Archive of Applied Mechanics最新文献

This work focuses on the nonlinear dynamic response of composite beams reinforced with carbon nanotubes (CNTs), and subjected to a moving mass, accounting for different reinforcement distributions. The Hamilton’s principle is here combined to the Euler–Bernoulli beam theory, including a von Kármán nonlinearity in the kinematic assumptions, to determine the nonlinear governing equation of the problem. Unlike previous finite element or semi-analytical studies that primarily relied on numerical discretization or linearized approximations, the present work provides a fully analytical treatment of the nonlinear dynamics by employing the Galerkin decomposition and method of multiple time scales (MMS) to investigate superharmonic and subharmonic resonance coupled with internal resonance. This allows a direct insight into the nonlinear resonance behavior, frequency–amplitude dependence, and parametric influence of moving-mass velocity, magnitude, and position on CNT-reinforced composite (CNTRC) beams—effects that have not been explicitly characterized in earlier finite element method (FEM)-based studies. The results yield useful benchmarks for future computational validation and material–structural design optimization.

This study investigates the intricate size-dependent electromechanical buckling behavior of composite nanobeams featuring a perforated functionally graded core and piezoelectric layers on an elastic foundation. Employing the nonlocal strain gradient theory, which integrates both piezoelectric and flexoelectric effects, governing equations are derived for Euler–Bernoulli and Timoshenko beam models. The core’s functionally graded material properties are assumed to vary continuously along the thickness direction, following a power-law distribution. Furthermore, closed-form expressions for the geometrical variables of the perforated core are developed. Analytical solutions for the electromechanical critical buckling loads are derived and rigorously validated against the established literature. Numerical simulations reveal the profound influence of material gradation, perforation geometry, and the interplay of nonlocal and flexoelectric effects on the buckling characteristics of these nanostructures. Key findings indicate that increasing the gradation index (n) from 0 to 14 leads to a significant reduction in the critical buckling load parameter. Specifically, a 31.44% decrease is observed for Timoshenko nonclassical electromechanical behavior at a filling ratio (α) of 0.75, and a 72.07% decrease for classical mechanical behavior at α = 0.5. Moreover, enhancing the normalized shear component of the elastic foundation parameter (Κ_p) from 0 to 2.5 results in a dramatic increase in the Timoshenko nonclassical mechanical critical buckling load by 1167.07% at n = 0, which reduces to 1087.06% at n = 2. These insights provide a valuable foundation for optimizing the design and performance of advanced nanoelectromechanical systems (NEMS).

In the present study, the modal behaviors of an elastic metamaterial (EM) rod with end-coupled inertial mass are investigated and its localized natural mode in the bandgap is revealed. The dispersion curves and the special modal properties in pass band and bandgap of the EM rod are elucidated both by theoretical and numerical methods. A unique mode is found to exist in bandgap and observed as a kind of localized mode, which may lead significant influences in the field of vibration control. The vibration properties are discussed numerically, and the phenomena are basically consistent with the experimental results. This work and relevant results may provide a useful reference for this research field.

Transient tractive rolling contact behavior of tires is critical for achieving high-precision motion control of wheels, especially for high-bandwidth in-wheel motor drive systems. When it comes to real-time simulation and motion control applications, a transient tire model with a simple form and good expression accuracy is essential. The paper aims to investigate the basic characteristics and influencing factors of transient tractive rolling contact behavior of tires, and to analytically point out the way to consider the effect of wheel inertia in simplified model. A wheel dynamics simulation model is established based on the discrete brush model, incorporating wheel inertia effect. Transient tractive rolling contact behavior of tires is investigated. The effect of model simplification on the expression accuracy and the improvement method is analytically illustrated.

The primary objective of this article is to implement an analytical study for nonlinear mechanical and thermal buckling of functionally graded (FG) porous piezoelectric cylindrical microtubes under the impacts of external electric field and hygrothermal conditions. To achieve this, the displacement field is formulated using a novel shear deformation beam theory. Moreover, the micro-scale impact is implemented by utilizing the hypothesis of modified couple stress, which includes merely one material length-scale component. The microtubes in the proposed model are constructed of a material called piezoelectric containing pores that may be steadily dispersed or smoothly varied according to a sinusoidal law. Additionally, three porosity distribution patterns are presented here. In order to derive the postbuckling load and temperature, the equations of motion are deduced within the framework of virtual work and then converted to a nonlinear algebraic system employing Galerkin’s method. The accuracy and efficiency of the proposed method are validated by comparing the results with those available in the existing literature. Furthermore, several parametric examples are conducted to analyze the effects of the length-to-depth ratio, porosity distribution type, porosity factor, and parameters of moisture and temperature on the postbuckling paths of the proposed model. The findings indicate that considering the small size impact boosts the microtube strength leading to an increment in mechanical and thermal postbuckling loads.

The paper deals with a combined technique and variational theory for solving highly nonlinear fractional-order oscillator problems, which are frequently encountered in practical applications. These methods are applicable to both weakly and strongly nonlinear equations. Since most such systems do not have analytical solutions, various numerical solutions are especially needed in applied sciences. The fractional equation is transformed into an ordinary differential equation by utilizing a fractional complex transformation, and an effective method based on a modification of He’s frequency formulation is proposed. In this method, for two conditions in which the amplitude is either extremely small or remarkably large, the oscillators are divided into two extreme cases, and by matching these extreme conditions, a new frequency formulation is obtained. Furthermore, the nonlinear oscillators are solved using a variational approach for balance. Examples of higher-order and unconventional fractional Duffing equations are given for comparison. The dynamic behavior of these equations is extremely rich. Numerical calculations are performed for various amplitudes, and the frequency-amplitude relationship and relative errors are presented in tables and graphs. The solution procedure is simple and does not require linearization, and the results obtained are valid over the whole solution domain. Finally, the effectiveness of the modification and iteration approaches is confirmed by showing that the approximate and exact frequency results are in good agreement. In addition, the performance of the proposed models is compared with results available in the literature, demonstrating that they are effective methods in terms of computational efficiency and accuracy.

This article presents the novel algorithm using 2D Bernstein polynomials in the solution of fractional derivative partial differential equation of dynamic viscoelastic (VE) beam rested on nonlinear elastic foundations, under various loading scenarios. Based on Euler–Bernoulli thin beam theory and the fractional Kelvin–Voigt viscoelastic model, the nonlinear multi-fractional partial differential equation governing the VE beam is established. Firstly, the integer and fractional differential matrices of Bernstein polynomials in one-dimensional are derived. Then, two-dimensional Bernstein polynomial operational matrices (2D-BPOM) for integer order and fractional order of differentiation is deduced. The 2D-BPOM is employed to discretize the governing nonlinear partial differential equation into a system of nonlinear algebraic equations, which are solved via Newton’s method. Verifications with exact solutions and numerical ones are presented to proof the solution technique and validate mathematical model. Comprehensive parametric studies are performed to examine the impact of loading conditions, foundation parameters and fractional orders on the dynamic response of VE beam. This study is limited to using a constant-order fractional derivative within the Kelvin–Voigt viscoelastic model for the VE thin beam’s governing equation neglecting a shear effect. The findings of this study may enable researchers to select an appropriate mathematical model that accurately aligns with a specific experimental model.

Traditional continuum mechanics faces challenges in solving discontinuity problems, such as cracks, due to the singularity of derivatives at the crack tip. While peridynamics can simulate spontaneous crack initiation and propagation via integral equations, bond-based peridynamics (BB-PD) is limited by fixed Poisson's ratios (0.25 for 3D, 0.33 for 2D), which limits its practicality for general engineering applications. This study establishes a three-dimensional (3D) crack propagation model for hull structures based on the ordinary state-based peridynamics theory. The specific research contents are as follows: (1) The "1D pre-screening + 3D precise search" algorithm is adopted to realize the fast adaptive modeling of hull structures; (2) combined with the fracture toughness test data of Q235 steel, a highly adaptable crack propagation analysis model is proposed. This model can automatically complete the construction of hull structures and preset cracks and realize the prediction of the whole process of natural crack initiation, propagation, and coalescence.

Soft structures composed of incompressible hyperelastic materials suffer from geometrical and material nonlinearities during deformation, which can lead to large deformations and large displacements, so it is required to maintain high continuity in the displacement field. However, it is difficult to ensure the high-order continuity requirement by using traditional finite element methods (FEM) which have the C° continuous elements. Nonlinear FEM represented by ANCF have been used to address issues in flexible multi-body systems. However, the ANCF method uses slope vectors as node coordinates, resulting in high degrees of freedom for each element and serious locking issues, which affect the computational efficiency and accuracy of this method. In this paper, a novel calculation method of large deformations and large overall motions for the Euler–Bernoulli beam is proposed based on the isogeometric analysis (IGA) method. The method combines the simplified neo-Hookean and Mooney-Rivlin models with a one-dimensional beam element. The middle section of the beam is modeled using the non-uniform rational B-spline (NURBS), and it is combined with Green’s strain tensor to derive elastic force and Jacobi matrix expressions in the fully Lagrangian formulations. This method accurately describes large deformations and large overall motions with fewer elements and control points, significantly improving computational efficiency. Compared to traditional methods and commercial software, computation time is reduced by over 77% while maintaining reliable accuracy. The research in this paper provides a theoretical basis for the dynamic analysis of flexible arms.

This study investigates the size-dependent thermoelastic dynamics of microbeams utilizing graphene as an integrated heat source. A sophisticated mathematical model is developed by synergistically combining modified couple stress theory (MCST) with a nonlocal heat conduction framework. This integrated approach effectively captures size-dependent phenomena, the influence of applied electrical voltage, and material resistance on the dynamic thermoelastic response of Euler–Bernoulli microbeams. The nonlocal heat conduction model incorporates thermal relaxation time and material length-scale parameters to accurately represent size effects in thermal transport, while MCST introduces additional stiffness mechanisms that enhance the predictive accuracy of mechanical behavior. The microbeam system, subjected to a sinusoidal heat pulse and thermoelectric effects from the graphene strip, is analyzed under simply supported boundary conditions. Governing equations are solved analytically using the Laplace transform method, yielding closed-form solutions for temperature distribution, lateral deflection, axial displacement, and stress components. Comprehensive numerical simulations elucidate the impact of critical factors, including couple stress effects, applied voltage magnitude, electrical resistance, and thermal boundary conditions, on the microbeam’s dynamic response. Results demonstrate that size-dependent effects significantly increase structural stiffness while reducing flexibility, leading to substantial modifications in both thermal and mechanical responses.