Archive of Applied Mechanics最新文献

The aim of this article is to explore the motion of an infinitesimal body (third body) in the vicinity of the out-of-plane equilibrium points of the restricted three-body problem under the effect of continuation fraction and radiation pressure perturbations. We investigate the effect of the radiation factor of the bigger primary and continuation fraction parameter of the smaller primary on the existence, position, zero-velocity curves and stability of the out-of-plane equilibrium points. It is discovered that the presence of these points is made possible by the bigger primary’s radiation. These equilibria arise in symmetric pair, and their number may be zero or two based on the values of the radiation and mass ratio parameters. Our results reveal that all the involved parameters have strong influence on the position of the out-of-plane equilibrium points. A numerical investigation found that the perturbing parameters have impact on the geometry of the zero-velocity curves. The stability of these points is studied in the linear sense. A detailed numerical investigation found that the equilibrium points are unstable in general.

Thermoelastic dissipation (TED) is a primary source of energy loss in extremely small structures, making the precise determination of its magnitude vital for the optimal design and performance of such components. The inclusion of two-dimensional (2D) heat conduction alongside size effects in both the structural and thermal domains plays a key role in enhancing TED analysis for small-scale beam resonators. The modified couple stress theory (MCST) and Moore–Gibson–Thompson (MGT) heat equation, within the context of the energy approach, are employed in this paper to create a novel size-dependent framework for TED in small-scale beams subjected to 2D heat conduction. After comparing the developed framework with existing research, numerical simulations are carried out to reveal the differences between 2 and 1D models, as well as the impact of employing size-dependent mechanical and thermal formulations. For beams with large thickness-to-length ratios, especially under clamped–clamped (CC) boundary conditions, the proposed model shows significant differences when compared to 1D model. Based on the findings, the ratio of 2D TED to 1D TED in CC beams with an aspect ratio of 10 can be up to 1.6 times. The integration of size effects and 2D heat transfer in the established framework is expected to provide benchmark results for accurate TED simulations and facilitate the optimal design of ultra-small beam resonators.

There exist complex deformation characteristics and torque transmission mechanisms of the structure whose boundary is constrained locally. This paper proposes the power series polynomial constraining method to establish the dynamical modeling of a rectangular thin plate with a localized constraint. The boundary condition can be constructed by applying the power series polynomial with undetermined coefficients to the free boundary directly. This means that the derivation of the admissible function no longer relies on the first term associated with a specific constraint. The undetermined coefficient of the power series polynomial can be obtained while calculating the weight coefficient of the admissible function by using the Rayleigh–Ritz method. Then natural frequencies are calculated and polynomial coefficients can be further obtained. The influence of variations in boundary length, constraint length, constraint position and multiple discontinuous localized constraints on natural frequencies of the plate is studied. Convergence verification is performed for the truncated number of orthogonal polynomials and power series multipliers. Then the appropriate number of the term for the power series multiplier is determined. Natural frequencies of the cantilever plate and the opposite sides simply supported plate obtained by using the proposed method are compared with those obtained using the traditional method. Then natural frequencies of the plate with a local boundary constrained are compared with those obtained from the finite element software MSC.Patran. The fairly low relative error demonstrates the validity of the proposed method. The dynamical response analysis shows the superiority of the proposed method for the boundary locally constrained boundaries, which cannot be adequately handled by the traditional method.. The power series polynomial overcomes the limitation that the traditional Lagrange multiplier method can only construct point constraints.

The transient response of porous media is an important aspect of dynamic research. However, existing studies seldom provide solutions to the transient response problem of layered unsaturated porous media. Based on the Biot-type unsaturated wave equations, dimensionless one-dimensional wave equations are established. An appropriate displacement function is introduced to homogenize the boundary conditions. Subsequently, the transfer matrix method is used to obtain the eigenvalues and eigenfunctions of the homogeneous governing equations. Leveraging the orthogonality of the eigenfunctions, the original problem is transformed into solving a series of initial value problems of ordinary differential equations. The temporal solution within the time domain is then obtained through an improved precise time integration method. The validity of the solution presented in this paper is verified by comparing it with existing solutions in the literature. Analysis of numerical examples shows that reflection waves of opposite phases will be generated at the hard-soft and hard-harder interface, which helps in the accurate identification of weak interlayers in practical engineering applications. With increasing saturation, there is a noticeable increase in the velocities of the (P_{1}) and (P_{3}) waves, whereas the velocity of the (P_{2}) waves tends to decrease, which can be used to assess the mechanical property of medium. The peak value of pore pressure in unsaturated can be 1.64 times higher than those in saturated condition.

In this study, we define Hilfer fractional Dirac system. Our main object is to analyze the main spectral structure of the Hilfer fractional Dirac system. To this end, the self-adjointness of the Hilfer fractional Dirac operator, orthogonality of the eigen-vector-functions, and reality of the eigenvalues are displayed. Also, we obtain the representation of the solution of the system by using Laplace transforms with analytical estimations. We investigate eigen-vector functions and eigenvalues for the Hilfer fractional Dirac boundary value problem and illustrate the results in detail with tables and figures.

This research concentrates on examining the dynamic responses of a system modeling the pole vault as mass–elastica, characterized by uncertain parameters. A first-order perturbation method (PM) is introduced and compared to the second-order PM and the reference Monte Carlo method. The results demonstrate an improvement in computational efficiency and accuracy under moderate uncertainties. This study highlights the impact of key parameters, such as the nondimensional velocity ((v_0)) and the deflection of the elastica due to the weight of the mass (w) on the performance of the system, providing useful information for a better understanding of the dynamic behavior.

The modeling and analysis of laminated composite plates are performed using a unified Higher Order Shear Deformation Theory (HSDT) that accounts for transverse stretching effect. The adopted unified HSDT formulation allows the implementation of various shear functions. To derive a weak form from the generalized displacement fields of HSDTs, a variational principle is applied within a two-field mixed approach. The stationarity of the functional for laminated plate structures is obtained through the application of the Hellinger–Reissner variational principle. Hence, displacements and stress resultants, namely two independent fields, are included in finite element equations. Four-noded, quadrilateral elements are employed for the discretization of the plate’s domain. While the generated functional initially had (C^{1}) continuity, benefiting from the two-fields property of the mixed finite element formulation, integration by parts is performed that results with a functional requiring only (C^{0}) continuity. To effectively capture the nonlinear and parabolic variation of transverse shear stress, it is determined that even with varying functions, the results are theoretically consistent with the elasticity method and the employed HSDT model. Also, when compared to the theories that are already accessible in the literature, for the bending behavior of composite plates, incorporating the stretching effect converges the exact results for laminated composite plates more than the studies where that effect is neglected.

Shape optimization is an increasingly prevalent tool for designing and manufacturing mechanical systems with gradient-free nonlinear performance metrics. Uncertainty quantification is an essential part of the process as optimality can be called into question in the presence of unavoidable discrepancies between numerical designs and manufactured parts. This paper combines isogeometric analysis (IGA) and polynomial chaos expansions (PCE) towards shape optimization of a disc brake for noise minimization under uncertainties. The proposed approach sets robustness to manufacturing uncertainties as an optimization objective in order to directly obtain robust optimal solutions. IGA is chosen over other shape design alternatives for its absence of meshing approximations, which makes it potentially more suitable in the presence of uncertainties. PCE is used to quantify robustness through the variance of the output, in an attempt to alleviate the computational burden of uncertainty quantification. The studied application is a simplified disc brake system whose shape is modified to minimize undesirable squeal noise, which is quantified through complex eigenvalue analysis. The noise prediction model, PCE model, and a genetic algorithm are then combined for the purpose of searching for robust optimal solutions. Results show the capability to converge to a Pareto front of robust noise-minimizing disc brake shapes and overall high computational efficiency compared to Monte Carlo simulation for output variance estimation. Furthermore, our findings confirm the superiority of sparse PCE methods over the classical ordinary least squares PCE method for output variance quantification.

Curved double-walled carbon nanotubes (CDWCNTs) are crucial components in nanoelectronics, mechanical sensors, and composite materials due to their unique geometry and structural properties. Electron microscopy images have revealed that carbon nanotubes are rarely perfectly straight, often exhibiting curvature or waviness along their length due to inherent geometrical imperfections. The accurate mechanical modeling of these structures is essential, particularly to capture size-dependent effects that classical elasticity theories fail to account for. In this study, a novel analytical framework was introduced for combining the initial value method with the approximate transfer matrix approach to analyze the mechanical behavior of CDWCNTs under anti-plane loading within the framework of nonlocal elasticity theory. The proposed methodology provides an effective and computationally efficient alternative to traditional analytical approaches. By analyzing displacements, rotations, bending moments, and shear forces, substantial deviations were revealed between classical and nonlocal elasticity solutions, particularly as the dimensionless nonlocal parameter (R/gamma ) decreased. The results show that nonlocal effects become dominant at smaller size parameters, especially in displacements, rotations, and bending moments, while shear forces remain unaffected. These findings emphasize the critical role of nonlocal effects in accurately predicting nanoscale mechanical responses and offer valuable insights for modeling advanced nanostructures in emerging technologies, such as microelectromechanical systems and nanotechnology. Convergence studies have confirmed the accuracy and stability of the proposed approach, thereby establishing this as a robust tool for modeling nanoscale structures.

This study proposes an innovative numerical approach combining the finite element method and high-order continuation algorithm (FE-HCA) to analyze the nonlinear buckling and post-buckling behavior of porous FGM sandwich plates, evaluating the impact of porosity distribution and boundary loading types on their response. The approach is based on a Taylor series expansion of the unknowns in the problem, which transforms the nonlinear equations into a sequence of linear problems solved using the finite element method. The continuation technique is then employed to search for solution curves branch by branch, inverting a single tangent stiffness matrix per branch and providing an adaptive step size that adjusts according to the local nonlinearity of the solution branch. The mathematical formulation of the problem, based on high-order shear deformation theory (HSDT), introduces parabolic shear deformations, thus eliminating the need for shear correction factors. However, the applicability of HSDT is primarily limited to moderately thick plates, as it does not fully capture three-dimensional stress effects in very thick structures. The results show that the FE-HCA algorithm significantly reduces computation time, as demonstrated by a numerical example in the results section, where the number of tangent matrix inversions decreases from 4086 to only 12. A detailed parametric study highlights the influence of key parameters, such as porosity distribution, layer thickness, and loading types, on the buckling behavior. Compared to traditional iterative methods, the FE-HCA approach is faster and more efficient, offering significant gains in accuracy and computational cost, making it a powerful tool for analyzing FGM structures.