Acta Mechanica最新文献

For the first time, the issue of the consequences of an earthquake on the state of the fractured environment of mountainous regions is investigated using a rigorous mechanical and mathematical approach. It is known that Earthquakes in mountainous areas are characterized by the repetition of high-magnitude aftershocks compared to the cases of lowland earthquakes. For this purpose, in order to approach reality, for the first time, a dynamic mixed problem on the unsteady impact on the shores of the semi-infinite Griffiths crack, as one of the objects of the mountain environment, is considered. It is assumed that the crack is located in a half-space parallel to its boundary. It is assumed that the fractured rock environment is an anisotropic composite and is described by the corresponding equations. The mechanical effects on the crack banks are described by a function that continuously depends on the time parameter and the geometric parameters of the coordinate system, which makes it possible to take into account the real non-stationary effect on the crack caused by an earthquake. It is assumed that the impact is carried out over a semi-infinite time interval, starting from zero initial conditions. The problem under consideration is related not only to the problem of seismic processes occurring in the Earth's crust of complex structure, including mountainous territories, but also to the engineering practice of composite materials of anisotropic structure. The case of a three-dimensional problem in which geometric and temporal parameters are equally included is studied. The mixed problem is reduced to the two-dimensional Wiener–Hopf integral equation, for which the authors have recently developed a rigorous mathematical method. The obtained solution, depending on the geometric and temporal parameters, made it possible to identify a previously undescribed surge effect at the initial moment of the stress intensity coefficient at the crack tip. It is established that the time-dependent stress intensity coefficient at the crack tip as a result of unsteady action can grow indefinitely at the initial moment, destroying the crack. The result explains the appearance of aftershocks after the main earthquake, as a result of its impact on existing cracks in the environment. Such a phenomenon in seismology as a swarm of earthquakes, consisting in the occurrence of more than ten small earthquakes within one hour, is also explained by the result obtained in the article.

Instability analysis is very important for the service safety of functionally graded materials (FGM) sandwich structures. However, there is a great difficulty in identifying the critical points by the existing numerical or analytical methods due to the multiple solutions of nonlinear responses of structures in complex loading conditions. This paper aims to present an analytical method for instability response of FGM sandwich beams in thermo-mechanical loads without a priori assumption of response mode and instability type. Firstly, an analytical method of Emam and Nayfeh is extended to obtain approximate analytic solutions for bending, buckling and snap-through responses of FGM sandwich beams under the framework of strictly satisfying the governing equations and boundary conditions. Secondly, the influence of carbon nanotube (CNT) material component and distribution on the instability condition, type of sandwich beams with functionally graded-CNT reinforced (FG-CNTRC) panels are thoroughly discussed by the bifurcation diagram. In addition, the post-buckling paths of FGM sandwich beams are analytically searched out by the free energy evaluation. The results indicate that the symmetry is broken by the introduction of transverse mechanical load, and this variation makes thermal buckling behavior shift easily from rare bifurcation instability to widespread snap-through instability. By carefully controlling the loading and material parameters, the energy consumption of the deformation jumps can be adjusted, thereby enhancing the resistance to snap-through instability.

Flow structures have been experimentally obtained for the circular cylinders with porous media coatings (PMC) at Reynolds number values from Re = 5000 to Re = 10,000. Furthermore, flow characteristics have been exhibited for different contour graphics and the velocity profiles have been indicated at four downstream stations. The regions having minimum streamwise velocity component values approached the circular cylinders by increasing Reynolds numbers. Nevertheless, it is not valid for the cases of PMC1 and PMC2 from Re = 7500 to Re = 10,000. Because of the separated flows from the upper and lower cylinder surfaces, the maximum streamwise velocity components have been attained. The same effect has been observed for the cross-stream velocity component values, and these clusters approached the circular cylinders. As expected, the flow separations caused wake fluctuations. Nonetheless, the cluster sizes have also been decreased by the decrement of Reynolds numbers. It is significant for the occurrence of turbulence intensity in the wake regions of the circular cylinders. However, there is no obvious difference between the bare cylinder and the PMC3 in terms of flow patterns. Another important result is that the coating effect is explicitly exhibited by the increase in Reynolds numbers. As explained by the velocity values, these zones moved away from the bodies due to the decrement of Reynolds numbers. As a parameter, Reynolds number is considerably dominant on the cluster positions. Similar patterns have been approximately observed for PMC1, PMC2 and PMC4 in terms of Reynolds stress correlations.

This study introduces a simulated method for detecting matrix cracking and assessing its density in cross-ply laminated composites by using guided Lamb wave propagation and surface-mounted fiber Bragg grating (FBG) sensors. A cross-ply laminated composite with a [0₂/90₆]_s lay-up under antisymmetric guided Lamb wave propagation was simulated using the finite element method. The Lamb wave-induced strain field was obtained along a specified path in the FE models of both intact and damaged composites with matrix cracks. This strain field served as input for the models developed in the FBG-SiMul software, where the time response diagrams of the reflected spectrum from surface-mounted FBG sensors were analyzed. The spectrum parameters, including the oscillation amplitude of the wavelength shift, the mean peak width variation, and the oscillation amplitude of the peak width variation, increased by up to 1000% at an excitation frequency of 200 kHz in the damaged specimen compared to the intact one. The proposed simulated method, combining Lamb wave propagation and FBG sensors, effectively detects matrix cracking damage and assesses its density in laminated composites.

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.