Applied Mathematical Modelling最新文献

The rigid-flexible coupled spacecraft, composed of flexible solar panels and a multilink manipulator, has gained prominence in on-orbit servicing due to rapid advancements in space technology. However, the intricate effects of rigid-flexible coupling pose significant challenges for dynamic modeling, trajectory planning, and control. This paper aims to develop general dynamic approaches for modeling and trajectory planning in such spacecraft, considering large deformations. The main distinguishing feature is the use of the referenced nodal coordinate formulation to accurately describe the large-deformed solar panels rather than directly treating them as disturbance for the free-floating system. Additionally, the common recursive model for the multilink manipulator is integrated into the same framework. The modal reduction method with modal derivatives techniques is employed to address geometric nonlinearity resulting from large deformations. Polynomial trajectory parameters with different performance characteristics are obtained by defining various optimization objectives. The coupling analysis is conducted based on an accurate reduced-order dynamic model, the results of which can be used for designing manipulator tasks. Coupling values are defined as the objective for trajectory optimization, offering advantages such as insensitivity to dynamic model accuracy and a fast optimization process. After validating the accuracy of the proposed dynamic model through simulations, the performances of different optimized trajectories are demonstrated using numerical examples.

With the purpose of planning and implementing pricing decisions on a tactical level as well as production decisions on an operational level, we consider – in an integrated form – the capacitated multi-item lot sizing problem with uncertain item demands and price-dependent discrete choice demand. The model is embedded into an overarching rolling horizon procedure allowing for adaptations to changes in demand and cost parameters. We first formulate the static problem version as a nonlinear mathematical program with underlying multinomial logit demand and subsequently linearize it to make it viable for mathematical programming solvers. Uncertainty of demands is taken into account by Monte Carlo simulation. More specifically, we generate random demand scenarios and utilize them as input data for the sample average approximation problem version. We further endow the problem setting with possibilities to incorporate pricing policy requirements such as restricting the number of price adaptations or defining periods without price adaptations. Overall, the developed approach yields a powerful tool for balancing item demands via pricing in a way favorable for adhering to available production capacities and thereby striking a balance between revenues and costs. Computational results confirm that adapting prices to time-dependent demand and cost parameters is exploited effectively to maintain a deliberately controlled production environment. Moreover, the integrated pricing and production setting allows to study the effect of pricing policy restrictions and demand uncertainties upon attainable profits.

In many statistical modeling problems, such as classification and regression, it is common to encounter sparse and blocky coefficients. Sparse fused Lasso is specifically designed to recover these sparse and blocky structured features, especially in cases where the design matrix has ultrahigh dimensions, meaning that the number of features significantly surpasses the number of samples. Quantile loss is a well-known robust loss function that is widely used in statistical modeling. In this paper, we propose a new sparse fused lasso classification model, and develop a unified multi-block linearized alternating direction method of multipliers algorithm that effectively selects sparse and blocky features for regression and classification models. Our algorithm has been proven to converge with a derived linear convergence rate. Additionally, our algorithm has a significant advantage over existing algorithms for solving ultrahigh dimensional sparse fused Lasso regression and classification models due to its lower time complexity. Note that the algorithm can be easily extended to solve various existing fused Lasso models. Finally, we present numerical results for several synthetic and real-world examples, which demonstrate the robustness, scalability, and accuracy of the proposed classification model and algorithm.

Flexoelectric nano-ultrasonic transducer is an important development direction of ultra-high frequency ultrasonic transducers. The key to its development lies in addressing the electromechanical coupling dynamics of a flexoelectric nano-element, that is, sandwich circular nano-plate. In this paper, a novel dynamic theoretical model of sandwich circular nano-plate is developed based on the transversely isotropic flexoelectricity couple stress and Kirchhoff plate theories. Based on the novel model, this study demonstrates the influence of flexoelectricity effect and size effect on its electromechanical responses of the core component in the nano-ultrasonic transducer. Simultaneously, using finite element software, the paper presents the first six mode shapes of the structure and reveals the mode shape most conducive to the energy conversion of the transducer. The main objective of this study is to provide a theoretical foundation for the development of nano-ultrasonic transducers based on flexoelectric materials. The novel model can also be applied in various energy conversion devices, including flexoelectric actuator and flexoelectric energy harvesters.

In this paper, we investigate the axisymmetric Hertzian contact problem at micro-/nanoscale. The deformation of material bulk is described by a simplified theory of strain gradient elasticity, and the influence of surface tension is integrated based on the surface elasticity theory. Using the Mindlin's potential function method and double Fourier integral transform, the normal surface displacement induced by a concentrated force is derived in a closed form. Following this, the contact between a rigid sphere and an elastic half-space is formulated in terms of singular integral equation, which is numerically solved by applying the Gauss-Chebyshev method. The results indicate that the distribution of contact pressure is distinctly different from that in classical elasticity theory. The indented substrate tends to perform stiffer due to the effects of surface tension and strain gradient elasticity. When the contact radius is comparable with the material length parameter, the indentation force (depth) can be ten (three) times of that given by classical Hertz theory.

A Slow Sand Filter (SSF) consists of biofilm attached to saturated packed sand with supernatant water on top, through which water flows by gravity. SSFs are used in the production of drinking water to improve water quality and remove pathogens, and, as they use biological filtration via the microbes present in the biofilm, they are simple and cheap to construct. A drawback of SSFs is that the difficult sampling and the complex dynamics associated with biofilm growth of microbes pose an obstacle for analysis and predictions. In order to overcome this issue, a mathematical model consisting of a non-linear convection-diffusion-reaction system with discontinuous flux is developed from first principles as a unified framework for the dynamics in time and depth of the biofilm and microbial community, where a variety of ecological models can be included in the reaction terms, which also contain attachment, detachment and transfer processes. The multi-phase approach considers three main physical volumes: a biofilm matrix, the water volume enclosed by it and the flowing suspension through the SSF surrounding the biofilm. The only input data needed are the inflow concentrations and rate, light irradiation and temperature. The model includes a Cahn–Hilliard-type equation for the biofilm velocity in the supernatant water. A numerical scheme that preserves physical properties of the solution is also presented. This is achieved with a time-splitting scheme using an upwind scheme with an adaptive time-step size that ensures positivity of the solution under a CFL condition and a reasonable assumption on the separate numerical solution of the Cahn–Hilliard-type equation. The latter is solved numerically with a semi-implicit finite-difference scheme using a mixed form of the equation. The flexible model framework with its numerical scheme allows for including a variety of ecological models, making the investigation and development of increasingly complex simulations possible. Simulations with different model parameters are shown to be qualitatively consistent with the literature.

A smooth and efficient isogeometric topology optimization (ITO) method for maximizing band gaps in two-dimensional phononic crystals is developed in the paper. The band gaps of phononic crystals are computed by the NURBS-based isogeometric analysis, and the material distributions of two-dimensional phononic crystals are represented by the smooth, high-order continuity of the NURBS surface. The densities defined at each control point of the NURBS surface are employed as optimized design variables. The isogeometric analysis optimization using the same spline technique for both geometry and numerical analysis can benefit the optimization procedure and obtain smooth optimized structures, which can be easily used in 3D printing. The maximizing band gaps of phononic crystals for both out-of-plane and in-plane wave modes are obtained here using the present ITO approach. Numerical examples validated the effectiveness and reliability of the ITO method in broadening the band gaps and finding the optimal phononic crystals. And the numerical results show that the smooth optimized structures are obtained with fewer iterations.

Suspended monorail vehicles (SMV), hung beneath box beams with open bottoms, exhibit significant transverse wobble when exposed to turbulent winds, markedly impacting passenger comfort. This study presents an effective methodology for comprehensively evaluating the dynamical behavior of suspended monorail vehicle-track beam systems (SMVTBS) under wind action. First, based on the multi-rigid body dynamics theory and finite element method, an integrated vehicle-track beam interaction model is established. Then, by applying the auto-regressive (AR) linear filtering method, a turbulent wind velocity field with inherent correlations is adequately simulated through a stochastic process, which is later converted into wind force acting on both the track beam and vehicles. On this basis, the vibration responses of the SMVTBS with and without wind actions are compared, and the effects of the wind load on the vehicle-track beam dynamical behavior are revealed. Furthermore, to improve the wind-resistant performance of the SMV, several crucial design parameters are reasonably selected and effective wind-resistant strategies are proposed. Finally, the dynamic performance of the SMV is evaluated under wind action, and suitable train running speeds were recommended at different wind velocities to guarantee vehicle riding comfort. The research results can provide useful guidance for the design and operation of SMVTBS against crosswinds.

The nonlinear terms resulting from temperature dependence of thermal conductivity and relaxation time must be considered when studying systems undergoing very short thermal pulses with non-negligible amplitude of the temperature perturbation. Two nonlinear formulations of the Maxwell-Cattaneo-Vernotte equation for thermal transport with relaxation effects are introduced. A comparison of the consequences of these two different nonlinear Cattaneo type equations on thermal pulse propagation is obtained and discussed. The differences in the corresponding velocities and in the corresponding heights of the perturbation peaks turn out to be significant and could be experimentally detected.