Acta Mechanica最新文献

The functionally graded carbon nanotube-reinforced composite thin plates can be applied to a part of the aircraft wing, and thin plates are always affected by external airflow and harmonic excitation. So this article investigates the aerodynamic stability and nonlinear forced vibration characteristics of functionally graded carbon nanotube-reinforced composite thin plates in a subsonic airflow environment. The composite plate system’s governing equations are constructed using Hamilton^’s principle. The assumed mode method is further applied to discretize the equation into a computable discrete form. The stability of the composite plate is discussed by observing the natural frequency variation with each parameter. In the research, the arc-length continuation algorithm is used to analyze the nonlinear amplitude–frequency response of the plate. The specific effects of different parameters on the nonlinear vibration characteristics of the system were explored. The effects of the distribution form, volume rate, and flow velocity on the nonlinear vibration property of the plate are researched. Based on in-depth theoretical analysis and numerical simulations, it can be seen that the flow velocity primarily influences the vibration frequency but has negligible impact on nonlinear behavior. The key factors governing the nonlinear phenomena in the plates are distribution pattern and volume fraction of carbon nanotubes. This study provides a valuable dynamic response analysis basis for the performance evaluation of functionally graded carbon nanotube-reinforced composite thin plates and their optimal design in an aerodynamic environment.

Although the existing literature has reported on the dynamic behavior of conical shells under moving loads, no studies have investigated the dynamic response of graphene platelet-reinforced metal foam (GPLRMF) conical shells with initial geometric imperfections. In this paper, a dynamic model of such GPLRMF conical shells under moving loads is established to investigate their dynamic response characteristics. The first-order shear deformation theory (FSDT), combined with Hamilton’s principle, is adopted to derive the governing equations. Subsequently, the Galerkin method is used to discretize the motion equations under simply supported boundary conditions, yielding a system of ordinary differential equations. The validity of the mechanical model is validated through two comparative examples. Additionally, convergence analysis for conical shells with different semi-vertex angles is performed to verify the accuracy of the proposed method. Finally, parametric analysis of the dynamic response is conducted using the Runge–Kutta method, presenting results including the time history of midpoint deflection and the velocity history of maximum midpoint deflection.

Wave propagation plays a critical role in the performance and functionality of micro/nanoelectromechanical systems (MEMs/NEMs). These systems’ ability to accurately detect and transmit mechanical waves at the micro/nanoscale is essential for sensing, communications, and energy harvesting applications. Accordingly, this study examines the 3D wave propagation in a laminated nanoplate (LNP), including bending, shear, and longitudinal waves, using nonlocal strain gradient (NSGT) and higher-order shear deformation (HSDT) theories. The proposed nanoplate comprises a Ti6Al4V auxetic core layer between magneto-electro-elastic (MEE) surface layers comprised of the volumetric combinations of cobalt-ferrite (CoFe₂O₄) and barium-titanate (BaTiO₃) materials. Also, the temperature dependency of all LNP materials is considered. Hamilton’s principle is employed to derive the nanoplate’s motion equations, and Navier’s method is employed to assess the system’s response. The effects of several cases, such as the auxetic core’s geometric parameters, the face layer’s MEE material content, as well as thermal, electric, magnetic, and size effects, on the wave propagation response, including phase velocity and wave frequency, are analysed through analytical computations. The research findings show that the LNP’s 3D wave propagation characteristics can be modified with geometrical and material parameters, as well as external effects. Therefore, the proposed LNP structure is anticipated to protect MEMs/NEMs operating in higher frequency and temperature environments and advance intelligent sensors, offering benefits such as temperature sensitivity, lightweight design, and applicability in wearable health equipment.

This paper presents an analytical study focused on the free vibration analysis of doubly curved composite micro panels that incorporate piezoelectric layers. We derive the total potential energy of the system using a combination of the modified Sander's shell theory and the first-order shear deformation theory. Applying Hamilton's Principle leads us to establish the governing equations, resulting in five mechanical equilibrium equations and two electrical equations. In our approach, we consider panels with different boundary conditions and utilize the Chebyshev–Ritz formulation to obtain numerical results. Additionally, we explore three different distribution patterns of graphene platelets within our study. The material properties for each layer of the micro composite shell, enhanced with graphene platelets, are determined through the Halpin–Tsai model. To validate our formulation and solution, we present a comparative study. Our case studies examine how boundary conditions, material and geometrical properties, as well as the applied voltage, influence the vibration behaviors of the doubly curved composite micro panels.

Functionally graded materials (FGMs) are widely used in engineering due to their superior mechanical properties. However, their impact behavior is typically studied through numerical simulations or experimental methods, which are often time-consuming and resource-intensive. In this study, we investigate the impact response of a two-phase functionally graded plate by establishing the governing equations based on the Zener model and a modified Hertz contact law. Compared with prior studies relying on numerical or experimental techniques, this analytical approach offers a more efficient and cost-effective tool. This study is the first to extend the homotopy method—previously applied to homogeneous plates—to derive analytical solutions for functionally graded plates under impact. From the analytical solution, we derive explicit expressions for the maximum impact force, maximum impact depth, total contact time, total compression time, and the coefficient of restitution. These expressions enable us to analyze the influence of the functionally graded index, as well as the ratios of elastic modulus and density between the top and bottom surfaces of the plate during the impact process. The results quantitatively explain the superior performance of functionally graded plates and determine the optimal functionally graded index corresponding to the maximum coefficient of recovery.

To address challenges in unified matrix integration and computational complexity for arbitrary cross-sectional beams in the Absolute Nodal Coordinate Formulation (ANCF), this study introduces Monte Carlo integration into the framework of fully parameterized 3D ANCF beam elements. A unified element matrix numerical integration scheme for beams with arbitrarily shaped cross-sections is developed. Further optimizations include the separation of axial and cross-sectional integrations: Gaussian quadrature is applied along the axial direction, while a quasi-Monte Carlo method with low-discrepancy sequences is adopted for cross-sectional integration. These enhancements significantly improve both accuracy and computational efficiency. Additionally, the proposed method is extended to multi-layer cross-sectional beams, enabling the modeling of structures such as sandwich beams with fillers and composite transmission lines, where material properties vary across layers. Static and dynamic numerical validations demonstrate good relative agreement between the proposed beam models and theoretical solutions or finite-element benchmarks. Among them, the dynamic prediction accuracy of the proposed double-layer cross-section beam element reached 98.61%. Results confirm the feasibility of this unified approach for constructing ANCF beam elements with arbitrary cross-sections.

In-plane analysis of a piezoelectric layer with several embedded and edge cracks is conducted using the distributed dislocation technique. The modeling of the crack is done by employing the continuous distribution of dislocations along its surface. By applying the integral transform method, we derived the stress and electric displacement fields induced by Volterra climb and glide edge dislocations, as well as electric dislocations, in the piezoelectric strip. These fields are employed to formulate integral equations governing the behavior of a cracked piezoelectric strip under in-plane electro-mechanical loading. The singular integral equations with the well-known Cauchy-type singularity are numerically solved for the dislocation density functions by generalizing a numerical method to obtain field intensity factors at the tips of embedded and edge cracks. Several examples are analyzed to investigate the fracture behavior of a piezoelectric strip weakened by edge and embedded cracks with various orientations. The effects of crack orientation, crack location, and electromechanical loading parameters under various mixed-mode conditions are investigated on Mode I and II stress intensity factors, as well as electric displacement intensity factors, for multiple interacting embedded and edge cracks. This study presents a novel analytical solution for the simultaneous modeling of embedded and edge cracks in a piezoelectric strip under mixed-mode loading conditions, a problem not previously addressed in the literature. Furthermore, the related problem is formulated for an arbitrary straight crack, which can also be used to analyze curved cracks.

This study investigates the dynamics and control of an undamped suspended Euler–Bernoulli beam suspended from an overhead crane, to eliminate residual vibrations during rest-to-rest maneuvers. The system governing equation is discretized using the finite difference method, and modal analysis is applied to construct the modal model matrix. Modal characteristics derived from this model are used to generate transfer functions, which form the basis for implementing input shaping methods and determining the corresponding input amplitudes. Two multimode input shaping methods, Multimode Zero Vibration and Multimode Zero Vibration and Derivative, are evaluated for their effectiveness in vibration suppression and parameter uncertainty. To streamline practical implementation, fitted functions of the input amplitudes are introduced to generalize the input profiles across various operating conditions. An Effectiveness Index is also proposed to assess input performance in terms of motor stress and maneuver time. Experimental validation is conducted on a scaled overhead crane setup, with beam responses analyzed in the frequency domain. Results demonstrate that both methods effectively reduce vibration, with Multimode Zero Vibration and Derivative showing greater robustness, while Multimode Zero Vibration yields smoother motion. The study highlights the importance of vibration modes in input shaping design and robustness evaluation for controlling flexible crane systems.

This study presents a comprehensive investigation into the vibrational behavior of functionally graded graphene nanoplatelet-reinforced composite (FG-GPLRC) plates interfacing with elastic substrates of variable stiffness. Utilizing a Winkler–Pasternak model, we examine how discrete substrate stiffness zones influence dynamic responses. Temperature-dependent material properties are rigorously characterized using a combined Halpin–Tsai micromechanical model and the rule of mixtures, capturing the nuanced effects of thermal environments. The governing equations, derived from Reddy’s third-order shear deformation theory and incorporating von Kármán geometric nonlinearity, are solved using the Galerkin method. The accuracy of the proposed approach is rigorously validated through comparisons with finite element method (FEM) simulations and benchmark results from the existing literature. This study explores key phenomena, including natural frequencies, central deflection time histories, resonance, and harmonic beat effects, while systematically assessing the impacts of thermal conditions, graphene reinforcement, applied voltage, and geometric parameters. Notably, an in-depth analysis of substrate stiffness variations leads to the formulation of a novel constraint equation for elastic substrates with equivalent stiffness. These findings not only enhance the theoretical framework of FG-GPLRC plates but also provide valuable insights for advancing structural design and engineering applications.

Metal-halide perovskites are gaining significant attention as highly promising materials for next-generation solar cells and optoelectronic devices. However, their structural responses under combined optical, electrical, thermal, and mechanical fields remain insufficiently understood, hindering their practical applications. This study introduces an opto-electro-thermo-elastic model for lead halide perovskites, incorporating photostriction, photothermal effects, electrostriction, and piezoelectricity, to analyze their buckling and vibration behaviors under multi-physical interactions. The governing equations for perovskite plates are formulated based on third-order shear deformation theory and solved analytically using the Navier method. Extensive parametric studies explore the effects of multi-physical fields on key performance metrics, including critical light intensity, critical electric field, critical temperature, and free vibration. The results demonstrate that light exposure, photo-induced heating, and external electric fields significantly influence natural frequencies, and bifurcation buckling. These factors must be carefully considered in the design of perovskite-based optoelectronic systems to optimize performance and reliability.