Acta Mechanica Sinica最新文献

The challenge of solving nonlinear problems in multi-connected domains with high accuracy has garnered significant interest. In this paper, we propose a unified wavelet solution method for accurately solving nonlinear boundary value problems on a two-dimensional (2D) arbitrary multi-connected domain. We apply this method to solve large deflection bending problems of complex plates with holes. Our solution method simplifies the treatment of the 2D multi-connected domain by utilizing a natural discretization approach that divides it into a series of one-dimensional (1D) intervals. This approach establishes a fundamental relationship between the highest-order derivative in the governing equation of the problem and the remaining lower-order derivatives. By combining a wavelet high accuracy integral approximation format on 1D intervals, where the convergence order remains constant regardless of the number of integration folds, with the collocation method, we obtain a system of algebraic equations that only includes discrete point values of the highest order derivative. In this process, the boundary conditions are automatically replaced using integration constants, eliminating the need for additional processing. Error estimation and numerical results demonstrate that the accuracy of this method is unaffected by the degree of nonlinearity of the equations. When solving the bending problem of multi-perforated complex-shaped plates under consideration, it is evident that directly using higher-order derivatives as unknown functions significantly improves the accuracy of stress calculation, even when the stress exhibits large gradient variations. Moreover, compared to the finite element method, the wavelet method requires significantly fewer nodes to achieve the same level of accuracy. Ultimately, the method achieves a sixth-order accuracy and resembles the treatment of one-dimensional problems during the solution process, effectively avoiding the need for the complex 2D meshing process typically required by conventional methods when solving problems with multi-connected domains.

Quasi-zero stiffness (QZS) isolators have received considerable attention over the past years due to their outstanding vibration isolation performance in low-frequency bands. However, traditional mechanisms for achieving QZS suffer from low stiffness regions and significant nonlinear restoring forces with hardening characteristics, often struggling to withstand excitations with high amplitude. This paper presents a novel QZS vibration isolator that utilizes a more compact spring-rod mechanism (SRM) to provide primary negative stiffness. The nonlinearity of SRM is adjustable via altering the raceway of its spring-rod end, along with the compensatory force provided by the cam-roller mechanism so as to avoid complex nonlinear behaviors. The absolute zero stiffness can be achieved by a well-designed raceway curve with a concise mathematical expression. The nonlinear stiffness with softening properties can also be achieved by parameter adjustment. The study begins with the force-displacement relationship of the integrated mechanism first, followed by the design theory of the cam profile. The dynamic response and absolute displacement transmissibility of the isolation system are obtained based on the harmonic balance method. The experimental results show that the proposed vibration isolator maintains relatively low-dynamic stiffness even under non-ideal conditions, and exhibits enhanced vibration isolation performance compared to the corresponding linear isolator.

Large-grain REBa₂Cu₃O_7−δ (REBCO, RE = rare earth) bulk superconductors offer promising magnetic field trapping capabilities due to their high critical current density, making them ideal for many important applications such as trapped field magnets. However, for such large-grain superconductor bulks, there are lots of voids and cracks forming during the process of melting preparation, and some of them can be up to hundreds of microns or even millimeters in size. Consequently, these larger size voids/cracks pose a great threat to the strength of the bulks due to the inherent brittleness of superconductor REBCO materials. In order to ensure the operational safety of related superconducting devices with bulk superconductors, it is firstly important to accurately detect these voids/cracks in them. In this paper, we proposed a method for quantitatively evaluating multiple voids/cracks in bulk superconductors through the magnetic field and displacement response signals at superconductor bulk surface. The proposed method utilizes a damage index constructed from the magnetic field signals and displacement responses to identify the number and preliminary location of multiple defects. By dividing the detection area into subdomains and combining the magnetic field signals with displacement responses within each subdomain, a particle swarm algorithm was employed to evaluate the location and size parameters of the defects. In contrast to other evaluation methods using only magnetic field or displacement response signals, the combined evaluation method using both signals can identify the number of cracks effectively. Numerical studies demonstrate that the morphology of voids and cracks reconstructed using the proposed algorithm ideally matches real defects and is applicable to cases where voids and cracks coexist. This study provides a theoretical basis for the quantitative detection of voids/cracks in bulk superconductors.

The thermochemical non-equilibrium phenomena encountered by hypersonic vehicles present significant challenges in their design. To investigate the thermochemical reaction flow behind shock waves, the non-equilibrium radiation in the visible range using a shock tube was studied. Experiments were conducted with a shock velocity of 4.7 km/s, using nitrogen at a pressure of 20 Pa. To address measurement difficulties associated with weak radiation, a special square section shock tube with a side length of 380 mm was utilized. A high-speed camera characterized the shock wave’s morphology, and a spectrograph and a monochromator captured the radiation. The spectra were analyzed, and the numerical spectra were compared with experimental results, showing a close match. Temperature changes behind the shock wave were obtained and compared with numerical predictions. The findings indicate that the vibrational temperatures are overestimated, while the vibrational relaxation time is likely underestimated, due to the oversimplified portrayals of the non-equilibrium relaxation process in the models. Additionally, both experimental and simulated time-resolved profiles of radiation intensity at specific wavelengths were analyzed. The gathered data aims to enhance computational fluid dynamics codes and radiation models, improving their predictive accuracy.

A new model of periodic structure is proposed and analyzed. This structure is composed of an inner fluid-conveying pipe with periodic material arrangement carrying periodic arrays of outer cantilever pipes. The generalized differential quadrature rule (GDQR) method combined with the Bloch theorem is used to calculate the vibration band gaps of the structure. Results are verified by the forced vibration responses obtained using the GDQR method. Results indicate that the first two band gaps of the fluid-conveying pipe with periodic material arrangement can get close to each other and move to low frequency regions by changing the length of cantilever pipes. For high fluid velocity values in which the first band gap starts from zero frequency, since the second band is very close to the first band, this periodic structure can be used for vibration reduction over a wide band gap starting from zero frequency. Based on these results, it can be concluded that instead of increasing the total size of the periodic structure, these periodic arrays of cantilever pipes can be implemented to create a wide ultra-low-frequency band gap. Finally, verification of the GDQR method shows that it can be used as a precise numerical method for vibration analysis of the structures such as fluid-conveying pipes and moving belts.

The high-speed reentry vehicle operates across a broad range of speeds and spatial domains, where optimal aerodynamic shapes for different speeds are contradictory. This makes it challenging for a single-Mach optimization design to meet aerodynamic performance requirements throughout the vehicle’s flight envelope. Additionally, the strong coupling between aerodynamics and control adds complexity, as fluctuations in aerodynamic parameters due to speed variations complicate control system design. To address these challenges, this study proposes an aerodynamic/control coupling optimization design approach. This method, based on aerodynamic optimization principles, incorporates active control technology, treating aerodynamic layout and control system design as primary components during the conceptual design phase. By integrating the design and evaluation of aerodynamics and control, the approach aims to reduce design iterations and enhance overall flight performance. The comprehensive design of the rotary reentry vehicle, using this optimization strategy, effectively balances performance at supersonic and hypersonic speeds. The results show that the integrated design model meets aerodynamic and control performance requirements over a broader range of Mach numbers, preventing performance degradation due to deviations from the design Mach number, and providing a practical solution for high-speed reentry vehicle design.

Parameterized level-set method (PLSM) has been proposed and developed for many years, and is renowned for its efficacy in addressing topology optimization challenges associated with intricate boundaries and nucleation of new holes. However, most pertinent investigations in the field rely predominantly on fixed background mesh, which is never remeshed. Consequently, the mesh element partitioned by material interface during the optimization process necessitates approximation by using artificial interpolation models to obtain its element stiffness or other properties. This paper introduces a novel approach to topology optimization by integrating the PLSM with body-fitted adaptive mesh and Helmholtz-type filter. Primarily, combining the PLSM with body-fitted adaptive mesh enables the regeneration of mesh based on the zero level-set interface. This not only precludes the direct traversal of the material interface through the mesh element during the topology optimization process, but also improves the accuracy of calculation. Additionally, the incorporation of a Helmholtz-type partial differential equation filter, relying solely on mesh information essential for finite element discretization, serves to regulate the topological complexity and the minimum feature size of the optimized structure. Leveraging these advantages, the topology optimization program demonstrates its versatility by successfully addressing various design problems, encompassing the minimum mean compliance problem and minimum energy dissipation problem. Ultimately, the result of numerical example indicates that the optimized structure exhibits a distinct and smooth boundary, affirming the effective control over both topological complexity and the minimum feature size of the optimized structure.

Although machine Learning has demonstrated exceptional applicability in thermographic inspection, precise defect reconstruction is still challenging, especially for complex defect profiles with limited defect sample diversity. Thus, this paper proposes a self-enhancement defect reconstruction technique based on cycle-consistent generative adversarial network (Cycle-GAN) that accurately characterises complex defect profiles and generates reliable artificial thermal images for dataset augmentation, enhancing defect characterisation. By using a synthetic dataset from simulation and experiments, the network overcomes the limited samples problem by learning the diversity of complex defects from finite element modelling and obtaining the thermography uncertainty patterns from practical experiments. Then, an iterative strategy with a self-enhancement capability optimises the characterisation accuracy and data generation performance. The designed loss function structure with cycle consistency and identity loss constrains the GAN’s transfer variation to guarantee augmented data quality and defect reconstruction accuracy simultaneously, while the self-enhancement results significantly improve accuracy in thermal images and defect profile reconstruction. The experimental results demonstrate the feasibility of the proposed method by attaining high accuracy with optimal loss norm for defect profile reconstruction with a Recall score over 0.92. The scalability investigation of different materials and defect types is also discussed, highlighting its capability for diverse thermography quantification and automated inspection scenarios.

The main goal of this paper is to present the free vibration and buckling of viscoelastic functionally graded porous (FGP) nanosheet based on nonlocal strain gradient (NSGT) and surface elasticity theories. The nanosheets are placed on a visco-Pasternak medium in a hygro-temperature environment with nonlinear rules. The viscoelastic material characteristics of nanosheets are based on Kelvin’s model. The unique point of this study is to consider the change of nonlocal and length-scale coefficients according to thickness, similar to the laws of the material properties. The Galerkin approach based on the Kirchhoff-love plate theory is applied to determine the natural frequency and critical buckling load of the viscoelastic FGP nanosheet with various boundary conditions. The accuracy of the proposed method is verified through reliable publications. The outcome of this study highlights the significant effects of the nonlocal and length-scale parameters on the vibration and buckling behaviors of viscoelastic FGP nanosheets.

This paper proposes a new step-by-step Chebyshev space-time spectral method to analyze the force vibration of functionally graded material structures. Although traditional space-time spectral methods can reduce the accuracy mismatch between temporal low-order finite difference and spatial high-order discretization, their time collocation points must increase dramatically to solve highly oscillatory solutions of structural vibration, which results in a surge in computing time and a decrease in accuracy. To address this problem, we introduced the step-by-step idea in the space-time spectral method. The Chebyshev polynomials and Lagrange’s equation were applied to derive discrete spatial governing equations, and a matrix projection method was used to map the calculation results of previous steps as the initial conditions of the subsequent steps. A series of numerical experiments were carried out. The results of the proposed method were compared with those obtained by traditional space-time spectral methods, which showed that higher accuracy could be achieved in a shorter computation time than the latter in highly oscillatory cases.