Journal of Applied and Computational Mechanics
Volume:8 Issue: 3, Summer 2022

The attachment of turbulators, such as baffles, fins, ribs, bars, and blocks, inside the thermal solar receiver ducts, is among the most effective mechanisms for important thermal exchange by creating the turbulence, extending the trajectory of the flow, increasing the surface of heat exchange, forcing recycling cells, and hence a high thermal exchange. The solar finned and baffled heat exchangers are employed in a wide application interval, and it is important to examine the design of a duct for this configuration of the flow field and its effect on the heat transport phenomenon. In This study, dynamic field simulations are reported in horizontal rectangular form ducts, using three obstacles with oil HTF (heat transfer fluid). Two various finned and baffled duct configurations are treated, i.e., case (A) with one fin and two baffles, and case (B) with two fins and one baffle. Different hydrodynamic fields, i.e., X-velocity and Y-speed, as well as various X-velocity profiles in many flow stations, related to Re value, are analyzed. A computational approach is applied in order to simulate the oil flow, using finite volume (FV) integration method, SIMPLE discretization algorithm, QUICK interpolation scheme, Standard k-epsilon turbulence model, and ANSYS FLUENT 12.0 software. Simulation results reported an unstable flow structure, with powerful recycling cells, on the backsides of each fin and baffle, as a result of fluid detachment at their upper front sharp edges, in both studied models (A and B). As expected, the first duct model, i.e., Case A, has better X- and Y-velocity values, due to its large recirculation regions. In This paper, many physical phenomena, such as the turbulence, instability, flow separation, and the appearance of reverse secondary currents, are reported. As its data confirmed by many previous numerical and experimental results, the suggested new models of finned and baffled heat exchangers filled with high thermal conductivity oil, allow an improvement in the dynamic thermal-energy behavior of many thermal devices such as flat plate solar collectors.

An analytical effort is made to achieve cognition on the effect of time-dependent mechanical loading ‎on the stress fields of rotating disks with non-uniform thickness and density. At high variable angular ‎velocities and accelerations, evaluation of the effect of shear stress on the values of von Mises stress is ‎significant and it is excellent to consider shear stress in this equivalent stress calculation alongside the ‎radial and tangential stress. In the proposed analytical model, the Homotopy perturbation method (HPM) ‎solves the general structure of rotating disks equilibrium equations in both radial and tangential ‎directions. HPM is an efficient tool to solve linear and nonlinear equations, providing solutions in quick ‎converging series. The results obtained through this process are then confirmed using the finite ‎difference method and the exact solution in the literature. The effect of parameters in angular velocity ‎and acceleration functions with the parameter in the thickness function and the effect of boundary ‎conditions on the values of elastic limit angular velocity and acceleration are established by performing ‎numerical examples. Furthermore, the effect of shear stress on the maximum values of ‎von Mises stress is discussed. It is shown that shear stress has more influence on the distribution of ‎equivalent von Mises stress in the elastic region. It is shown the introduced analytical model is useful for ‎evaluating rotating disk with any arbitrary shape of thickness and density function, without using the ‎commercial finite element simulation software.

In this research, possible methods to improve the air distribution patterns of an operating room (OR) employing CFD method are investigated. Laminar airflow (LAF), turbulent airflow (TAF), and LAF with the air curtain are examined. It is found that LAF and LAF with the air curtain cases are superior to TAF-based cases. The study shows that the LAF and LAF with the air curtain cases as the proposed configurations have an acceptable capability to maintain the indoor air conditions within the range recommended by the standards. According to the simulations, the LAF with the air curtain case is the most suitable case in terms of the contamination risk, and it is recommended to be implemented in the existing OR.

In order to investigate the shape effect of nanoadditives on thermal conductivity of nanofluids, different length carbon nanotubes (CNTs) are made and using a two-step method, different nanofluids are prepared. The CNTs are cut into different lengths by functionalization at different refluxing times of 1, 2 and 4 hours. To probe the effect of aspect ratio of CNTs on the obtained experimental data, modified Hamilton-Crosser and Nan models are developed. It is found that the original Hamilton-Crosser and Nan models could not predict the experimental thermal conductivities. By replacing n = 6 + xL/D instead of the shape factor of n=6 in the Hamilton- Crosser, where L and D were length and diameter of CNTs and also by replacing φ (xL/D) instead of φ (volume fraction) in the Nan model, the prediction of modified equations show very good accordance with the experimental data which means the shape of nanoadditives has high impact on nanofluids’ properties.

Shot-peening is a mechanical surface treatment used extensively in the industry to enhance the performance of metal parts against fatigue. Thus, it is important to determine main parameters of shot-peening in order to obtain its optimal values. The purpose of this study is to achieve a statistical model to determine the important parameters of the shot-peening process by considering the effect of sample thickness on the responses and achieving the multi-objective optimal parameters. To do this, response surface methodology are used to determine the governing models between the response variable and the input parameters. Shot velocity, shot diameter, coverage percentage and sample thickness are selected as shot-peeningparameters. Residual compressive stress, its depth and roughness are considered as the response variable. Using finite element analysis, shot-peening process are simulated. The desirability function approach is used for multi-objective optimization so that the optimal shot-peeningparameters, which simultaneously provide two response variables in optimal mode, are obtained. The results show that surface stress and maximum residual stress are independent of shot velocity, whereas, the depth of the compressible stress and roughness are directly related to shot velocity. In addition, thickness modifies surface stress and the depth of the compressible stress. The optimal conditions for surface stress, maximum compressive stress, and roughness simultaneously with high-coverage and low-velocity can be achieved as well.

In the present paper, a comparison between the simulation performance of a highly nonlinear model in MATLAB/Simulink and a compiled language has been drawn. A complete powertrain layout was formed in Simulink and the same model was developed from scratch in Fortran 2003 which led to creating a complete simulation software program named Powertrain Simulator. The results show that for a system with not many details and phase changes, both of the simulation environments offer acceptable performance. However, when the modeling layout is overly complicated, developing the model in a compiled language is a smarter choice.

In this paper, we numerically solve the equations for hydromagnetic nanofluid flow past semi-infinite parallel plates where thermal radiation and a chemical reaction are assumed to be present and significant. The objective is to give insights on the important mechanisms that influence the flow of an electrically conducting nanofluid between parallel plates, subject to a homogeneous chemical reaction and thermal radiation. These flows have great significance in industrial and engineering applications. The reduced nonlinear model equations are solved using a Newton based spectral quasilinearization method. The accuracy and convergence of the method is established using error analysis. The changes in the fluid properties with various parameters of interest is demonstrated and discussed. The spectral quasilinearization method was found to be rapidly convergent and accuracy is shown through the computation of solution errors.

The magnetohydrodynamic flow of a viscous fluid over a constant wedge in three- dimensional boundary-layer has been analyzed both numerically and asymptotically. The magnetic field is applied normal to the flow. The mainstream flows aligned with wedge surface are assumed to be proportional to the power of the coordinate distances. The system is described using three-dimensional MHD boundary-layer equations which are converted to couple nonlinear ordinary differential equations using similarity transformations. The resulting equations are solved numerically using the Keller-box method which is second-order accurate and asymptotically for far-field behavior. Both numerical and asymptotic solutions give good agreement in predicting the velocity behaviors and wall shear stresses. The effects of Hartmann number, pressure gradient and shear-to- strain-rate on the velocity fields are studied. Particularly, it is shown that the solutions of three-dimensional boundary-layer for variable pressure gradient exist, its effects are important on the boundary-layer flow. Results show that there are new families of solutions for some range of shear-to-strain-rate and there exists a threshold value of it beyond which no solutions exist. For some range of parameters, there is a reverse flow at which our boundary-layer assumptions are no longer valid. Various results for the velocity profiles, wall-shear stresses and displacement thicknesses are also obtained. The physical mechanisms behind these results are discussed.

The main purpose of this study is to develop an understanding of the turbulent boundary layer calculation to analyze displacement of the separating point in diffusers. An approximate method has been used which is based on an analogy with the rheological power law and is applied in the study of non-linear viscous flows. At first, the method has been validated with the experimental data in the same experimental cases study. An appropriate geometric with and without the Nano-fluids in the straight-wall and curved-wall conical diffusers has been investigated. Its analyses output was compared with the results obtained by a numerical code. Also, the proposed method is more practical and can be used in diffuser design procedures.

High-resolution schemes are designed for resolving shocks without significant numerical dissipation and dispersion. Achieving higher-order and high-resolution is a challenging task because of the non-monotonicity of the higher-order schemes. In this article, we have presented second-order and third-order slope limiters having an improved shock resolution and accuracy. The present limiters are tested on one-dimensional and two-dimensional unstructured grids and compared with the existing limiters. The numerical result shows that the present limiters have an excellent shock resolving property and accuracy than other limiters. In blast wave problems, it has shown over 200% more accurate results than the other limiters.

The current study is involved to analytical solution of nonlinear oscillators under initial velocity. By using energy conservation principle, system initial condition converts to condition which oscillator’s velocity become zero. When oscillator’s speed is zero and placed out of movement’s origin, the relation between frequency and amplitude could be extracted. By paying attention to energy conservation principle and relation between the initial velocity and amplitude, the frequency-amplitude relation is extended to frequency-initial velocity relationship. In order to demonstrate the effectiveness of proposed method, Duffing oscillator with cubic nonlinearity and oscillator with discontinuity are considered. Comparison of results with numerical solution shows good agreement. The proposed method is simple and efficient enough to achieve the analytical approximation of nonlinear autonomous conservative oscillator with initial velocity.

The present article reports the transient response of longitudinal fins having linear and non-linear temperature dependent thermal conductivity, convection coefficient and internal heat generation under two cases of base boundary condition, (i) step change in base temperature and (ii) step change in base heat flux. The fin tip is assumed to be adiabatic. Both, linear and non-linear, temperature dependency of thermo-physical properties is addressed in the mathematical formulation and the solution for the above cases is obtained using Lattice Boltzmann method (LBM) implemented in an in-house source code. LBM, being a dynamic method, simulates the macroscopic behavior by using a simple mesoscopic model and offers enormous advantages in terms of simple algorithm to handle even the most typical of boundary conditions that are easy and compact to program even in case of complicated geometries too. Although the transient response of longitudinal fins has been reported earlier, however power law variation of thermophysical properties for the above two base condition has not been reported till date. The present article first establishes the validity of LBM code with existing result and then extends the code for solving the transient response of the longitudinal fin under different sets of application-wise relevant conditions that have not been treated before. Results are reported for several combination of thermal parameter and are depicted in form of graphs.

In this work, the combined impacts of magnetohydrodynamics and fin surface inclination on thermal performance of convective-radiative porous fin with temperature-invariant thermal conductivity is numerically study using finite difference method. Parametric studies reveal that as the inclination of fin, convective, radiative, magnetic and porous parameters increase, the adimensional fin temperature decreases which leads to an increase in the heat transfer rate through the fin and the thermal efficiency of the porous fin. It is established thatthe porous fin is more efficient and effective for low values of convective, inclination angle, radiative, magnetic and porous parameters. The thermal performance ratio of the fin increases with the porosity parameter.

This work reports the heat and mass transfer of the 2- D MHD flow of the Casson and Williamson motions under the impression of non-linear radiation, viscous dissipation, and thermo-diffusion and Dufour impacts. The flow is examined through an extending zone along with inconsistent thickness. The partial differential equations are extremely nonlinear and lessen to ODEs throughout of the appropriate similarity transformation. The system of nonlinear and coupled ODEs is handled applying a numerical approach with shooting procedure. Numerical solutions for momentum and energy descriptions are deliberated through graphs and tabular form for the impacts of magnetic parameter, Soret and Dufour variables, momentum power index variable, Schmidt number, wall thickness variable, without dimensions velocity slip, heat jump and mass jump variable. Outcomes illustrate that the momentum, temperature, and concentration transfer of the laminar boundary layers of equally non-Newtonian liquid motions are non-consistent. A comparison made with the existing literature which shows an good agreement and confidence of the present outcomes. It shows that Casson parameter restricted the skin friction, local heat and mass transfer while l enhanced the skin friction, local heat and mass transfer. Velocity slip constant decreases the skin friction, local heat and mass transfer and a similar observation for thermal slip constant while an opposite phenomena for the solutal slip constant.

In this work, the axisymmetric-vibrational behavior of a size-dependent circular nano-plate with functionally graded material with different types of boundary conditions was investigated. The analysis was performed based on the Stress-driven model (SDM) and Strain-gradient theory (SGT) in conjunction with classical plate theory. The governing equations of motion and their corresponding equations for boundary conditions were obtained based on Hamilton’s principle and solved using the generalized differential quadrature rule. Results show that this method is applicable to the vibrational analysis of such structures with a fast convergence rate; as N approaches 6 for the first mode, and 10 for the second as well as the third and fourth modes, regardless of the type of boundary condition. In both models, the influences of various parameters such as size-effect parameter Lc, material heterogeneity index n, and types of boundary conditions were obtained on the first four modes and compared with each other. Results indicate that the natural frequencies in these modes increase with an increase in the heterogeneity index n, and size-effect parameter Lc. Additionally, these parameters appear to have a stiffening effect on the nano-plate vibrational behavior. However, for a nano-plate resting on a knife or simply supported edge, in the first mode, the SDM shows a more stiffening effect on the plate behavior as compared with the SGT. Nonetheless, for the clamped and free edge boundary conditions, both models predicted the same behavior. The SGT showed a higher-stiffening effect only in the fourth mode, for all types of considered boundary conditions.

The paper presents the results of an experimental study and numerical simulation of dynamic deformation of dry clay at strain rates of ~103 s-1. The main physical and mechanical characteristics of the clay were determined using the modified Split Hopkinson Pressure Bar method for testing of lowly cohesive media in a rigid cage. Three series of experiments were carried out at strain rates of 1400 s-1, 1800 s-1 and 2500 s-1. The maximum values of the realized in the experiment axial stresses in clay were about 400 MPa and maximum pressures were 250 MPa. Based on the results of the experiments, the dependences of axial stresses on axial deformations σx-εx, shear stresses on pressure τ-P and pressure on volumetric deformation P-e (curves of volumetric compressibility) were plotted. The shear resistance of clay is noted to be well described by the Mohr-Coulomb law. The obtained deformation diagrams are found to be practically independent of deformation rate. The clay behavior under dynamic loads is shown to be essentially nonlinear. On the basis of the obtained experimental data, a parametric identification of the clay deformation model in the form of Grigoryan's constitutive relation was carried out, which was implemented in the framework of the LS-DYNA software in the form of MAT_SOIL_AND_FOAM model. Using the LS-DYNA computational complex, a numerical simulation of the deformation process of a sample under real experimental conditions was carried out. In the computational experiment, the clay behavior was described by the identified model. Good agreement was obtained between numerical and experimental results.

The beam theory allowing for rotary inertia and shear deformation and without the fourth order derivative with respect to time as well as without the slope inertia, as was developed by Elishakoff through the dynamic equilibrium consideration, is derived here by means of both direct and variational methods. This formulation is important for using variational methods of Rayleigh, Ritz as well as the finite element method (FEM). Despite the fact that literature abounds with variational formulations of the original Timoshenko-Ehrenfest beam theory, since it was put forward in 1912-1916, until now there was not a single derivation of the version without the fourth derivative and without the slope inertia. This gap is filled by the present paper. It is shown that the differential equations and the corresponding boundary conditions, used to find the solution of the dynamic problem of a truncated Timoshenko-Ehrenfest via variational formulation, have the same form to that obtained via direct method. Finally, in order to illustrate the advantages of the variational approach and its adaptability to the finite element formulation, some numerical examples are performed. The calculations are implemented through a software developed in Mathematica language and results are validated by comparison with those available in the literature.

Shang et al. (Commun. Nonlinear Sci. 94, 105556, 2022) proposed an efficient and robust synchronization estimation between two not necessarily stationary time series, namely the refined cross-sample entropy (RCSE). This method considered the empirical cumulative distribution function of distances using histogram estimator. In contrast to classical cross-sample entropy, RCSE only depends on a fixed embedding dimension parameter. In this paper, the RCSE is revisited as Freedman-Diaconis rule was considered to estimate the number of bins for the cumulative distribution function. Results are illustrated with some simulations based on 2D Hénon maps, the sinusoidal model, and the Lorenz attractor. In addition, a practical study of foreign exchange rate time series is presented. Specifically, the Canadian/US and Singaporean/US dollar time series were considered to compute the synchrony level between the 1995-1998 (before the 1999 Asian financial crisis) and the 1999-2003 (post-crisis) periods.

The paper proposes a new technique for the well-test data interpretation using two different steady-state flow tests of gas condensate well to determine the initial value of the effective reservoir permeability and the permeability change factor. The described technique has been developed on the base of the Binary filtration model of a multicomponent hydrocarbon system which considers the gas-condensate mixture as a composition of two pseudo components, taking into account the phase transformation of pseudo components and the mass exchange between the phases. The implementation of the new method requires data on well flow rates measured in two different steady-state conditions. The presented algorithm is verified on a number of examples (including real data) covering a wide range of changes in reservoir pressure and reservoir compaction factor. The results of a number of numerical experiments have confirmed the high reliability of the proposed technique.

Perturbed motions of a rigid body, close to the Lagrange case, under the action of restoring and perturbation torques of forces are investigated in the paper. The following problem is formulated: investigating solutions behavior of system of equations of motion for nonzero values of small parameter on a sufficiently long time interval. To analyze a nonlinear system of equations of motion, the averaging method is used. The problem can be decomposed into slowly and quickly changing variables. Conditions for the possibility of averaging the equations of motion with respect to the phase of nutation angle are presented and averaging procedure for slow variables of a perturbed motion of a rigid body in the first approximation is described. As an example of the developed procedure, we investigate a perturbed motion, close to Lagrange case, taking into account constant dissipative and small torque, and dissipative torques depending on slow time. A new class of rotational motions of a dynamically symmetric rigid body about a fixed point has been investigated with restoring and perturbation torques of forces being taken into account.

Exact solutions for non-Newtonian fluids are rare, particularly for Maxwell fluids [1], such solutions do not exist. Generally, in non-Newtonian fluids, the relation which connects shear stress and shear rate is non-linear and the constitutive relation forms equations of non-Newtonian fluids which are higher order and complex as compared to Navier-Stokes equation governing the flow of viscous fluid. Due to this high nonlinearity, closed form solutions for non-Newtonian fluid flows are not possible for the problems with practical interest. More exactly, when such fluids problems are tackled via Laplace transform technique, often the inverse Laplace transforms of the transformed functions do not exist. Due to this difficulty, the researchers are usually using numerical procedures for finding the inverse Laplace transform. However, those solutions are not purely regarded as exact solutions. Owing the great diversity in the physical structure of non-Newtonian fluids, researchers have proposed a variety of mathematical models to understand the dynamics of such fluids. Mostly, these models fall in the subcategory of differential type fluids or rate types fluids. However, a keen interest of the researchers is seen in studying rate types fluids due to the fact that they incorporate both the elastic and memory effects together. The present comments concern some doubtful results included in the above paper [2].

This paper discusses the problem of evaluating the microhardness gradient effect on surface wear of an ultra-high molecular weight polyethylene (UHMWPE) films treated with low-pressure plasma. Its solution was first obtained on the basis of the well-known Archard's wear law, modified taking into account the use of approximating dependences of negative depth gradients of surfaces microhardness, calculated on the basis of experimental data obtained by the nanoindentation method for samples with different plasma processing times (from 3 to 12 minutes). The wear evaluation was carried out in the ANSYS and MATLAB software in accordance with the requirements of ISO 14242-1 using the method of numerical simulation developed by authors. The simulation results show that such an integral parameter as cumulative volume wear is significantly lower for specimens treated with low-pressure plasma as compared to untreated ones. It has been found that both linear and cumulative volume wear decrease with an increase in the plasma processing time of the sample. The largest reduction (4 times compared to untreated) has been obtained for samples with a hardness gradient obtained by plasma surface treatment for 12 minutes. This time can be considered the maximum possible for processing UHMWPE with low-pressure plasma, since further increase in this time enhances the sample surface roughness and, consequently, the coefficient of friction. The use of low-pressure plasma treated UHMWPE films in THR will significantly reduce their wear and the likelihood of osteolysis, and thus increase the THR lifespan.

In this article, two-layer shallow flow model with non-flat basal topography is considered. The presence of coupling terms in two layers make the system conditional hyperbolic. The kinetic flux-vector splitting (KFVS) scheme is applied to approximate the corresponding one-dimensional two-layer shallow flow equations. Our interest lies in the numerical approximation of the model referred to above, the complexity of which poses numerical problems. The higher order accuracy of the scheme is achieved by using a MUSCL-type initial reconstruction and Runge-Kutta time stepping method. The scheme is able to treat variety of flow conditions. A number of test cases are carried out to verify the performance of the suggested method. The conservation and solution element (CESE) scheme is used for comparison. It is observed from the comparison that KFVS resolves the shocks more effectively than CESE scheme.

The mathematical description of various processes such as the nonlinear Klein-Gordon equation occurring in mathematical physics leads to a nonlinear partial differential equation. The mathematical model is only the first step, however, towards finding the solution of the problem under consideration. It has become possible to develop realistic mathematical models with the currently available computing power for complicated problems in science and engineering. To the best of our knowledge, systematically using the collocation method to acquire the numerical solution has not been previously used for the Klein-Gordon equation. The main aim of this paper is to systematically use the collocation method to acquire the numerical solution of the two coupled nonlinear non-homogeneous Klein-Gordon partial differential equations. We examine and analyze their stability, in detail. To this aim, we use the Von Neumann stability method to show that the proposed method is conditionally stable. A numerical example is introduced to demonstrate the performance and the efficiency of the proposed method for solving the coupled nonlinear non-homogeneous Klein-Gordon partial differential equations. The numerical results demonstrated that the proposed algorithm is efficient, accurate, and compares favorably with the analytical solutions.

A two-dimensional stress-function method describing the stress transfer in a three-layered adhesive bonded graphene and poly(methyl methacrylate) nanocomposite structure, subjected to axial load is developed and applied. The governing ordinary differential equation of fourth order with constant coefficients for the axial stress in the first layer is obtained minimizing the strain energy in the whole structure and solved analytically. The two-dimensional stresses and strains (axial, shear and peel) in the structure’s layers are expressed and calculated as functions of this axial one and its derivatives and illustrated with graphics. The model graphene strain is compared with experimental data for strain in graphene and shear-lag model results from literature and shows good agreement at 0.4% external strains.

In the present day, non-ductile reinforced concrete (RC) members have still appeared in certain parts of the existing old buildings and bridges. These structures always exhibit shear failure when they have been subjected to seismic loading, resulting in a complicated problem for studying or simulating the behaviors of these structures. The soil-structure interaction is a part of these problems that are of interest and motivated in the current study. Therefore, this paper proposes a novel frame model on the Kerr-type foundation with the inclusion of the shear-flexure interaction for the analysis of the non-ductile RC members resting on the foundation. The proposed model is derived from the displacement-based formulation together with the Timoshenko beam theory. The effects of shear-flexure interaction are taken into account in the proposed model through the shear constitutive law. Finally, two numerical simulations are used to assess the capability, accuracy, and efficiency of the proposed model to characterize non-ductile RC members resting on the foundation. Furthermore, these simulations demonstrate the impact of the shear-flexure interaction on the responses of non-ductile RC members on the foundation.

In racing motorcycles, the maximization of power transmission from the engine to the rear wheel is one of the critical aspects for improving the performance. Therefore, it is important to improve as much as possible the efficiency of the chain drive, consisting of a front sprocket on the output shaft of the transmission and a rear sprocket connected to the rear wheel, linked by a roller chain. In this study, a multibody model of a chain drive of a racing motorcycle involving high rotational speeds is developed and validated. The energy losses are analyzed, highlighting their dependency on working conditions, and the efficiency is studied as a function of number of teeth on the sprockets, mounting of the chain and sprockets, selected speed ratio, and chain pitch. As a result, it is found that the efficiency is improved by a larger number of teeth with an equal speed ratio, by reducing the chain pitch (while keeping the sprocket diameters constant), and by larger diameter sprockets (in every working condition, including those of high rotational speeds, in contrast to findings in previous literature). Variations in clearances in the chain influence the efficiency, while variations of center distance between sprockets is not influential if the clearances are kept constant.

Volumetric self-priming pumps with deformable impeller blades are very common devices in the food industry, especially in the presence of viscous liquids that tend to foam or contain suspended solids, but also when working under vacuum with good suction capacity is needed. These pumps are characterized by a circular chamber with an eccentric, in which the impeller rotates: due to the continuous deformation of flexible blades, the liquid is moved up to the discharge. The exact evaluation, moment by moment, of the hyperelastic behaviour of the impeller represents a quite complex task, involving several miscellaneous phenomena. In this study a simplified quasistatic analysis by finite element discretization is proposed, able to evaluate with reasonable approximation the stress/strain state of the impeller blades during their rotation. Aspects such as material hyperelasticity, large displacements, large deformations, non-linearity in contacts, frictional and inertial forces were considered.

With the aid of the decomposition method and the Lyapunov direct method, stability of linear gyroscopic systems with switching and a constant delay in positional forces is investigated. The cases of synchronous and asynchronous switching are studied. The efficiency of the application of the Razumikhin approach and Lyapunov—Krasovskii functionals for the stability analysis of such systems is compared. The results of a numerical simulation are presented to illustrate the obtained theoretical conclusions.

Microelectromechanical systems (MEMS) is a very vast field and has been identified as lots of potential in tiny instruments. Because of their unique and exciting properties such as small sizes, low power consumption, reliability, and their capability of batch fabrications, their role in the production of microstructures has gained much importance for researchers and industries. The following study includes an overview of current asymptotic approaches and novel innovations which are applicable not only to weakly nonlinear equations but also to highly nonlinear equations derived from MEMS models. Moreover, the approximate analytical solutions obtained by these asymptotic approaches are valid across the whole solution domain. Various limitations of traditional perturbation method and variational iteration method are discussed and different modified versions of perturbation approaches and variational theory are provided to overcome these existing flaws. Two-scale idea for MEMS technology is also described. Some examples are given to elucidate the effectiveness and convenience of these methodologies.