Applied Mathematical Modelling最新文献

The internal structure of shock waves is well known for shocks with a Prandtl number of the order of unity, but it is still poorly understood for shocks with extremely large and small Prandtl numbers, and the latter case is of particular interest given the non-existence of smooth solutions for strong inviscid shocks. The literature has suggested unequal contributions of viscosity and heat conduction to shock compression, specifically that viscosity is of more significance, but the observations therein do not provide further insight into the exact role of viscosity in shock waves, i.e., how viscosity affects the shock structure such that a smooth transition is maintained. To elucidate it, this research numerically investigates the internal structure of shock waves, with emphasis on the asymptotic behavior and features of shock profiles in the inviscid (zero-Prandtl-number) limit. The asymptotic analysis demonstrates a curious fact: the distinction between strong shock solutions with positive and zero Prandtl numbers does not vanish as the former's Prandtl number tends to zero. The only way to avoid this gap is to allow the emergence of an unphysical discontinuity (e.g., an isothermal jump) in inviscid solutions, which clearly indicates the essentiality of viscosity. For a better understanding of the underlying mechanisms, features of small-Prandtl-number shocks are further studied and compared with those of ordinary shocks. The result shows a peak in viscous local entropy generation rates within small-Prandtl-number shocks, and reducing the viscosity paradoxically makes it higher. Through this peak, the effect of lowered viscosity is neutralized, and the isothermal jump is smoothed, hence the critical role of viscosity in shock transition.

For achieving high-performance control of hydraulic actuator systems, an adaptive sliding mode control with disturbance estimation algorithm is proposed and successfully applied to the hydraulic actuator systems of rock drilling jumbo. A switching extended state observer for hydraulic actuator systems is proposed, which combines the advantages of the linear extended state observer and the nonlinear extended state observer to estimate system disturbances more efficiently. The designed parameter adaptive law provides adaptivity to the system parameters, while the disturbance estimation algorithm can online estimate the unknown disturbances, such integration can enhance the adaptability and robustness of the sliding mode control algorithm. Rigorous simulation tests and practical application experiments are conducted to evaluate the performance of the proposed controller. The reliability of the designed parameter adaptive law and switching extended state observer is validated in detail in simulation studies. In the application experiments of rock drill jumbo, the results indicate the proposed controller is superior to sliding mode control with disturbance estimation and PID control. The average error of the developed controller is reduced by 58 %, 54 %, and 56 % compared to the sliding mode control with disturbance estimation controller, and 82 %, 78 %, and 79 % compared to the PID controller in tracking the low-frequency, high-frequency, and superimposed sinusoidal signals, respectively. Moreover, both the convergence of the uncertain parameters and the estimation of the unknown disturbances in the experiments are satisfactory. These experimental results adequately demonstrate the practical application value of the proposed controller.

This study investigates the effect of coupling configuration on a state-of-the-art harvesting system consisting of a series of spring-coupled piezoelectric nonlinear monostable tip-loaded cantilever-based vibration energy harvesters (VEHs). The investigation finds favorable coupling configurations that exploit complex nonlinear interaction for improving system performance. The system model incorporates the beam's geometric nonlinearities in the governing equation using inertial and stiffness nonlinear terms. The study first analytically investigates the effect of grounding stiffness on a single harvester's performance. Then, it numerically investigates the effect of increasing array size and changing stiffness distribution. The study discovers a novel hardening/softening transition phenomenon at a critical grounding stiffness value induced by the inertial nonlinear effect. This critical event also maximizes peak output power near the largest eigenfrequency at an optimum grounding stiffness value. At larger arrays, the peak power shows a complex bifurcation behavior, hinting at the presence of multiple attractors. The numerical study of different stiffness configurations and linearized eigenanalysis reveals the necessity of a multilevel optimization strategy focused on both the stiffness ratio between the coupling springs' and their overall stiffness level. This study bridges the gap between previous studies on spring-coupled linear and bistable arrays, offering new insights into coupled nonlinear interactions and proposing novel optimization strategies.

This paper presents a numerical model for addressing thermo-mechanical coupling problems in topology optimization, utilizing the element-free Galerkin (EFG) method. A multi-parameter density-based topology optimization framework is introduced to interpolate the thermal stress coefficient, encompassing thermal conductivity, thermal expansion coefficient, and elastic modulus. Two numerical examples are provided to investigate the model's characteristics and associated considerations, including the impact of EFG node distribution, quantity, calculation points layout, design variables, and filtering techniques on optimized results. Numerical findings indicates that the present model allows for adaptable adjustments in nodes number and distribution, calculation points layout, choice of design variables, and application of various filtering techniques while maintaining consistent background grids. Although these adjustments may affect convergence rates and final objective values, they can promise satisfactory optimization structures. Additionally, the study highlights the critical influence of filtering radius on optimization outcomes and the objective value, recommending a value of approximately 16∼20 calculation points.

The integration of topology optimization and additive manufacturing (AM) is seen as a pivotal approach for creating products with high added value. Nevertheless, the inherent layer-by-layer fabrication process of AM and the widespread manufacturing errors lead to both anisotropy and uncertainty in the printed parts, which poses challenges to constructing material models and optimization strategies. To address these issues, this paper presents a robust topology optimization (RTO) approach coupled with an anisotropic material model and a hybrid interval random model for additively manufactured structures. The method utilizes the bi-directional evolutionary structural optimization (BESO) framework and defines the uncertain material parameters with anisotropic mechanical behavior. An efficient hybrid uncertainty perturbation analysis (HUPA) method is then proposed for estimating the robust objective function, and the sensitivity values of the design variables are further derived. Several 2D and 3D numerical examples are given to verify the effectiveness of the proposed method. The results show that both the material off-angle and the material properties fluctuation exert significant influences on the structural performance, indicating the necessity of considering both anisotropy and uncertainty caused by the AM process in engineering structural optimization.

Spacecrafts usually suffer from the thermal shock during operation, leading to large control error or even failure. At the same time, spacecrafts are often rigid-flexible coupled multibody systems with large degrees of freedom and multiple varying parameters. The real-time control and condition monitoring require effective order reduction methods. In this investigation, the displacement and temperature fields are discretized by the Absolute Node Coordinate Formulation (ANCF) to achieve unified description. The coupled thermal-dynamic reduced-order model (ROM) is established based on the Proper Orthogonal Decomposition (POD) method. For the purpose of further increase efficiency, a linearization method is introduced so that the calculation times of the elastic force can be significantly reduced. In order to predict the response of the thermal-dynamic coupled system with multiple varying parameters, the interpolation on Grassmann manifold is introduced to maintain the orthogonality of the basis. As verification and validation, three numerical examples are presented to show the feasibility and efficacy of the proposed method.

Accurately determining the electric field and capacitance in multilayer-structured interdigital electrode capacitor (IDC) transducers is an important prerequisite for designing the structure, estimating properties, and optimizing performance. In this paper, a semi-analytical model of the electric field and capacitance in a multilayered IDC is introduced utilizing the method of separation of variables. The general solutions for the field and capacitance, considering arbitrary numbers and permittivities of the dielectric layers, are analytically expanded in infinite series form, while these physical quantities cannot be accurately obtained by the traditional analytical model that employs the conformal mapping technique and the partial capacitance technique with boundary condition approximations at the dielectric interface. The proposed model with the recommended number of expanded terms successfully generates precise electric field images and capacitance values agreeing well with simulated data, even when there is a significant difference in the permittivity of adjacent layers. Moreover, based on the model, it can be concluded that the sensing range, referred to as the penetration depth, of a three-layer-structured IDC sensor, peaks at the optimal metallization ratio of η=0.5 regardless of the permittivity and the number of electrodes. Experimental results demonstrate that the proposed model yields outstanding capacitance outcomes across different metallization ratios and various upper layers. This showcases the model's potential for designing and optimizing an IDC transducer for precise sensitive detection.

The coupling effects between the plane motion and the flexible vibration of the completely free plate bring a great challenge of the dynamic analysis on which. In this paper, the single variable simple plate theory is employed to establish the dynamic model of the completely free weightless thick plate describing the dynamic problem of some spatial plate-type structures in the geostationary orbit. Then, a 49-point multi-symplectic scheme is constructed to solve the proposed dynamic model in the symmetric form. Considering the initial conditions associated with the first six modes, the transverse displacements of the numbered nodes on the plate with different thickness ratios are presented respectively employing the 49-point multi-symplectic scheme, from which, the effect of the thickness ratio on the natural vibrational frequency of the plate is reproduced. From the numerical results of the transverse displacements, it can be found that, the existence as well as the distribution characteristics of the straight line of zero displacement in the initial conditions codetermine the motion pattern of the plate, which reveals the key role of the straight line of zero displacement in the rigid-flexible coupling dynamic behaviors (coupling behaviors between the translation, rotation and vibration) of the plate. To verify the validity and the precision of the numerical results reported in this work, the relative errors between the obtained dimensionless natural frequency with the reported dimensionless natural frequency in current documents are given. The main contributions of this work include that, the applicability of the single variable simple plate theory for the describing of the coupling dynamic problem of the completely free weightless thick plate is illustrated and the high-precision of the multi-symplectic method employed is verified, which provide an effective modeling method and an effective simulation approach for the vibration problem of the completely free weightless thick plate.

This paper proposes an analytical method to investigate the out-of-plane vibration of thin-walled curved beams under a moving mass. This method comprehensively considers the warping stiffness, shear deformation, and rotatory inertia, as well as the inertia force caused by moving mass and damping. The Fourier sine integral transform and Laplace-Carson integral transform are used to decouple the system of equations for out-of-plane vibration of the thin-walled curved beam under a moving mass. Two dynamic response expressions in two directions involving vertical and torsional responses are easily obtained after using their inverse transforms. Numerical results demonstrate a strong agreement between the outcomes obtained from the proposed expressions and those obtained using numerical methods in existing literature. Furthermore, the effects of variables such as slenderness ratio, the center angle, velocity of the moving mass and eccentricity on the dynamic response of the thin-walled curved beam are discussed. For beams with small cross-sectional shear correction factor k and slenderness ratio, ignoring the shear deformation, rotatory inertia, and warping stiffness of the beam can cause obvious errors for the natural frequency of the beam. Moreover, when the speed and mass of the moving load are large, it is necessary to consider the inertial force caused by the mass for studying the out-of-plane vibration of the thin-walled curved beam. The influence of shear deformation is less affected by the velocity and mass velocity of moving loads, and primarily depends on the structural characteristics of the curved beam itself. For beams of the same length, shear deformation becomes more pronounced with increasing radius of curvature.

Magnetic nanoparticles have the potential to be used in various biomedical applications, including magnetic drug targeting and hyperthermia for cancer treatment. In both cases, precise prediction of the local particle concentration is required to plan a successful therapy, which is a challenging task due to several complex flow phenomena. Computational macroscopic and microscopic models have been developed to support this process, but they have limitations in terms of interactions implementation, micromagnetic dynamics or computational costs. This study aims to develop a model that can represent micromagnetic dynamics and being employed to study equilibrium properties of particle ensembles in viscous media. Therefore, a kinetic Monte Carlo method in combination with Langevin equations is used. So, magnetization dynamics and mechanical motion can be simulated in combination very efficiently. The new model is validated with another model based on the stochastic Landau-Lifshitz-Gilbert equation. Various interaction potentials like Van der Waals, steric and electrostatic interactions are included to study their specific influence on structural properties. Also, methods to control the errors while integrating the equations of motion and using the Ewald method for calculating interaction quantities are implemented. As a validation we studied equilibrium and time dependent properties of non-interacting particle ensembles as well as errors made by the Ewald-method used for interaction quantities calculation. In all studies we found very good agreement of the simulation results with the theoretical predictions. The developed models can now be used for investigating equilibrium and dynamic properties of ferrofluids, or more general for biomedical research for magnetic drug targeting, hyperthermia, or imaging techniques. Furthermore, the new hybrid model can be also used for simulations in the range of milliseconds with reasonable computational effort.