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In this paper, the authors propose the application of the Gibbs–Appell equations to obtain the equations of motion in the case of a mechanical system that has elements with a micro-polar structure, containing voids. Voids can appear as a result of the processing or manufacturing of the parts, or can be intentionally introduced. This research involves a model of the considered solid material containing voids. To determine the dynamic behavior of such a system, the Gibbs–Appell (GA) method is used to obtain the evolution equations, as an alternative to Lagrange's classical description. The proposed method can be applied to any mechanical system consisting of materials with a micro-polar structure and voids. The study of such systems is interesting because the literature shows that even a reduce number of small voids can produce significant variations in physical behavior. The proposed method requires a smaller number of mathematical operations. To apply this method, the acceleration energy is calculated, which is then used to derive the equations. The method comes with advantages in the application to multibody systems having the mentioned properties and, in particular, in the study of robots and manipulators. Using the GA method, it is necessary to do a fewer differentiation operations than applying the Lagrange's equations. This leads to a reduced amount of computation for obtaining the evolution equations. [ABSTRACT FROM AUTHOR]

Let D be a relatively compact domain in an n-dimensional Kähler manifold with a C 2 smooth boundary that satisfies some "Hartogs-pseudoconvexity" condition. Assume that Ξ is a positive holomorphic line bundle over X whose curvature form Θ satisfies Θ ≥ C ω , where C > 0 . Then, the ∂ ¯ -Neumann operator N and the Bergman projection P are exactly regular in the Sobolev space W m (D , Ξ) for some m , as well as the operators ∂ ¯ N , ∂ ¯ ⋇ N . [ABSTRACT FROM AUTHOR]

This article introduces a new model that can be used to describe elastic thermal vibrations caused by changes in temperature in elastic nanobeams in response to transverse external excitations. Using the idea of nonlocal elasticity and the dual-phase lagging thermoelastic model (DPL), the coupled equations of motion and heat transfer were derived to explain small-scale effects. Additionally, modified couple stress theory (MCST) and Euler–Bernoulli (EB) beam assumptions were considered. The proposed theory was verified by considering the thermodynamic response of nanobeams moving horizontally at a constant speed while one end is subjected to a periodic thermal load. The system of governing equations has been solved numerically with the help of Laplace transforms and one of the tested evolutionary algorithms. The effects of changing the nonlocal modulus, the magnitude of the external force, and the length scale parameter on the system fields were investigated. It is also shown how the behavior of the thermal nanobeam changes depending on the phase delay factors in addition to the horizontal velocity of the beam. To determine this model's accuracy, its results were compared with the results of the classical continuity model and thermoelastic concepts. The numerical results show that when the nanobeam moves, the length scale can change the studied thermal and mechanical vibration wave patterns and physical fields. Additionally, during thermally stimulated vibrations, thermodynamic effects that have implications for the dynamic design and performance improvement of nanostructures must be considered. [ABSTRACT FROM AUTHOR]

By laminating piezoelectric and flexible materials, we can increase their performance. Therefore, the electrical and mechanical properties of layered piezoelectric materials subjected to electromechanical loads and heat sources must be analyzed theoretically and mechanically. Since the problem of infinite wave propagation cannot be addressed using classical thermoelasticity, extended thermoelasticity models have been derived. The thermo-mechanical response of a piezoelectric functionally graded (FG) rod due to a moveable axial heat source is considered in this paper, utilizing the dual-phase-lag (DPL) heat transfer model. It was supposed that the physical characteristics of the FG rod varied exponentially along the axis of the body. Both ends hold the rod, and there is no voltage across them. The Laplace transform and decoupling techniques were used to obtain the physical fields that have been analyzed. A range of heterogeneity, rotation, and heat source velocity measures were used to compare the results presented here and those in the previous literature. [ABSTRACT FROM AUTHOR]

In engineering practice, structures with identical components or parts are useful from several points of view: less information is needed to describe the system; designs can be conceptualized quicker and easier; components are made faster than during traditional complex assembly; and finally, the time needed to achieve the structure and the cost involved in manufacturing decrease. Additionally, the subsequent maintenance of this system then becomes easier and cheaper. The aim of this Special Issue is to provide an opportunity for international researchers to share and review recent advances in the finite element modeling of computational friction contact mechanics. Numerical modeling in mathematics, mechanical engineering, computer science, computers, etc. presents many challenges. The finite element method applied in solid mechanics was designed by engineers to simulate numerical models in order to reduce the design costs of prototypes, tests and measurements. This method was initially validated only by measurements but gave encouraging results. After the discovery of Sobolev spaces, the abovementioned results were obtained, and today, numerous researchers are working on improving this method. Some of applications of this method in solid mechanics include mechanical engineering, machine and device design, civil engineering, aerospace and automotive engineering, robotics, etc. Frictional contact is a complex phenomenon that has led to research in mechanical engineering, computational contact mechanics, composite material design, rigid body dynamics, robotics, etc. A good simulation requires that the dynamics of contact with friction be included in the formulation of the dynamic system so that an approximation of the complex phenomena can be made. To solve these linear or nonlinear dynamic systems, which often have non-differentiable terms, or discontinuities, software that considers these high-performance numerical methods and computers with high computing power are needed. This Special Issue is dedicated to this kind of mechanical structure and to describing the properties and methods of analysis of these structures. Discrete or continuous structures in static and dynamic cases are also considered. Additionally, theoretical models, mathematical methods and numerical analysis of these systems, such as the finite element method and experimental methods, are used in these studies. Machine building, automotive, aerospace and civil engineering are the main areas in which such applications appear, but they can also be found in most other engineering fields. With this Special Issue, we want to disseminate knowledge among researchers, designers, manufacturers and users in this exciting field. [ABSTRACT FROM AUTHOR]

The hybrid architecture of the driven qubit–photon–magnon system has recently emerged as a promising candidate for novel quantum technologies. In this paper, we introduce the effective wave-function of a superconducting single qubit and a magnon mode contained within a cavity resonator and an external field. The non-classicality of the magnon and resonator modes are investigated by using the negative values of the Wigner function. Additionally, we discuss the non-classicality of the qubit state via the Wigner–Yanase skew information. We find that the mixture angle of the qubit–resonator plays a controllable role in non-classicality. However, the strength of the magnon–photon increases the non-classical behaviour of the system. [ABSTRACT FROM AUTHOR]

The paper aims to identify the situations in which a complex elastic system, which is subject to mechanical vibrations, can act as a dynamic absorber of vibrations for certain frequencies. The conditions that the system must fulfill in order to achieve this goal are determined and then a calculation example is presented. The method is interesting because it allows to avoid attaching an absorber specially built for this, a situation that complicates the project and increases manufacturing costs. [ABSTRACT FROM AUTHOR]

In this paper, we extend some results involving the energy release rate in the case of the propagation of a straight crack in an elastic solid. These results, approached by Gurtin and Yatomi in classical elasticity, are generalized in order to cover a Cosserat-type elastic body. We also investigate the effects of the microinertia and the couple stresses on the energy release rate. [ABSTRACT FROM AUTHOR]

In the current article, the nonlocal thermoelastic theory is used to discuss the wave propagation in unbounded thermoelastic materials. Due to the inclusion of relaxation time in thermal conduction formulation and the equations of motion, this model was developed using Lord and Shulman's generalized thermoelastic model. The theory of the nonlocal continuum proposed by Eringen is used to obtain this model. The integral transforms of the Laplace transform methods used to generate an analytical solution for physical variables are utilized to produce the analytical solutions for the thermal stress, displacement, and temperature distribution. The effects of nonlocal parameters and relaxation time on the wave propagation distributions of physical fields for material are visually shown and explored. [ABSTRACT FROM AUTHOR]

The current study focuses on the natural-convection flow of nanofluids with boundary layer over a circular cylinder of uniform thermal wall with varying magnetic force from 0 to 1.5, radiative effects from 0 to 1, heat generation effects from 0 to 1, and Joule heating effects from 0 to 1. The problem is represented in the form of partial differential equations. The dimensional form of the equations is converted into a dimensionless form with the help of suitable stream functions. Then, the resultant equations are further reduced into the system of first-ordered differential equations, and the Keller box scheme is applied to obtain a solution numerically with the help of MATLAB code. The numerical solutions for Nusselt number, skin friction coefficient, Sherwood number, velocity profile, temperature profile, and concentration profile are represented with the help of graphs. The most interesting fact of the analysis is the flow of the fluid; the heat-mass and energy transfer rates could be managed in a controlled way through slight variations in the Brownian motion parameter from 0.1 to 0.7, in the Lewis number from 1 to 40, in the Eckert number from 0.1 to 0.4, in the thermophoresis parameter from 0.1 to 0.7, in the Prandtl number from 0.1 to 0.7, and in the buoyancy ratio from 0.1 to 0.7, as it is here analyzed and discussed. [ABSTRACT FROM AUTHOR]

The study of the effect of the microstructure is important and is most evident in elastic vibrations of high frequency and short-wave duration. In addition to deformation caused by temperature and acting forces, the theory of micropolar thermoelasticity is applied to investigate the microstructure of materials when the vibration of their atoms or molecules is increased. This paper addresses a two-dimensional problem involving a thermoelastic micro-polar half-space with a traction-free surface and a known conductive temperature at the medium surface. The problem is treated in the framework of the concept of two-temperature thermoelasticity with a higher-order time derivative and phase delays, which takes into consideration the impact of microscopic structures in non-simple materials. The normal mode technique was applied to find the analytical formulas for thermal stresses, displacements, micro-rotation, temperature changes, and coupled stress. The numerical results are graphed, and the effect of the discrepancy indicator and higher-order temporal derivatives is examined. There are also some exceptional cases that are covered. [ABSTRACT FROM AUTHOR]

This paper presents the main analytical methods, in the context of current developments in the study of complex multibody systems, to obtain evolution equations for a multibody system with deformable elements. The method used for analysis is the finite element method. To write the equations of motion, the most used methods are presented, namely the Lagrange equations method, the Gibbs–Appell equations, Maggi's formalism and Hamilton's equations. While the method of Lagrange's equations is well documented, other methods have only begun to show their potential in recent times, when complex technical applications have revealed some of their advantages. This paper aims to present, in parallel, all these methods, which are more often used together with some of their engineering applications. The main advantages and disadvantages are comparatively presented. For a mechanical system that has certain peculiarities, it is possible that the alternative methods offered by analytical mechanics such as Lagrange's equations have some advantages. These advantages can lead to computer time savings for concrete engineering applications. All these methods are alternative ways to obtain the equations of motion and response time of the studied systems. The difference between them consists only in the way of describing the systems and the application of the fundamental theorems of mechanics. However, this difference can be used to save time in modeling and analyzing systems, which is important in designing current engineering complex systems. The specifics of the analyzed mechanical system can guide us to use one of the methods presented in order to benefit from the advantages offered. [ABSTRACT FROM AUTHOR]

This article focuses on the study of redial displacement, the carrier density, the conductive and thermodynamic temperatures and the stresses in a semiconductor medium with a spherical hole. This study deals with photo-thermoelastic interactions in a semiconductor material containing a spherical cavity. The new hyperbolic theory of two temperatures with one-time delay is used. The internal surface of the cavity is constrained and the density of carriers is photogenerated by a heat flux at the exponentially decreasing pulse boundaries. The analytical solutions by the eigenvalues approach under the Laplace transformation approaches are used to obtain the solution of the problem and the inversion of the Laplace transformations is performed numerically. Numerical results for semiconductor materials are presented graphically and discussed to show the variations of physical quantities under the present model. [ABSTRACT FROM AUTHOR]

The current study investigates thermophotovoltaic interactions using a new mathematical model of thermoelasticity established on a modification of the Green–Naghdi model of type III (GN-III). The basic equations, in which the heat transfer is in the form of the Moore–Gibson–Thompson (MGT) equation, are derived by adding a single delay factor to the GN-III model. The impact of temperature and electrical elastic displacement of semiconductors throughout the excited thermoelectric mechanism can be studied theoretically using this model. The proposed model was used to investigate the interactions between the processes of thermoelastic plasma in a rotating semiconductor solid sphere that was subjected to a thermal shock and crossed to an externally applied magnetic field. The influence of rotation parameters on various photothermal characteristics of silicon solid was presented and explored using the Laplace technique. [ABSTRACT FROM AUTHOR]

In this study, we will prove that the presence of the voids and of the internal state variables in an elastic body with dipolar structure have no effect on the result of uniqueness regarding the solution of the initial-boundary value problem from this context. First, we put down the basic equations and conditions which define the initial-boundary value problem in the context. Then, by means of three theorems, we prove some auxiliary estimates that underlie the result of uniqueness. Finally, by means of these estimates and by using the Gronwall's inequality, we prove our main result. [ABSTRACT FROM AUTHOR]

In this work, a new model for porothermoelastic waves under a fractional time derivative and two time delays is utilized to study temperature increments, stress and the displacement components of the solid and fluid phases in porothermoelastic media. The governing equations are presented under Lord–Shulman theory with thermal relaxation time. The finite element method has been adopted to solve these equations due to the complex formulations of this problem. The effects of fractional parameter and porosity in porothermoelastic media have been studied. The numerical outcomes for the temperatures, the stresses and the displacement of the fluid and the solid are presented graphically. These results will allow future studies to gain a detailed insight into non-simple porothermoelasticity with various phases. [ABSTRACT FROM AUTHOR]

In this work, numerical estimations of a nonlinear hyperbolic bioheat equation under various boundary conditions for medicinal treatments of tumor cells are constructed. The heating source components in a nonlinear hyperbolic bioheat transfer model, such as the rate of blood perfusions and the metabolic heating generations, are considered experimentally temperature-dependent functions. Due to the nonlinearity of the governing relations, the finite element method is adopted to solve such a problem. The results for temperature are presented graphically. Parametric analysis is then performed to identify an appropriate procedure to select significant design variables in order to yield further accuracy to achieve efficient thermal power in hyperthermia treatments. [ABSTRACT FROM AUTHOR]

In this paper, we consider boundary stabilization problem of heat equation with multi-point heat source. Firstly, a state feedback controller is designed mainly by backstepping approach. Under the designed state controller, the exponential stability of closed-loop system is guaranteed. Then, an observer-based output feedback controller is proposed. We prove the exponential stability of resulting closed-loop system using operator semigroup theory. Finally, the designed state and output feedback controllers are effective via some numerical simulations. [ABSTRACT FROM AUTHOR]

The paper studies the vibration behavior of a concrete structure, currently used in civil engineering. The truss structure considered has symmetries that can be used to facilitate both the design and construction of the building. Moreover, the symmetries encountered can be used to simplify the calculation of vibrations of the system. Based on the mechanical model built, eigenvalues and eigenvectors of such mechanical system are determined, and properties, specific to these symmetries, are identified. In this way, the dynamic analysis of the structure can be simplified and also, the design as well as the costs related to this stage. [ABSTRACT FROM AUTHOR]

In classical mechanics, determining the governing equations of motion using finite element analysis (FEA) of an elastic multibody system (MBS) leads to a system of second order differential equations. To integrate this, it must be transformed into a system of first-order equations. However, this can also be achieved directly and naturally if Hamilton's equations are used. The paper presents this useful alternative formalism used in conjunction with the finite element method for MBSs. The motion equations in the very general case of a three-dimensional motion of an elastic solid are obtained. To illustrate the method, two examples are presented. A comparison between the integration times in the two cases presents another possible advantage of applying this method. [ABSTRACT FROM AUTHOR]

The study of the mixed initial-boundary value problem, corresponding to the thermoelasticity of porous micromorphic materials under the influence of microtemperatures, represents the main objective of this article. Achieving qualitative results on the existence, uniqueness and continuous dependence on the initial data and loads, of the solution of the mixed problem, implies a new perspective of approaching these topics, imposed by the large number of unknowns, which increases the complexity of equations and conditions that characterize the thermoelastic porous micromorphic materials with microtemperatures. The use of the semigroup theory of operators represents the optimal solution for deducing these results, the theory being adaptable to the requirements of the demonstrations, the mixed problem turning into a problem of Cauchy type, with regards to an equation of evolution on a Hilbert space, chosen appropriately. [ABSTRACT FROM AUTHOR]

In this article, a nonlocal thermoelastic model that illustrates the vibrations of nanobeams is introduced. Based on the nonlocal elasticity theory proposed by Eringen and generalized thermoelasticity, the equations that govern the nonlocal nanobeams are derived. The structure of the nanobeam is under a harmonic external force and temperature change in the form of rectified sine wave heating. The nonlocal model includes the nonlocal parameter (length-scale) that can have the effect of the small-scale. Utilizing the technique of Laplace transform, the analytical expressions for the studied fields are reached. The effects of angular frequency and nonlocal parameters, as well as the external excitation on the response of the nanobeam are carefully examined. It is found that length-scale and external force have significant effects on the variation of the distributions of the physical variables. Some of the obtained numerical results are compared with the known literature, in which they are well proven. It is hoped that the obtained results will be valuable in micro/nano electro-mechanical systems, especially in the manufacture and design of actuators and electro-elastic sensors. [ABSTRACT FROM AUTHOR]

The Lagrange's equation remains the most used method by researchers to determine the finite element motion equations in the case of elasto-dynamic analysis of a multibody system (MBS). However, applying this method requires the calculation of the kinetic energy of an element and then a series of differentiations that involve a great computational effort. The last decade has shown an increased interest of researchers in the study of multibody systems (MBS) using alternative analytical methods, aiming to simplify the description of the model and the solution of the systems of obtained equations. The method of Kane's equations is one possibility to do this and, in the paper, we applied this method in the study of a MBS applying finite element analysis (FEA). The number of operations involved is lower than in the case of Lagrange's equations and Kane's equations are little used previously in conjunction with the finite element method (FEM). Results are obtained regardless of the type of finite element used. The shape functions will determine the final form of the matrix coefficients in the equations. The results are applied in the case of a planar mechanism with two degrees of freedom. [ABSTRACT FROM AUTHOR]

The main concern of this study is an extension of some results, proposed by Green and Lindsay in the classical theory of elasticity, in order to cover the theory of thermoelasticity for dipolar bodies. For dynamical mixed problem we prove a reciprocal theorem, in the general case of an anisotropic thermoelastic body. Furthermore, in this general context we have proven a result regarding the uniqueness of the solution of the mixed problem in the dynamical case. We must emphasize that these fundamental results are obtained under conditions that are not very restrictive. [ABSTRACT FROM AUTHOR]

The main method used to determine the equations of motion of a multibody system (MBS) with elastic elements is the method of Lagrange's multipliers. The assembly of equations for the whole system represents an important step in the elastodynamic analysis of such a system. This paper presents a new method of approaching this stage, by applying Maggi's equations. In this way, the links that exist between the finite elements and the connections that exist between different bodies of the MBS system are conveniently taken into account, each body having a distinct velocity and acceleration field. Although Maggi's equations have been used, sporadically, in some applications so far, we are not aware that they have been used in the study of elastic systems using the finite element method. Finally, an algorithm is presented that uses the Maggi formalism to obtain the equations of motion for an MBS system. [ABSTRACT FROM AUTHOR]