Acta Mechanica Sinica最新文献

Numerical simulation is dominant in solving partial differential equations (PDEs), but balancing fine-grained grids with low computational costs is challenging. Recently, solving PDEs with neural networks (NNs) has gained interest, yet cost-effectiveness and high accuracy remain a challenge. This work introduces a novel paradigm for solving PDEs, called multi-scale neural computing (MSNC), considering spectral bias of NNs and local approximation properties in the finite difference method (FDM). The MSNC decomposes the solution with a NN for efficient capture of global scale and the FDM for detailed description of local scale, aiming to balance costs and accuracy. Demonstrated advantages include higher accuracy (10 times for 1D PDEs, 20 times for 2D PDEs) and lower costs (4 times for 1D PDEs, 16 times for 2D PDEs) than the standard FDM. The MSNC also exhibits stable convergence and rigorous boundary condition satisfaction, showcasing the potential for hybrid of NN and numerical method.

Legendre polynomial method is well-known in modeling acoustic wave characteristics. This method uses for the mechanical displacements a single polynomial expansion over the entire sandwich layers. This results in a limitation in the accuracy of the field profile restitution. Thus, it can deal with the guided waves in layered sandwich only when the material properties of adjacent layers do not change significantly. Despite the great efforts regarding this issue in the literature, there remain open questions. One of them is: “what is the exact threshold of contrasting material properties of adjacent layers for which this polynomial method cannot correctly restitute the roots of guided waves?” We investigated this numerical issue using the calculated guided phase velocities in 0°/φ/0°-carbon fibre reinforced plastics (CFRP) sandwich plates with gradually increasing angle φ. Then, we approached this numerical problem by varying the middle layer thickness h_90° for the 0°/90°/0°-CFRP sandwich structure, and we proposed an exact thickness threshold of the middle layer for the Legendre polynomial method limitations. We showed that the polynomial method fails to calculate the quasi-symmetric Lamb mode in 0°/φ/0°-CFRP when φ > 25°. Moreover, we introduced a new Lamb mode so-called minimum-group-velocity that has never been addressed in literature.

Engineering tests can yield inaccurate data due to instrument errors, human factors, and environmental interference, introducing uncertainty in numerical model updating. This study employs the probability-box (p-box) method for representing observational uncertainty and develops a two-step approximate Bayesian computation (ABC) framework using time-series data. Within the ABC framework, Euclidean and Bhattacharyya distances are employed as uncertainty quantification metrics to delineate approximate likelihood functions in the initial and subsequent steps, respectively. A novel variational Bayesian Monte Carlo method is introduced to efficiently apply the ABC framework amidst observational uncertainty, resulting in rapid convergence and accurate parameter estimation with minimal iterations. The efficacy of the proposed updating strategy is validated by its application to a shear frame model excited by seismic wave and an aviation pump force sensor for thermal output analysis. The results affirm the efficiency, robustness, and practical applicability of the proposed method.

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.

During the re-entry of a hypersonic aircraft into the earth’s atmosphere, the surrounding air experiences dissociation, ionization, and other complex chemical phenomena due to extreme temperature by shock wave. To ensure thermal safety, the thermochemical non-equilibrium effects resulting from real-gas behavior should be taken into account. In this paper, the characteristics of a double-cone hypersonic laminar flow, including distributions of wall pressure, heat flux, and species dissociation are numerically analyzed with incoming enthalpy of 9.65–21.77 MJ/kg. The thermochemical non-equilibrium flow at different enthalpy and wall temperatures is performed with two-temperature model and Park’s seven chemical reaction model. It is found that the double-cone flow features complex shock-shock interactions to form triple points. The flow topology is further brought out from the analysis of streamlines. At the lowest incoming enthalpy with isothermal wall conditions, two foci points appear. While others highlight only one focal point. As the increment of incoming enthalpy, the heat flux and dissociation of nitrogen and oxygen also increase. An increasing wall temperature leads to a larger separation bubble and a lower value of heat flux and pressure peak, while massive dissociation occurs without obvious ionization under considered cases.

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.

In this study, the sliding friction contact problems associated with the indentation of an elastic half-plane by rigid cylindrical and flat punches were investigated within the context of the micropolar theory. The micropolar theory of elasticity introduces the characteristic material length and the dimensionless coupling number to describe the size effect. Coulomb’s friction law is satisfied by a punch when it is subjected to both normal and tangential forces. Using the Fourier integral transformation technique, these mixed-boundary value problems were reduced to singular integral equations of the second kind in which the unknown quantity is the contact stress on the contact surface. The collocation method was utilized to solve the integral equations numerically. An extensive parametric study was conducted to investigate the effects of the friction coefficient, the characteristic material length, and the dimensionless coupling number on the normal and in-plane stresses. The results show that the contact stress predicted by the micropolar theory differs significantly from those predicted by the couple stress theory and the classical elasticity theory.

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.