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The present study investigates the vibration analysis of cylindrical shells composed of fiber metal laminate (FML) with embedded piezoelectric layers, undergoing fluid-structure interaction (FSI) and resting on a Pasternak elastic foundation based on the principles of three-dimensional elasticity theory. Using the state space approach, the equations of motion were derived under simply supported boundary conditions. The natural frequencies of the FML cylindrical shell, accounting for the presence of a moving fluid, were computed by solving the eigenfrequency equations. The study examined the influence of various parameters, including boundary conditions, length-to-radius ratio, fluid type, fluid velocity, circumferential wave number, and radius-to-thickness ratio, on glass-reinforced aluminum laminate (GLARE), aramid-reinforced aluminum laminate (ARALL), and carbon-reinforced aluminum laminate (CARALL). A constant composite/metal volume ratio was assumed. The results obtained were validated by comparing with natural frequency values from the existing literature, confirming the agreement and convergence with previous studies. The results confirm that the highest natural frequency values are assigned to the CARALL, ARALL and GRALE structures in descending order. Furthermore, an increase in fluid flow velocity through the cylindrical shell correlates with a reduction in natural frequency. [ABSTRACT FROM AUTHOR]

This paper investigates the wave propagation in the graphene platelets (GPLs)-enhanced functionally graded porous plates. The governing equations of motion are obtained using the first-order shear deformation plate theory (FSDT). Subsequently, the equations are transformed into the state-space form. The wave dispersion relation is derived by solving the state space equation by means of the method of reverberation-ray matrix and the accuracy of this approach is validated through a comparative analysis with the results from relevant literature. In addition, parametric analyses are carried out, including boundary conditions, porosity coefficient, GPL mass fraction, porosity distribution, GPL distribution, and thickness-to-width ratio, on the dispersion behavior of functionally graded GPLs-reinforced porous plates. The use of GPLs in these composites is particularly promising, and the findings offer valuable insights into the design of composites with tailored properties for specific engineering applications. [ABSTRACT FROM AUTHOR]

The stability of the parametric resonance of a controlled stay cable with time delay is investigated. The in-plane nonlinear equations of motion are initially determined via the Hamilton principle. Then, utilizing the method of multiple scales, the modulation equations that govern the nonlinear dynamics are obtained. These equations are then utilized to investigate the effect of time delays on the amplitude and frequency-response behavior and, subsequently, on the stability of the parametric resonance of the controlled cable, that it is shown to depend on the excitation amplitude and the commensurability of the delayed-response frequency to the excitation frequency. The stability region of the parametric resonance is shifted, and the effects of control on the cable become worse by increasing time delay. The work plays a guiding role in the parametric design of the control system for stay cables. [ABSTRACT FROM AUTHOR]

In this work, a rectangular cellular microplate is taken into consideration which is embedded between two functionally graded carbon nanotube-reinforced composite layers that have the piezoelectric ability. Different patterns for the carbon nanotube dispersion are considered. Moreover, an external electrical voltage is applied to them. The displacements are described based on a higher-order shear deformation theory which is called hyperbolic theory and the size influence is captured via the modified couple stress formulations. The governing motion equations are then derived using the variational technique and Hamilton’s principle. Then, for simply supported edge conditions, a closed-form solution is provided. Next, it turns to validate the results in simpler states, and after that, the effect of the most prominent parameters on the results is investigated. It is observed that by increasing the external applied voltage to the face sheets, the frequencies are reduced. Also, the natural frequencies have a tendency to decrease as the dimensionless material length scale parameter increases. This study’s outcomes may help design and manufacture micro-/nano-electro systems, sensors and actuators, small-scale devices, and other engineering structures. [ABSTRACT FROM AUTHOR]

A feedback control method is proposed to asymptotically stabilize the chain-like multi-degree-of-freedom (MDOF) nonlinear structural system under purely parametric Gaussian white noises. First, the motion equation of a chain-like nonlinear structural system with n coupled elements and an undetermined control law is derived. It is reduced to a one-dimensional partially averaged Itô stochastic differential equation of the controlled Hamiltonian by applying the stochastic averaging method, which bypasses the challenge of calculating multiple Lyapunov exponents. Next, based on the dynamical programming principle, the dynamical programming equation of the averaged system with an undetermined cost function is established and addressed to obtain the optimal control law. Then, the Lyapunov exponent of the completely averaged Itô equation is derived. For the given requirement of stabilizing the system, the Lyapunov exponent is entirely fixed and used to analyze the stability of the originally chain-like MDOF nonlinear structural system. A controlled chain-like 8-DOF nonlinear structural system is taken as an example to illustrate the application and effectiveness of the proposed procedure and the effect of control forces on stabilizing the system. [ABSTRACT FROM AUTHOR]

In this paper, we proposed a generalized Lagrangian for three different classes of scalar fields namely quintessence (α = − 1), phantom (α = 0) and tachyonic (α = 1) parameterized by α. These three scalar fields can be described by a common single Lagrangian called generalized scalar field Lagrangian (GSL). We obtain mathematically consistent forms of generalized equations of motion parameterized by α. It can recover the individual equation of motion of quintessence, phantom and tachyon scalar fields from generalized equation of motion of the unified scalar field. [ABSTRACT FROM AUTHOR]

The interaction between an atom and the quantized electromagnetic field depends on the position of the atom, leading to a force which is the negative gradient of this interaction. At zero temperature, the mean of this force vanishes, but it has a nonzero value for a thermal electromagnetic background. By applying the Heisenberg equations of motion and the Born–Markov approximation, we obtain the mean and correlation of the force, which show that the center-of-mass motion of the atom is damped and diffused. This approach can be easily extended to multi-level atoms, and it is shown that the damping force and diffusion coefficients are invariant under Galilean transformations. In principle, this effect can be utilized to determine the velocity of the laboratory relative to the thermal background. [ABSTRACT FROM AUTHOR]

The heat transfer occurring on boundary layer flows during dilute suspension of Cu–Al2O3 nanoparticles-based non-Newtonian Casson hybrid nanofluid over diverging channel is to be characterized in this model. The governing equations comprise continuity, momentum, energy and concentration equations which incorporated variable viscosity and magnetic effects in the momentum equation, variable thermal conductivity, chemical reaction, thermal radiative heat flux, uniform magnetic field, Joule heating and viscous dissipative effects in the energy equation and Brownian motion and thermophoretic effects in the concentration equation. The modeled equations are nondimensionalized using nonsimilar variables and linearized using quasilinearization technique. The system of linearized partial differential equations is solved numerically using implicit finite difference and successively iterated with the help of Varga's algorithm. The physical impacts of viscous dissipation parameter (Ec), Brownian motion ( N b ) on velocity, temperature, concentration and Schmidt number (Sc) influences on skin friction, Nusselt number, Sherwood number profiles, Bejan lines and total entropy production profiles are simulated graphically. The velocity profiles are enhanced and the temperature profile declines for augmented values of Eckert number. Moreover, for augmented values of Schmidt number the heat and mass transfer rates are enhanced and the Bejan lines dropped a decreasing trend whereas total entropy production is augmented near the wall region. The improved values of the Schmidt number physically increased Sc in the heat transfer rate. The ascending profile of the mass transfer rate with increased values of the viscous dissipation parameter Ec demonstrated that the graph is raised for larger values of the viscous dissipating parameter (Ec). The physical behavior of incremental mass transfer rate led to the conclusion that the relative diffusivity of nanoparticles is characterized by both nondimensional numbers Ec and Sc which are directly proportional to the viscous forces. [ABSTRACT FROM AUTHOR]

This paper elaborates on the wave propagation characteristics of a smart sandwich plate consisting of smart piezo composite layers on a plate's upper and lower borders via an auxetic core. This study's equation of motion was derived using a refined version of the Shear-deformation theory at a higher order, or HSDT. Additionally, detecting the properties of the auxetic core and piezoelectric composite layers employs a micromechanical model. The fundamental equations of the smart sandwich plates were formulated utilizing the Hamiltonian principle and Maxwell's law. Then, the governing equations of a sandwich plate are solved using an exponential form and an analytical method. Furthermore, the phase velocity of the intelligent sandwich plate is provided based on the layer thicknesses of the auxetic core and thicknesses of intelligent piezoelectric composite layers. In addition, each figure calculates and presents the weight of the Winkler–Pasternak coefficient, the viscoelastic substances factor, the source of the outside electricity, and the volume percent of reinforcement in the matrix on the phase velocity. [ABSTRACT FROM AUTHOR]

This paper presents a new semi-analytical approach for the nonlinear vibration and dynamic responses of functionally graded graphene platelet-reinforced composite (FG-GPLRC) panels with complex curvature reinforced by orthogonal and/or inclined stiffeners in the thermal environment resting on the nonlinear viscoelastic foundation with the nonlinearities of von Kármán in the framework of the higher-order shear deformation theory (HSDT). The three curvature types of complexly curved panels are considered to be cylindrical, sinusoid, and parabola panels. Orthogonal and/or inclined stiffeners are modeled utilizing an improved smeared stiffener technique. The stress function form is estimated by applying the like-Galerkin method for complexly curved panels. By applying the Lagrange function and Euler–Lagrange equation, the nonlinear equations of motion of the panels are obtained. The viscous damping effects of the viscoelastic foundation are considered by utilizing the Rayleigh dissipation function. Numerical results are examined utilizing the Runge–Kutta method to acquire the time-deflection curves, and by utilizing the Budiansky–Roth criterion, the critical dynamic buckling loads are determined. From the investigated results, it is possible to evaluate the nonlinear vibration and buckling dynamic responses of three forms of panels with stiffeners. [ABSTRACT FROM AUTHOR]

This study investigates free vibration analysis of a microplate featuring a honeycomb (HC) core and incorporates two nanocomposite piezoelectric (NP) layers. Carbon nanotubes (CNTs) are hired to enhance the electro-mechanical performance of the piezoelectric patches, which are subjected to an externally applied electric voltage. All layers are tightly bonded together and are supported by an elastic substrate according to the Pasternak model, capable of withstanding both normal and shear loads. To establish the kinematic relations, a trigonometric plate theory is employed. The governing equations of motion are deduced through the application of Hamilton's principle and variational technique. The modified strain gradient theory, which includes three material length-scale parameters (MLSPs), is used to account for the scale effect. An analytical approach based on Fourier series functions is employed to solve the differential equations of motion. Subsequently, the impact of various factors, such as the geometrical characteristics of the HC core, distribution patterns of CNTs, and other significant parameters, on the normalized frequencies of the model is assessed after validating the accuracy of the results. The outcomes of this research have the potential to facilitate the advancement and production of lightweight and intelligent structures and devices, ultimately enhancing their efficiency. [ABSTRACT FROM AUTHOR]

In this study, nonlinear vibrations and stability of multilayer functionally graded (FG) pipes conveying fluid laying on nonlinear elastic foundation and reinforced by graphene nanoplatelets (GPLs) are investigated with an emphasis on optimized analytical method. Various types of GPL distribution patterns are considered and to estimate the mechanical characteristics of the reinforced pipe the Halpin–Tsai micromechanics theory is applied. The nonlinear differential equation of motion is obtained by using Von–Kármán strain relations in conjunction with the Euler–Bernoulli beam theory and applying Hamilton's principle. The Galerkin technique has been used for discretizing the partial differential equation. The optimized homotopy analysis method (HAM), as a strong analytical method, is utilized to solve the nonlinear differential equation by considering different initial excitations. The convergence-control parameter is taken into account to guarantee the convergence of the analytical solution. In this study, an exact solution based on HAM for the critical flow velocity and n th nonlinear frequency is presented. Additionally, series solutions for the nonlinear time responses of the transverse and longitudinal vibrations of fluid-conveying pipe based on optimized HAM are obtained for the first time. In the numerical results, the effects of arbitrary initial conditions and different physical characteristics on the nonlinear frequencies and time responses are extensively examined. It is shown that the nonlinear frequencies and critical flow velocity of the pipe depend not only on the initial excitation amplitude, but also on the entire initial excitation function applied on the pipe. [ABSTRACT FROM AUTHOR]

Dynamic response analysis of multi-span beams is one of the important topics in the field of highway and railway engineering, which provides valuable guidance for the design, operation and maintenance of multi-span bridges. It is worth considering how to calculate the dynamic characteristics of multi-span beams quickly and conveniently. In this study, an effective analytical method is developed for the dynamic modeling and investigations of multi-span Timoshenko beams under moving loads by employing the assumed mode method (AMM). Based on Hamilton’s principle, the equation of motion of the Timoshenko multi-span beam subjected to moving loads is formulated and the natural frequencies are calculated. A comprehensive investigation is conducted on the dynamic responses of the multi-span Timoshenko beam considering different factors, including the length-to-thickness ratio, disorder degree, arrangement order, number of spans and related parameters of moving loads. In addition, the influence of the interval and velocity of the moving load series on the dynamic responses, including displacement, velocity and acceleration of the multi-span beam, are analyzed in detail. The theoretical calculation results of multi-span Timoshenko beams under moving loads are compared with numerical results obtained from ANSYS software, and the results are in good agreement. This demonstrates that the developed method, which utilizes the AMM to analyze the dynamic characteristics of multi-span beams subjected to moving loads, significantly simplifies the calculations and is well-suited for practical engineering applications. [ABSTRACT FROM AUTHOR]

In this paper, we present comparisons of the deflection angles of massless and massive particles in the Schwarzschild space-time. For the case of photons in a general static space-time, we construct a spatial 3D equation of motion for their path that leads to an implicit formula for the deflection angle. We then compare our results with well-known results of the literature in the Schwarzschild space-time. For the case of massive particles, we calculate the deflection angle only in the Schwarzschild space-time. The end result is that as the velocity of any massive particle diminishes, the deflection angle increases. To show the relevance of these comparisons, we constructed different black hole shadows for massive particles in order to be compared with a shadow made by photons. [ABSTRACT FROM AUTHOR]

In this paper, we study Little Rip (LR) and Pseudo Rip (PR) cosmological models containing two coupled fluids: dark energy and dark matter. We assume a spatially flat Friedmann–Robertson–Walker (FRW) universe. The interaction between the dark energy and the dark matter fluid components is described in terms of the parameters in the generalized Equation of State (EoS) in presence of the bulk viscosity. We consider entropic cosmology and use a description based on a new generalized entropy function, which was proposed by Nojiri–Odintsov–Faraoni [From nonextensive statistics and black hole entropy to the holographic dark universe, Phys. Rev. D105(4) (2022) 044042]. Conditions for the appearance of the (LR) and the (PR) in terms of the parameters of the (EoS) are obtained. Introducing an energy density ρ g corresponding to a specified entropy function S g , together with an interaction term Q in the gravitational equations of motion, we derive modified forms of the EoS parameters. We discuss the corrections of the thermodynamic parameters associated with the generalized entropy function. Properties of the late universe as well as in the early universe in this formalism are pointed out. [ABSTRACT FROM AUTHOR]

The utilization of functionally graded graphene platelet-reinforced composites (FG-GPLRC) and honeycomb sandwich constructions is prevalent in the field of engineering. Therefore, it is crucial to investigate the buckling and vibration properties of these materials under heat circumstances. This paper specifically focuses on the vibration and thermal buckling characteristics of a novel multi-arc concave honeycomb sandwich plate (MACHSP) equipped with an adjustable positive-negative Poisson's ratio. The governing equations of motion for the system are derived based on the first-order shear deformation theory in conjunction with Hamilton's principle. The formulation of the system's characteristic equation involves the establishment of displacement functions that satisfy distinct boundary conditions. Using computational programming, natural frequencies, mode shapes, and critical buckling temperatures of MACHSP with three different FG-GPLRC distributions under thermal influences are determined. Subsequently, these results are compared with outcomes from finite element simulations and findings from previously published literature. Additionally, the amplitude-frequency response characteristics of the structure under harmonic excitation are analyzed, followed by a discussion of the impact of structural parameters on its buckling and vibration characteristics. The results indicate that the established theoretical model for predicting the buckling and vibration characteristics of MACHSP with FG-GPLRC distribution aligns well with simulation models and prior research. In contrast to solid plates, MACHSP not only achieves a substantial reduction in weight but also demonstrates a significant increase in natural frequency. Furthermore, graphene platelets have the potential to enhance the structure's natural frequency values and critical buckling temperatures. Lastly, various structural parameters exert a notable influence on the structure's performance. [ABSTRACT FROM AUTHOR]

The aerodynamic performance of a moving flapping wing is investigated numerically using a fluid–solid interaction model. The flow field is assumed to be two-dimensional, viscous, unsteady, and incompressible. Galerkin-least/squares finite element method is used to account for the convective nature of the flow field. The flow solver is coupled with the rigid body equations of motion describing the movement of the flapping wing. An interface-capturing technique is developed and tailored to the present model to capture the flapping wing during its movement. The developed algorithm is validated against published data with a great degree of success. Then, simulations for a flapping wing with a stationary center of gravity and free center of gravity motion, are performed. This is followed by a parametric study through which the effects of the wing’s initial position, maximum flapping angle, Reynolds number, the mass of the wing, the gravitational acceleration, and the critical frequency for each Reynolds number are studied. Finally, the voluntary vertical takeoff of a fruit fly, Drosophila Melanogaster is simulated using the proposed model. [ABSTRACT FROM AUTHOR]

In this paper, we explore some cosmological solutions of the Friedmann–Lemaître–Robertson–Walker (FLRW) closed universe with nonlocal de Sitter gravity d S and nonlocal scalar field which has its origin in p -adic string theory. In this case, we have that both geometrical and matter sectors of equations of motion (EoM) are nonlocal. The cosmological constant Λ plays a role of dark energy (DE) and is related to the mass of scalar field as m = ℏ c Λ 6 = 1. 5 × 1 0 − 6 9 kg. We found that the cosmological constant Λ depends on prime number p as a discrete parameter and we conjectured that Λ is not constant during the universe evolution. [ABSTRACT FROM AUTHOR]

A relativistic version of the correspondence principle, a limit in which classical electrodynamics may be derived from quantum electrodynamics (QED), has never been clear, especially when including gravitational mass. Here we introduce a novel classical field theory formulation of electromagnetism, and then show that it approximates QED in the limit of a quantum state which corresponds to a classical charged continua. Our formulation of electromagnetism features a Lagrangian which is gauge invariant, includes a classical complex field from which a divergenceless four-current may be derived, and reproduces all aspects of the classical theory of charged massive continua without any quantum effects. Taking a geometric approach, we identify the four-current as being in the direction of extremal phase velocity of the classical field; the field equations of motion determine this phase velocity as being equal to the mass, which makes the rest density proportional to the squared modulus of the field. [ABSTRACT FROM AUTHOR]

This paper provides a summary of the fractal calculus framework. It presents higher-order homogeneous and nonhomogeneous linear fractal differential equations with α -order. Solutions for these equations with constant coefficients are obtained through the method of variation of parameters and the method of undetermined coefficients. The solution space for higher α -order linear fractal differential equations is defined, showcasing its non-integer dimensionality. The solutions to α -order linear fractal differential equations are graphically depicted to illustrate their non-differentiability. Additionally, equations of motion governing the behavior of two masses in fractal time are proposed and solved. [ABSTRACT FROM AUTHOR]

In this study, we investigate the behavior of the Dirac–Born–Infeld (DBI) scalar field as a candidate for the nature of dark energy in a non-minimal coupling scenario with the scalar torsion within the framework of teleparallel gravity. We present numerical solutions for the equations of motion and analyze the behavior of various cosmological parameters for different values of the parameter ṽ and f̃. Our findings reveal that the DBI scalar field can contribute significantly to the energy density of the universe and drive the late-time acceleration of the universe, with a transition from deceleration to acceleration occurring within a redshift range consistent with recent observational bounds. We show that the present-day value of the deceleration parameter is consistent with recent observational constraints, and the DBI scalar field behaves like a cosmological constant model. Our results suggest that the DBI scalar field can play a significant role in driving the late-time acceleration of the universe and that it has the potential to be a viable alternative to the cosmological constant model. Further investigations are necessary to better understand the nature of the dark energy component and its implications for cosmology within the framework of teleparallel gravity. [ABSTRACT FROM AUTHOR]

An inerter system, based on electromechanical similarity theory and vibration mitigation and isolation technology, represents a category of vibration damping systems. These systems typically improve damping performance by increasing mass or inertia, a method often found to be inefficient, leading to inadequate damping and limited applicability in real-world engineering scenarios. The lightweight inerter system (LwIS) introduced herein offers a more flexible and efficient means of altering structural inertia. Initially, this paper establishes the motion control equations for LwIS, followed by a stochastic analysis to derive the analytical expression for the root mean square displacement under Gaussian white noise excitation. A parametric analysis of LwIS is subsequently conducted, developing a displacement-based parametric strategy. Design examples for single-degree-of-freedom (SDOF) engineering structures under various requirements are provided, demonstrating the validity of LwIS’s optimal parameters through responses to simple harmonic excitation and seismic impacts. The findings indicate that the optimization approach of LwIS, unlike traditional methods, simultaneously addresses the displacement performance of the primary structure and the deformation efficiency of the damping element, thereby facilitating comprehensive optimization. Four optimal design parameters for LwIS are identified, underscoring its applicability to stochastic excitation and a broader range of load cases, thus enhancing its practicality in engineering contexts. LwIS’s design philosophy aims to improve deformation efficiency through an increased deformation enhancement coefficient in the damping element, enhancing damping performance, controlling seismic responses, and achieving superior energy dissipation. The optimal parameters, smaller in value, maximize the potential of the inerter system, aligning with the dual objectives of performance optimization and lightweight design, consequently reducing engineering costs. [ABSTRACT FROM AUTHOR]

This paper seeks to study and investigate the wave dispersion behavior in porous functionally graded (FG) carbon nanotube-reinforced composite (CNTRC) beams. The beams comprise four patterns of single-walled carbon nanotubes (SWCNTs) distributed in the polymer matrix. The mixture rule is used to estimate the CNTR beams’ material properties. Innovative to this study are three porosity models describing the porosity distributions within the matrix and a three-unknown integral higher-order shear deformation theory (HSDT) modeling analytically the CNTRC beams with a novel shape function expressing the distributions of shear stresses and strains. The equations of motion for CNTRC beams are derived based on Hamilton’s principle. The stiffness and mass matrices are formulated by a generalized solution of harmonic wave propagation to express the wave dispersion relations. Numerical comparisons with previously published works verify the applicability of this mathematical model. The paper studies the effects of CNTs patterns through the polymer matrix, porosity models, and volume fractions of the porosity and CNTs. Based on the analytical results, augmenting the porosity and CNTs volume fractions leads to faster phase and group velocities. Furthermore, the impact of CNTs volume fractions, porosity models, and porosity volume fractions becomes more pronounced as the wavenumber increases. [ABSTRACT FROM AUTHOR]

In this research, a thick hollow cylindrical shell made of bidirectional functionally graded open cell porous materials under internal thermal shock according to the classical theory of linear thermo-elasticity is examined for the first time. The cylinder is made of a porous cellular material and its porosity varies along both radial and axial directions continuously. The governing motion equations are obtained by using 2D-axisymmetric theory of linear thermo-elasticity rather than shell theories. This theory represents thickness stretching and gives more precise results. Graded finite element method is employed to model the problem. Applying this method rather than conventional FEM leads to more accurate results, especially for dynamic analyses. The cubic higher order element is used for dividing the solution domain. To obtain transient temperatures, Crank–Nicolson algorithm is used and then the Newmark procedure is used to derive time responses of displacement and stress components. The time history of displacements and stress components for different radial and axial power law exponents, porosity coefficient, boundary conditions, length-to-thickness ratio and two different porosity patterns are investigated in detail. The obtained results show that thermal-induced vibration is generally caused by hoop stress, and frequency and amplitude of vibrations and velocity of stress waves are considerably influenced by the porosity distribution, porosity coefficient and power law exponents in both directions. [ABSTRACT FROM AUTHOR]

In this paper, propagation of thermoelastic waves in semi-conducting nanostructure medium is studied. First, the governing equations are formulated with the help of coupled nonlocal elasticity theory, thermoelastic three-phase-lag model, and equation of motion. Heat equation with fractional order is incorporated to study thermal effects on the propagation of wave. The problem is solved using Fourier series and Laplace transform to obtain the exact expressions of physical fields. The distributions of the nondimensional carrier density and stresses are obtained and illustrated graphically. The effects of nonlocal parameter, fractional order parameter, and time parameter on these wave characteristics are concerned and discussed in detail. Some semiconductor materials as Silicon (Si) and Germanium (Ge) are used to make the numerical simulation and some comparisons in different thermal memories are made. [ABSTRACT FROM AUTHOR]

In a dilaton gravity model, we revisit the calculation of the temperature of an evaporating black hole that is initially formed by a shock wave, taking into account the quantum backreaction. Based on the holographic principle, along with the assumption of a boundary equation of motion, we show that the black hole energy is maintained for a while during the early stage of evaporation. Gradually, it decreases as time goes on and eventually vanishes. Thus, the Stefan–Boltzmann law tells us that the black hole temperature, defined by the emission rate of the black hole energy, starts from zero temperature and reaches a maximum value at a critical time, and finally vanishes. It is also shown that the maximum temperature of the evaporating black hole never exceeds the Hawking temperature of the eternal AdS2 black hole. We discuss physical implications of the initial zero temperature of the evaporating black hole. [ABSTRACT FROM AUTHOR]

The nonlinear vibrations of composite cylindrical–cylindrical shells with bolt loosening connections are investigated. First, a theoretical model of such a combined shell is developed, with a multisegmental virtual material ring technique being adopted to replicate the partial bolt looseness in the bolted connection zone of two single shells. Furthermore, to consider the nonlinear vibration issue of such a bolted connection zone affected by external excitation amplitude, the equivalent Young’s modulus of the virtual material is defined, and the equation of motion is derived to solve nonlinear vibration parameters. Finally, three single composite cylindrical shells are connected with 12 bolts to form two combined shell specimens, and experimental tests are carried out to validate the model and examine the nonlinear vibration characteristics of such combined shells. Also, the impact of partial bolt loosening parameters on the nonlinear vibration behaviors is investigated with some important findings being summarized. The analysis methods, modeling techniques, test methods and important conclusions proposed in this study provide a useful reference for the study of the vibration issues of bolted composite shells. [ABSTRACT FROM AUTHOR]

With a Kiselev spacetime around Schwarzschild black holes that have undergone quantum correction, the goal of this work is to examine the geometric structure of a thin-shell. In order to do so, we take into consideration black hole solutions and match the inner Minkowski spacetime using a cut and paste method. Our findings indicate that the use of a phantom-like equation of state, such as quintessence, dark energy, and phantom energy, in the linearized radial perturbation technique shows stable thin-shell configurations that lie beyond the outer manifold’s predicted position of the event horizon. Moreover, we discover that the characteristics of the black hole solutions have a significant impact on the thin-shell stability. We examine the behavior of a thin-shell configuration with massless and massive scalar fields by using Klein–Gordon’s equation of motion. According to our findings, the thin-shell system dynamics are significantly influenced by the scalar field, resulting in interesting phenomena including expansion and collapse. These results provide fresh light on the behavior of black hole solutions by providing important insights into the interaction between quantum correction factors related to scalar fields and thin-shell dynamics. In particular, our research suggests that the quantum correction parameter decreases the stable configuration of a Schwarzschild black hole encircled by a quintessence field. [ABSTRACT FROM AUTHOR]

In this paper, a three-dimensional dynamic model of a dual-cable winding hoisting system is presented to simulate and analyze its coupled vibrations. The equations of motion of this system are derived based on a substructure method and Lagrange's equations of the first kind, in which the longitudinal–torsional coupled mechanical characteristics of the hoisting cables are considered. Longitudinal and transverse natural frequencies of the system are obtained and studied, and its dynamic responses due to some assumed displacement excitations are calculated. Numerical results agree well with those from ADAMS simulation, and the results have shown that longitudinal and transverse resonances are inevitable, but the transverse resonance has little effect on the conveyance; Slow longitudinal excitations should be avoided, thus avoiding the first-order longitudinal resonance since the system longitudinal vibration is dominated by its first-order mode; the torque in the hoisting cable is mainly induced by its tension under longitudinal–torsional coupled mechanical characteristics of the cable, and a torque release device is suggested to protect the hoisting cable from torsion failure; Torsional and transverse vibrations of the conveyance are been well restricted by the guiding cables even when the guiding cable pre-tension is zero. The results of this paper can be used to improve the parameter design of the ultra-deep shaft hoisting systems. [ABSTRACT FROM AUTHOR]

In order to investigate the applicability of the ground motion generated by different methods in the seismic study of high-speed railways, this paper presents a multiple comparative analysis of the ground motion produced by the ground motion prediction equation method (GMPE) and the physically-based seismic simulation method (PBS), taking the Chi-Chi earthquake as an example. First, the ground motions of typical stations were obtained by GMPE and PBS methods and compared with the original seismic records. It is found that the PGAs of the simulated ground motions are closer to the original seismic records, and the median value of the PGAs of the ground motions selected by the GMPE method is slightly larger. There are differences between the two ground motion acceleration response spectra and the original seismic record, but there are also partially valid intervals. After that, the PBS ground motion (PBS-GM), GMPE ground motion (GMPE-GM), and original seismic record (Oril-SR) were inputted into the High-Speed Railway Track Bridge System (HSRTBS) for the dynamic history analysis, respectively. It was found that the PBS-GM overestimated the dynamic response of the HSRTBS at locations closer to the epicenter and underestimated it at locations farther away, but the error was small. In contrast, the GMPE-GM accurately estimates the dynamic response of the HSRTBS at locations moderately close to the epicenter and overestimates it at locations closer to the epicenter but with flat topography. In summary, the PBS-GM has a reliability that is not inferior to that of the GMPE-GM. [ABSTRACT FROM AUTHOR]

The main goal of this research is to analyze the natural frequencies and dynamic response, and to utilize nonlinear control techniques for vibration control of a smart nanocomposite sector plate, while taking into consideration the effects of agglomeration and internal pores. The proposed composite configuration includes a porous core layer reinforced with agglomerated GPLs, as well as two layers of piezoelectric sensors and actuators. Both complete and partial agglomeration states are considered based on the Eshelby–Mori–Tanaka approach to predict the effective properties of the nanocomposite. The mechanical properties of the porous core are characterized using an open-cell metal foam with interconnected pores, notable for their low density and high surface area. The governing equations of motion are derived using Hamilton’s principle, which is based on the First-order Shear Deformation Theory (FSDT) plate theory and the finite element method. The nonlinear fuzzy PID controller is designed as a combination of a fuzzy PI component and a nonlinear PD component. The gains of the PD controller are dynamically adjusted using nonlinear gains to optimize its performance. In addition, a comprehensive analysis has been conducted to examine the effects of geometric dimensions, distribution of reinforcement, weight fractions of nanofillers, parameters of agglomeration, porosity coefficient, porosity pattern, and boundary conditions on the natural frequencies and dynamic response of smart porous nanocomposites. Numerical simulations demonstrate the efficacy of the proposed controller in significantly reducing vibration amplitudes compared to velocity feedback. The velocity feedback controller decreases deflection from 24.39μm to 8.37μm, whereas the proposed controller achieves 3.66μm, representing a 56.27% improvement in performance. [ABSTRACT FROM AUTHOR]

In this paper, an adaptive backstepping-based control scheme is proposed to perform autonomous lateral maneuvers under significant lateral offset in the center of gravity (c.g.) position in a UAV. It is first shown that the coupled equations of motion arising from lateral c.g. shift can be simplified and cast in block strict feedback form making it amenable to a two-step backstepping control design. Useful nonlinear terms in the equations of motion are identified and retained in the backstepping design to ensure a less conservative control. Adaptation law is incorporated to dynamically adjust to changes in the c.g. position by adding an adaptive term to each step of the backstepping control. Lyapunov’s direct method and LaSalle’s invariance principle are applied to establish asymptotic stability of both tracking errors and errors in the c.g. estimate. To validate the effectiveness of the proposed control strategy, simulation results for horizontal turn maneuver are presented for the fixed wing Aerosonde UAV and maneuver performance is observed to remain highly insensitive to a wide range of lateral c.g. positions on either side of the fuselage centerline. Furthermore, a comparative control performance analysis is carried out against an ad-hoc model-based adaptive backstepping control scheme available in the literature and the results show significant performance enhancement in the proposed scheme. Along with the c.g. variations, the effects of steady crosswind are also investigated and the control formulation is modified to mitigate these effects too. Real-time control hardware in loop simulations are also provided in support of the real time viability of the proposed control. [ABSTRACT FROM AUTHOR]

The present study examines a microplate with a porous structure and two nanocomposite piezoelectric layers. All the layers' properties are graded functionally, bonded to each other, and supported by an elastic foundation that can withstand both normal and shear loads. Additionally, carbon nanotubes are used to increase the electro-mechanical performance of the piezoelectric patches, which are exposed to an externally applied electric voltage. Using a higher-order trigonometric shear deformation theory and von Karman's assumptions, the kinematic relations are demonstrated. The governing motion equations are derived using Hamilton's principle and variational technique, and the modified couple stress theory is employed to take the scale effect into account. An analytical method based on Fourier series functions is used to solve the differential motion equations, and the impact of diverse factors such as porosity percentage, pore distribution patterns, carbon nanotubes distribution patterns, and other key parameters on the normalized frequencies of the model is analyzed after verifying the accuracy of the results. The findings of this research may aid in the development and production of smart structures and devices with increased efficiency. [ABSTRACT FROM AUTHOR]

This study presents a method for determining the mass, angular momentum, and charge of Kerr–Newman black holes by analyzing the red/blue shifts of photons emitted by geodesic neutral massive objects. We derive the equations of motion for photons in the Kerr–Newman spacetime. We obtain explicit expressions for redshift/blueshift photons emitted by an object orbiting a Kerr–Newman black hole. Finally, using the Boyer–Lindquist coordinates, we express the red/blue shifts in terms of the metric parameters. [ABSTRACT FROM AUTHOR]

This paper introduces a novel numerical method for investigating the dynamic stability of a flutter panel exposed to a supersonic gas flow and a fluctuating axial excitation force. Initially, the system equation of motion was derived using Lagrange’s equation, where the first two modes are coupled Mathieu–Hill equations with damping, constituting a system of linear second-order differential equations with periodically variable coefficients. Subsequently, a new numerical method was proposed to analyze the dynamic stability of coupled Mathieu–Hill equations with damping. This method involves breaking down an arbitrary parametric load into discrete segments to approximate the variable excitation function using a step function. The system responses of each segment are then accumulated in matrix form. The proposed numerical method proves particularly effective for dynamic systems whose parameters cannot be treated as small. In practical application, the method allows the construction of instability regions corresponding to natural frequencies, subharmonics, and combination frequencies. Dynamic stability diagrams were generated based on dynamic pressure ratio, air/panel density ratio, Mach number, panel thickness—length ratio, and excitation frequency. The results demonstrated general agreement with those obtained through Hsu’s perturbation method, however, our numerical results have proven more accurate. The paper concludes by offering suggestions for suppressing panel flutter through appropriate parameter combinations. [ABSTRACT FROM AUTHOR]

In this study, a thermomechanical rigid-flexible coupling vibration model of the rotating pre-twisted porous functionally graded (PP-FG) thick microplate in a thermal environment is established based on the third-order shear deformation theory (TSDT) and modified couple stress theory (MCST). Three thermal distributions are considered. The effects of temperature and porosity on the equivalent material parameters are accounted for in the modified Voigt rule of mixture. The governing equations of motion are derived using the Euler–Lagrange equation and numerically solved through the complex modal analysis method and the Chebyshev–Ritz method. After validating the convergence and accuracy of the proposed model, the effects of temperature, material length scale parameter (MLSP), rotational speed, porosity index, gradient index, presetting angle, and pre-twist angle on the vibration behavior of microplates were examined. The key findings of the study are as follows: (1) The effects of rotational speed on in-plane and out-of-plane frequencies are opposite. Temperature elevation weakens the size effect and centrifugal stiffening effect on the frequencies. (2) The effects of the porosity index on the frequencies are the opposite when the gradient index exceeds a specific critical value. (3) The effects of the presetting angle on the frequencies are periodic and symmetrical at about 0. The frequencies reach an extreme value when the pre-twist angle is approximately 2π/3 for the cantilever microplate. The proposed model is more sophisticated and comprehensive than others reported in the literature. It offers a more thorough analysis and insight into the behavior and performance of micro-electro-mechanical systems (MEMS) and micro air vehicles (MAVs), particularly when operating in challenging conditions. [ABSTRACT FROM AUTHOR]

We present on shell-scheme for the 2PI formalism with a particular focus on the renormalized equations of motion. We first revisit the so-called Hartree approximation where we give the counterterms for both the broken and unbroken phases. Moreover, we give explicit formulas for the renormalized three- and four-point functions in the broken phase. We then turn to the sunset approximation, with only scalars and then including fermions. We give explicit formulas for the wave function and mass counterterms. Moreover, we show that, in particular, the two-point functions can be obtained numerically in a fast converging scheme even for large couplings of order one. [ABSTRACT FROM AUTHOR]

In this paper, we use the cosmographic approach to discuss Friedmann space-time in the presence of torsion. For this, we explore equations of motion that explain creation in an isotropic and homogeneous cosmic backdrop with nonzero torsion. Here, we consider the energy density of holographic dark energy model ρd = 3c2(z)M p2L−2 where c2 is a dimensionless parameter depending on redshift parameter z,Mp = 1 κ is the reduced Planck mass and L represents the holographic length scale. We examine this dark energy model with both constant and variable holographic length scales in terms of Hubble parameter to determine the best-fit scale. The interaction between dark sector components is taken to evaluate cosmographic parameters, like Hubble, equation of state, deceleration, jerk, snap, lerk and statefinder parameters. We consider four c(z) parametrizations, which are Chevallier–Polarski–Linder, Jassal–Bagla–Padmanabhan, Wetterich and Ma–Zhang for both cases. We obtain consistent results for specific choices of constant parameters in the underlying scenario. [ABSTRACT FROM AUTHOR]

In this paper, the vibration and stability of spinning viscoelastic tapered shafts with axial motion are investigated. The model of the shaft system is developed by incorporating the spinning motion, axial motion, axial load, viscoelasticity, and geometric properties. The coupled governing equations of motion of the spinning shaft system are obtained by applying Hamilton's principle. By employing the Laplace transform and Galerkin discretization method, the natural frequency and modal damping are computed. Also, the critical divergence axial and spinning velocities, as well as the flutter axial velocity, are determined. As a result, the divergence and flutter instability conditions of the system are examined. The effects of the main parameters, such as taper ratio, axial load, and viscoelasticity of material, on the vibration behavior of the shaft system are evaluated. The results show that compared to the homogeneous spinning shaft system with uniform cross-section, the vibration and stability of the viscoelastic tapered shaft system undergo an essential evolution. It is further demonstrated that the axial load and viscoelasticity are also the key parameters governing the stability of the system. [ABSTRACT FROM AUTHOR]

This study explores the nonlinear free vibrations of anisogrid lattice cylindrical panels under clamped circumstances for the first time. The lattice panel is made of repeating circumferential hexagonal unit cells with helical and circumferential isotropic ribs. The panel's stiffness and mass are calculated using a continuous model based on orthotropic deep panel theory. The strain–displacement relationships are based on von-Kármán's geometrically nonlinear theory. Using the Hamilton principle, nonlinear two-dimensional (2D) motion equations are extracted in their strong form. A 2D collocation approach based on the Sinc functions with double exponential (DE) transformation with a high convergence rate is used to solve the governing motion equations. The time variable is then eliminated from the equations using the weighted residual Galerkin procedure. Finally, the system's nonlinear natural frequencies are computed using an iterative algorithm based on the bilateral displacement control. The influence of unit cell features, such as the angle of helical ribs, the number and thickness of ribs, and the panel dimensions, is examined in detail on the panel's linear and nonlinear vibration behavior. [ABSTRACT FROM AUTHOR]

In this paper, to investigate the dynamic responses of underground circular shells subjected to subsurface denotations and provide a feasible engineering design method, a simplified mathematical modelling was proposed. The dynamic medium–structure interaction (MSI) was introduced into the equations of motions through an interfacial damping between the structure element and the surrounding geomaterial, in which the effects of the shear and the rotary inertia were neglected. By means of modal superposition, the analytical solutions of the dynamic responses were deduced. The effects of geometric parameters and acoustic impedances on the dynamic responses were discussed. It is suggested that protective structures are better to be constructed in geomaterial with small impedance to attenuate the intense shock wave effects. [ABSTRACT FROM AUTHOR]

This paper studies the motion of charged test particle, moving in the outermost layer of a heterogeneous body (taken as first primary) filled with incompressible homogeneous viscous fluid and second primary is taken as point mass, whereas both the primaries are assumed to be charged. We compute the equations of motion of test particle (the third body) and stationary points (circular, axial and out-of-plane stationary points). And also, the stability of stationary points is examined utilizing characteristics equations and Routh–Hurwitz criterion. In addition to this, the numerical analysis of stationary points and their stability are worked out for different values of parameters. [ABSTRACT FROM AUTHOR]

In this paper, the free vibration of a sandwich plate with an anisogrid core and two face sheets reinforced with graphene platelets (GPLs) is investigated. A continuous approach is considered for the lattice core and the equivalent properties are calculated. Adopting the Halpin–Tsai micromechanics, the effective Young’s modulus of the nanocomposites/graphene platelets is extracted. Also, mass density and Poisson’s ratio are earned with the simple rule of mixtures. A quasi-3D theory is applied to model the kinematics of the sandwich plate with simply supported boundary conditions. Hamilton’s principle is implemented to obtain the equations of motion that are solved based on the Navier solution. The validity of the results of this study is confirmed by comparing the analytical results with those presented in other researches and also a finite element model. The effect of the parameters of the lattice core such as the width of ribs, the number of helical ribs in one direction, and the ratio of thickness of face sheets to core on the natural frequencies of the sandwich plate was investigated. Additionally, the impact of the pattern of graphene platelets and their weight fraction on the natural frequencies were investigated. The results show that by decreasing the ratio of the thickness of face sheets to the thickness of core and increasing the number of ribs and their width, the natural frequencies will decrease. Moreover, the patterns FG-V and FG-A have the highest and the lowest natural frequencies, respectively, among the other distribution of graphene platelets. [ABSTRACT FROM AUTHOR]

This research focuses on examining the vibrational properties of intelligent curved microbeams (CMBs) that incorporate metal foams and are enhanced with carbon nanotubes-reinforced piezoelectric (CNTRP) actuators. An advanced four-variable theory for shear and normal deformation is applied in the polar coordinate framework to investigate the microstructure, thereby negating the need for a shear correction factor. Additionally, the modified couple stress theory (MCST) is utilized to account for scale effects. The structural attributes exhibit thickness-dependent alterations following predefined functions. The governing equations of motion are deduced using Hamilton’s principle. In instances where the structure has simply supported ends, Fourier series functions are utilized to solve these equations. The outcomes are cross-validated in contradiction with previously documented works with more straightforward setups. The inquiry investigates the effects of critical parameters on the vibrational response of the structure. The results are corroborated in simpler scenarios using existing data in the literature to ensure accuracy. [ABSTRACT FROM AUTHOR]

This study centers on the analysis of a scale-dependent microplate configuration characterized by a porous core enveloped by nanocomposite patches embedded with graphene nanoplatelets. The microplate’s behavior is explored within a humid environment to comprehend the effects of moisture variations on its dynamic performance. Additionally, the microplate rests upon a Kerr foundation, a three-parameter elastic substrate. The material properties of all three layers are contingent upon thickness. To enhance precision, an innovative quasi-three-dimensional shear and normal trigonometric theory is employed, elucidating the kinematic interrelations of the microstructure. Notably, this novel theory accommodates the presence of transverse normal strain. For a comprehensive analysis of size influences, the modified couple stress theory is harnessed. This theory integrates a material length-scale parameter to anticipate outcomes at the micro-scale. By invoking Hamilton’s principle, differential motion equations are deduced and subsequently solved analytically. The investigation centers on probing the consequences of varied parameters on the natural frequencies. The findings underscore that the incorporation of GPLs amplifies the microplate’s stiffness, thus elevating its natural frequencies. In contrast, an escalation in the porosity index leads to a reduction in natural frequencies. [ABSTRACT FROM AUTHOR]

In order to improve the computational efficiency of the vehicle–road coupled response in long-distance driving, this paper proposes a cyclic road modeling method to equivalent an infinitely long road. The road is built using a closed model, and the vehicle–road coupled response is calculated assuming that the vehicle numerically cyclic driving. First of all, the concept of the cyclic road model is introduced, and the modal analysis is performed. Secondly, the principle for determining the optimal length of the cyclic road model is proposed based on the attenuation properties of the road response in time and space. Next, the vibration analysis of the vehicle–road coupled system is conducted, and its equation of motion is constructed using the mode superposition method (MSM). Further, the optimal length of the cyclic road model is derived regarding to road parameters via numerical analysis. At last, the application of this cyclic road model on computing the vehicle–road coupled response in long-distance driving is discussed via numerical simulation. The results indicate that this model has a consistent performance with the widely used models, while significantly improves computational efficiency. The proposed method also provides a new idea for the fast modeling of roads. [ABSTRACT FROM AUTHOR]

It is crucial to comprehend the nonlinear vibration behavior of sophisticated engineering constructions to aid in the examination, creation and production procedures. The primary objective of this study, therefore, is to focus on exploring the nonlinear forced vibrational characteristics of two-directional functionally graded (TDFG) cone-shaped shell for the first time. To accomplish this, the motion equations of the TDFG cone-shaped shell are derived based upon the framework of first-order shear deformation theory (FSDT) in conjunction with von Kármán assumption. TDFG cone-shaped shell models have mechanical properties that can change smoothly and continuously across the thickness and length of the shell, following a power law distribution pattern. To discretize the partial differential equations and transform them into ordinary differential equations, the Galerkin approach was used and ultimately, these equations were solved using the multiple time scales method. The accuracy and effectiveness of this analytical model are indicated through comparison with existing solutions. Finally, some comprehensive parametric investigations are carried out to gain insight into the impacts of several factors on the nonlinear behavior of the shell, highlighting the significant influence of transverse and longitudinal gradient indices on the nonlinear frequency response, which is not considered before. The new insights gained from this research could serve as valuable benchmark outcomes as well as contribute to a more comprehensive understanding of the nonlinear vibrations in future analysis and design processes. [ABSTRACT FROM AUTHOR]

Replacing fossil fuels with renewable energy is one of the important means to improve energy scarcity and environmental protection, and is of great significance for achieving sustainable development of human society. Vertical axis wind turbine (VAWT) is one of the key equipment for applying green energy — wind energy. During the operation of VAWT, its blades not only have to withstand periodic aerodynamic loads, but also suffer from centrifugal force effects and the Coriolis force effect caused by coupling with multi-dimensional deformation. The complex stress situation makes the blades susceptible to damage, resulting in structural resonance and instability of aeroelastic stability. This paper applies the Euler beam model and Hamilton principle to establish a nonlinear structural vibration motion equation for large-span vertical axis wind turbine blades with fully coupled four-dimensional deformation (i.e. lateral bending deformation, chord bending deformation, axial torsion deformation, and axial tensile deformation), and retains the nonlinear term of the motion equation to the third-order infinitesimal. Separating the motion equation into equilibrium equation and dynamic equation, it can be seen that the displacement of equilibrium state caused by the centrifugal force of the rigid body exists in the form of a coefficient in the dynamic equation, which will have an impact on the dynamic characteristics. This modeling work can provide a research foundation for exploring the dynamic characteristics and aeroelastic stability of VAWT blades in the future. [ABSTRACT FROM AUTHOR]

This research investigates the free vibration of a rotating annular microplate under the flexoelectric effect. Initially, the Kirchhoff plate theory assumptions are used to express the displacement fields. After considering the displacement field, strains and their gradients are derived and substituted into the electric enthalpy and kinetic energy expressions. Subsequently, by applying Hamilton’s principle to the aforementioned equations, the electric and mechanical equations are computed. To derive the equations of motion, initially, the polarization vectors and their gradients are derived from the electric equations and associated boundary conditions. Subsequently, these are incorporated into the mechanical equations, which also encompass electric components. It is notable that by removing the time-dependent terms from the in-plane equations of motion, the static displacement due to rotation at each speed is obtained. After deriving the equations of motion and boundary conditions, these equations are non-dimensionalized using non-dimensionalizing relations. In the next step, Hamilton’s principle is used to discretize the equations and boundary conditions. Consequently, by applying the generalized differential quadrature method and extracting the stiffness and mass matrices resulting from the transverse equation of motion and boundary conditions, the natural transverse frequency of the rotating annular microplate under the flexoelectric effect is calculated. The results of this research are useful for promoting the use of rotating annular microplants under flexoelectric effect for microelectromechanical systems designers with high efficiency. [ABSTRACT FROM AUTHOR]