always made their tools and instruments they need using patterns in nature. Mimicking nature has become the foundation of a new science called Biomimetics. In the present article, multiple forms and levels in nature were utilized to design and create a mouse. The rivers are a good source for choosing the shape of a mouse with lots of stones abraded through the centuries which also have smooth surfaces. In this research, a significant number of stones fitted to hand size were collected and then the best ones were scanned by an optical scanner. The point cloud model obtained was used to design and create the mouse and determine the geometric parameters of the mouse. After extracting the 3D model of the point cloud using a rapid prototyping technique with the Fused Deposition Modeling (FDM) method, some mouse models were designed ambidextrously for left-handed and right-handed people. Considering the results of the mouse evaluation by 30 people who were provided with the mouse, it can be concluded that the created mouse provided a high rate of satisfaction.

The inclusion of complex obstacles within solar channels is the aim of this article. Two obstacles of the form ꞌ+ꞌ interlaced within a two-dimensional and rectangular channel are the subject of our study. The fluid is Newtonian, turbulent, incompressible and has constant properties. The Reynolds number varies from 12,000 to 32,000 with a constant temperature along the upper surface of the channel. The thermal and dynamic analysis of the channel's internal structure has been carefully processed. Different fields of speed and heat, with various profiles of frictions and heat exchange coefficients, have been included in this research. Future work will involve more complex geometries and using nanofluids to assess the optimum conditions for heat transfer enhancements.

Green’s function, an analytical approach in inhomogeneous linear differential equations, is the impulse response, which is applied for deriving the wave equation solution in composite materials mediums. This paper investigates the study of SH wave’s transmission influenced by concentrated point source disturbance in piezomagnetic material resting over heterogeneous half-space. Green function approach is used to solve differential equation and obtain the dispersion relation in determinant form and match with existing classical Love wave equation for the authenticity for the article. The properties of SH wave throughout the considered framework and their state of relying on varied geometrical and physical parameters are scrutinized. The simulated outcomes of disparate physical quantities viz., dimensionless phase velocity, elastic parameter, group velocity, initial stress, piezomagnetic/heterogeneity parameter and stress distribution of SH wave in the considered structure are investigated and used to regulate the behavior of dispersion characteristics of smart material waveguides.