Search Results (125)

This study presents a closed-form solution for the dynamic response of a sandwich beam subjected to arbitrary impact loading, with a particular focus on energy harvesting from an attached piezoelectric layer. A thin piezoelectric patch is bonded to the bottom surface of the beam to convert mechanical vibrations into electrical energy. The governing equations of motion are derived using Hamilton’s principle, considering a non-symmetric sandwich cross-section and incorporating higher-order shear deformation effects. The state–space method is employed to obtain the exact dynamic response of the beam under impact excitation. The differential equations governing the output voltage and harvested power are solved analytically based on the derived response. The natural frequencies and dynamic responses are validated against classical beam theory, highlighting the significance of shear deformation. Numerical examples are provided to evaluate the generated voltage and energy harvesting efficiency. The results demonstrate the strong potential for energy harvesting from sandwich beam vibrations and elucidate the influence of impact loading conditions, distributed load amplitude, and the geometric dimensions of the beam on the harvested output. Full article

Dynamic post-buckling behavior of microscale cylindrical shells reinforced with functionally graded carbon nanotubes (FG-CNTs) and conveying microfluid is discussed for the first time. The microshell is embedded in a Kerr foundation and subjected to an axial compressive load and a two-dimensional magnetic field effect. CNTs dispersion across the shell thickness follows a power law, with five distribution types developed. The modified couple stress theory is applied to incorporate the small-size effect using a single material parameter. Furthermore, the Knudsen number is used to address the small-size effect on the microfluid. The external force between the magnetic fluid and microshell is modeled by applying the Navier–Stokes equation depending on the fluid velocity. Nonlinear motion equations of the present model are derived using Hamilton’s principle, containing the Lorentz magnetic force. According to the Galerkin method, the equations of motion are transformed into an algebraic system to be solved, determining the post-buckling paths. Numerical results indicate that the presence of the magnetic field, CNT reinforcement, and fluid flow improves the load-bearing performance of the cylindrical microshells. Also, many new parametric effects on the post-buckling curves of the FG-CNT microshells have been discovered, including the shell geometry, magnetic field direction, length scale parameter, Knudsen number, and CNT distribution types. Full article

The primary resonance responses of high-performance nanocomposite materials used in spacecraft components in complex electromagnetic field environments were investigated. Simultaneously considering the interfacial effect, agglomeration effect, and percolation threshold, a theoretical model that can predict Young’s modulus and electrical conductivity of graphene nanocomposites is developed by the effective medium theory (EMT), shear lag theory, and the Mori-Tanaka method. The magnetoelastic vibration equation for an axially moving graphene nanocomposite current-carrying beam was derived via the Hamilton principle. The amplitude-frequency response equations were obtained for different external loading conditions. The study reveals the significant role of graphene concentration, external force, and magnetic field on the system’s primary resonance, highlighting how electromagnetic forces play a critical role similar to external excitation forces. It is shown that the increase in graphene content could lead the system from period-doubling motion into chaotic behavior. Moreover, an enhanced magnetic field strength may lower the minimum graphene concentration needed for period-doubling motion. This work provides new insights into controlling nonlinear vibrations of such systems through applied electromagnetic fields, emphasizing the importance of designing multifunctional nanocomposites in multi-physics coupled environments. The concentration of graphene filler would significantly affect the primary resonance and bifurcation and chaos behaviors of the system. Full article

This paper investigates Mean Field Game methods to solve missile interception strategies in three-dimensional space, with a focus on analyzing the pursuit–evasion problem in many-to-many scenarios. By extending traditional missile interception models, an efficient solution is proposed to avoid dimensional explosion and communication burdens, particularly for large-scale, multi-missile systems. The paper presents a system of stochastic differential equations with control constraints, describing the motion dynamics between the missile (pursuer) and the target (evader), and defines the associated cost function, considering proximity group distributions with other missiles and targets. Next, Hamilton–Jacobi–Bellman equations for the pursuers and evaders are derived, and the uniqueness of the distributional solution is proved. Furthermore, using the $ϵ$-Nash equilibrium framework, it is demonstrated that, under the MFG model, participants can deviate from the optimal strategy within a certain tolerance, while still minimizing the cost. Finally, the paper summarizes the derivation process of the optimal strategy and proves that, under reasonable assumptions, the system can achieve a uniquely stable equilibrium, ensuring the stability of the strategies and distributions of both the pursuers and evaders. The research provides a scalable solution to high-risk, multi-agent control problems, with significant practical applications, particularly in fields such as missile defense systems. Full article

A nonlinear finite element model for circular and annular micro-plates under thermal and mechanical loading was developed using a third-order shear deformation theory. In the kinematic assumptions, a change in plate thickness is allowed, and no transverse shear strains are considered on the top and bottom surfaces. A power-law distribution was utilized to account for variations in two constituents through the thickness of the plate. Three different types of porosity distributions are considered. The strain gradient effect in micro-scale structures is accounted for by using the modified couple stress theory. Hamilton’s principle is used to obtain the equations of motion, and conforming plate elements are used in the development of the finite element model. The developed finite element model was verified against the available literature and analytical solutions. The effects of the material and porosity distribution, microstructure-dependency, geometric nonlinearity, and various boundary conditions on the bending response of functionally graded and porous circular and annular micro-plates were studied using the developed nonlinear finite element model. Full article

This paper takes as its starting point the distributed parameter models for both torsional and axial vibrations of the oilwell drillstring. While integrating several accepted features, the considered models are deduced following the Hamilton variational principle in the distributed parameter case. Then, these models are completed in order to take into account the elastic strain in driving signal transmission to the drillstring motions—rotational and axial (vertical). Stability and stabilization are tackled within the framework of the energy type Lyapunov functionals. From such “weak” Lyapunov functionals, only non-asymptotic Lyapunov stability can be obtained; therefore, asymptotic stability follows from the application of the Barbashin–Krasovskii–LaSalle invariance principle. This use of the invariance principle is carried out by associating a system of coupled delay differential and difference equations, recognized to be of neutral type. For this system of neutral type, the corresponding difference operator is strongly stable; hence, the Barbashin–Krasovskii–LaSalle principle can be applied. Note that this strong stability of the difference operator has been ensured by the aforementioned model completion with the elastic strain induced by the driving signals. Full article

This research examines the free vibration characteristics of composite ring-like structures enhanced with carbon nanotubes (CNTs), taking into account the effects of CNT agglomeration. The structural framework comprises two concentric composite rings linked by elastic springs, creating a coupled beam ring (CBR) system. The first-order shear deformation theory (FSDT) is applied to account for transverse shear deformation, while Hamilton’s principle is employed to formulate the governing equations of motion. The effective mechanical properties of the composite material are assessed with regard to CNT agglomeration, which has a significant impact on the elastic modulus and the overall dynamic behavior of the structure. The numerical analysis explores the influence of porosity distribution, boundary conditions (BCs), and the stiffness of the springs on the natural vibration frequencies (NVFs). The results demonstrate that an increase in CNT agglomeration leads to a reduction in the stiffness of the composite, consequently decreasing the NVFs. Furthermore, asymmetric porosity distributions result in nonlinear fluctuations in NVFs due to irregularities in mass and stiffness, whereas uniform porosity distributions display a nearly linear relationship. This study also emphasizes the importance of boundary conditions and elastic coupling in influencing the vibrational response of CBR systems. These findings offer significant insights for the design and optimization of advanced composite ring structures applicable in aerospace, nanotechnology, and high-performance engineering systems. Full article

The dynamic behavior of pipelines subjected to additional masses is crucial for optimizing the design and reliability of engineering systems, particularly in offshore and industrial applications. This study investigates the effect of slenderness on the dynamic response of a pipe with one or more additional masses placed at different positions along its length, considering the symmetry of the system in mass distribution. The aim is to analyze how mass placement influences vibration characteristics under fluid–structure interaction (FSI) conditions. The pipe is modeled as a Rayleigh beam, and the governing equations of motion are derived using Hamilton’s principle while preserving the inherent symmetry of the system. A non-dimensionalized approach is employed to ensure broad applicability across different geometric and material configurations. The vibration frequencies are obtained using the Galerkin method (GM) and validated via a two-way FSI technique, integrating computational fluid dynamics (CFDs) and structural mechanics using ANSYS 2022 software. The results demonstrate the relationship between the concentrated mass ratio and vibration frequency for the first three modes, highlighting the influence of slenderness ratio on system stability. These findings provide valuable insights for the engineering design of pipeline systems subjected to dynamic loading. Full article

This paper is dedicated to studying the optimal investment proportions of three types of assets with symmetry, namely, risky assets, risk-free assets, and wealth management products, when the stochastic expenditure process follows a jump-diffusion model. The stochastic expenditure process is treated as an exogenous cash flow and is assumed to follow a stochastic differential process with jumps. Under the Cox–Ingersoll–Ross interest rate term structure, it is presumed that the prices of multiple risky assets evolve according to a multi-dimensional geometric Brownian motion. By employing stochastic control theory, the Hamilton–Jacobi–Bellman (HJB) equation for the household portfolio problem is formulated. Considering various risk-preference functions, particularly the Hyperbolic Absolute Risk Aversion (HARA) function, and given the algebraic form of the objective function through the terminal-value maximization condition, an explicit solution for the optimal investment strategy is derived. The findings indicate that when household investment behavior is characterized by random expenditures and symmetry, as the risk-free interest rate rises, the optimal proportion of investment in wealth-management products also increases, whereas the proportion of investment in risky assets continually declines. As the expected future expenditure increases, households will decrease their acquisition of risky assets, and the proportion of risky-asset purchases is sensitive to changes in the expectation of unexpected expenditures. Full article

In this work, an analytical solution for the natural frequencies of elastically supported stepped beams with rigid segments is presented. The elastic end boundary conditions are modeled with a translational stiffness element, a rotational stiffness element, and an end-concentrated mass. This model is of great significance in machine construction studies. Under the assumption of Euler–Bernoulli beam theory, the non-dimensional equations of the motion and main equations that can give all of the boundary conditions were obtained by using Hamilton’s principle. After deriving the transverse displacement functions by means of using the separation-of-variables technique, the frequency equation was found by setting the determinant of the coefficient matrix to zero. The natural frequencies of the transverse vibrations were found according to physical and geometric parameters. The method was validated by using FEM results and findings from the literature. This study indicates that the physical and geometric parameters of the elastic supports and rigid segments affect the natural frequencies of the beam. The revealed analytical method can be used to calculate the natural frequencies and mode shapes of all beam types, such as elastically supported uniform beams and single-step beams with or without concentrated mass and/or rigid segments. Full article

This study presents an advanced mathematical model for the high-energy shaker mill process, incorporating thermal interactions among the milling ball, shaker mill vial, and the air contained within. Unlike previous models focusing solely on the ball’s temperature, this research emphasizes the heat produced by impacts and the thermal exchange among all three components. Incorporating these thermal interactions allows the model to provide a more comprehensive depiction of the energy dynamics within the system, leading to more precise predictions of temperature changes. Utilizing a lumped parameter method, the study simplifies complex airflow dynamics and non-uniform temperature distributions in the milling system, enabling efficient numerical analysis. Hamilton’s equations are extended to include supplementary state variables that account for the internal energies of both the vial and the air, in addition to the thermomechanical state variables of the ball. High-energy milling techniques are essential in mechanochemical synthesis and various industrial applications, where the optimization of heat transfer and energy efficiency is crucial. Numerical simulations computed using the Bogacki–Shampine integration algorithm significantly align with experimental data, confirming the model’s accuracy. This comprehensive framework enhances understanding of heat transfer in one-dimensional ball motion, optimizing milling parameters for better performance. The mathematical model facilitates the computation of heat production due to collisions, based on operational parameters like shaking frequency and amplitude, thereby allowing for the anticipation of chemical reaction activation potential in mechanochemistry. Full article

The stability of a nonlinear aero-thermo-elastic panel in supersonic flow is analyzed numerically. In light of Hamilton’s principle, the governing equation of motion for a two-dimensional aero-thermo-elastic panel is established taking geometric nonlinearity and curvature effect into account. Coupling with the panel vibration, aerodynamic pressure is evaluated by first order supersonic piston theory and aerothermal load is approximated by the quasi-steady theory of thermal stress. A Galerkin method based on approximate inertial manifolds is deduced for low-dimensional dynamic modeling. The efficiency of the method is discussed. Finally, the complex stability regions of the system are presented within the parametric space. The Hopf bifurcation is found during the onset of flutter as the dynamic pressure increases. The temperature rise imposes a significant effect on the stability region of the panel. Since the material parameters of the panel (elastic modulus and thermal expansion coefficient in this case) are the function of temperature, the panel tends to lose its stability as the temperature gets higher. Full article

This paper presents numerical investigations into the free vibration properties of a sandwich composite plate with two fiber-reinforced plastic (FRP) face sheets and a functionally graded carbon nanotube-reinforced composite (FG-CNTRC) core made of functionally graded carbon nanotube-reinforced composite resting on Winkler/Pasternak elastic foundation. The material properties of the FG-CNTRC core are gradient change along the thickness direction with four distinct carbon nanotubes reinforcement distribution patterns. The Hamilton energy concept is used to develop the equations of motion, which are based on the high-order shear deformation theory (HSDT). The Navier method is then used to obtain the free vibration solutions. By contrasting the acquired results with those using finite elements and with the previous literature, the accuracy of the present approach is confirmed. Moreover, the effects of the modulus of elasticity, the carbon nanotube (CNT) volume fractions, the CNT distribution patterns, the gradient index p, the geometric parameters and the dimensionless natural frequencies’ elastic basis characteristics are examined. The results show that the FG-CNTRC sandwich composite plate has higher dimensionless frequencies than the functionally graded material (FGM) plate or sandwich plate. And the volume fraction of carbon nanotubes and other geometric factors significantly affect the dimensionless frequency of the sandwich composite plate. Full article

This paper presents a mathematical model of a typical lumped-parameter electromagnetic assembly, which consists of two subassemblies: one includes a magnetic circuit and the other with selected elements of electric circuits. An interdisciplinary research approach is used, which assumes the use of a modified integral method based on the variational Hamilton–Ostrogradsky principle. The modification of the method is the extension of the Lagrange function by two components. The first one reflects the dissipation of electromagnetic energy in the system, while the second one reflects the effect of external non-potential forces acting on the electromagnetic system. This approach allows for the avoidance of the inconvenience of the classical theory, which assumes the decomposition of the entire integrated system into individual electrical subsystems. The state equations of the electromagnetic subassembly are presented solely on the basis of the energy approach, which in turn allows taking into account various latent motions in the system, because the equations are derived based on non-stationary constraints between subsystems. The adopted theory allows for the formulation of the model of the system in a vector form, which gives much more possibilities for the analysis of higher-order electromagnetic circuits. Another important advantage is that the state equations of the considered electrical object are given in Cauchy normal form. In this way, the equations can be integrated both explicitly and implicitly. The results of computer simulations are presented in graphical form, analysed, and discussed. Full article

The dynamic stiffness method is developed to analyze the natural vibration characteristics of functionally graded beams, where material properties change continuously across the beam thickness following a symmetric law distribution. The governing equations of motion and associated natural boundary conditions for free vibration analysis are derived using Hamilton’s principle and closed-form exact solutions are obtained for both Euler–Bernoulli and Timoshenko beam models. The dynamic stiffness matrix, which governs the relationship between force and displacements at the beam ends, is determined. Using the Wittrick–Williams algorithm, the dynamic stiffness matrix is employed to compute natural frequencies and mode shapes. The proposed procedure is validated by comparing the obtained frequencies with those given by approximated well-known formulas. Finally, a parametric investigation is conducted by varying the geometry of the structure and the characteristic mechanical parameters of the functionally graded material. Full article