Applied Mathematical Modelling最新文献

Aiming at the problems of unreasonable search range and low optimization performance in meteorological drone trajectory planning under complex obstacle threat environments, as well as the shortcomings of sometimes low and unstable optimization accuracy of the basic Jaya algorithm and easy to fall into local optima, a meteorological drone trajectory planning method based on multi-strategy improvement Jaya algorithm optimization is proposed. In order to meet the practical applications, the performance index trajectory planning model based on the weight coefficient method with the spherical coordinate system is established using the shortest trajectory, the minimum threat, the flight altitude, and the flight angle as the performance indexes, as well as the obstacles as the constraints. The simulation results of the improved algorithm for its solution are given, and the performance is compared with other heuristic algorithms. The results show that the planned path can be safer and more effective in avoiding hazardous sources by comprehensively considering the performance of the meteorological drone. Compared with other algorithms, the improved algorithm performs well in terms of searching accuracy and stability and generates the higher-quality trajectory.

In δ-shock modeling, the life behavior of systems suffering from random shocks depends on the length of inter-arrival times between successive shocks. In this paper, a generalized version of the classical δ-shock model is studied, under which the system fails when the inter-arrival time falls in the interval $[\alpha ,\delta ]$ for $0\le \alpha <\delta$. Furthermore, with an innovative approach, the classical δ-shock model is studied under this new assumption that the inter-arrival times are overdispersed in the critical interval of the model. This is a new assumption compared to the traditional assumptions in the context of shock models and actually introduces a situation wherein the system is under pressure to fail. Under this assumption, two situations are considered for the system, which are regular and critical situations, and then the reliability behavior of the system's lifetime is investigated under these situations. Some examples are also provided to illustrate the theoretical results of the application.

Piezoelectric materials as the controlling element have been widely utilized to produce intelligent engineering structures, while these smart structures may fail to realize effective control of composite structures with large deformations. However, investigations on such issues are less reported in published literature, as an accurate and efficient model is required to well forecast the geometrically nonlinear behaviors of smart sandwich structures. As a result, a novel sinusoidal Legendre global-local higher-order shear deformation plate theory (SLHSDT) has been developed to accurately capture geometrically nonlinear behaviors of piezoelectric sandwich plates. The proposed model can fulfill the compatible conditions of transverse shear stresses and contain transverse normal strain, which can ensure precision in predicting electromechanical behaviors. The multi-patch isogeometric analysis (IGA) method for sandwich plates partially bonded with piezoelectric layers is proposed to overcome C¹-continuity between patches for the first time. Moreover, the Newmark-β method and Newton-Raphson technique are attempted to solve the nonlinear equations. The present model has been utilized to investigate electromechanical behaviors of laminated structures with piezoelectric layers, which has been compared with the published results. In addition, experiments on macro fiber composite (MFC) integrated sandwich plates have been also carried out in the present work, which can effectively verify the performance of proposed model. Subsequently, the proposed model is employed to study electromechanical behaviors of the five-layer piezoelectric sandwich plates containing internal pores and graphene platelets. Then, influences of the porosity coefficient and GPLs weight fraction on the nonlinear electromechanical behaviors of sandwich plates are investigated. Eventually, the active control on nonlinear behaviors of piezoelectric porous sandwich plates with GPLs reinforcement is studied by using a closed-loop control system, and an effective approach slowing down large deformation has been proposed by selecting an appropriate distribution of GPLs along the thickness direction.

Bolted flange joint disk-drum structures (BFJDDSs) are key components in aero-engines, however, bolt looseness inevitably occurs due to extreme service conditions. This can cause the bolted joint interface to exhibit complex contact behaviors, which significantly complicate the vibration characteristics of BFJDDSs. Existing dynamic models for BFJDDSs have not considered the effect of bolt looseness (slip and separation), so their vibration behaviors are not well understood. In this study, a unified nonlinear dynamic model for BFJDDSs considering different interface states (stick, slip, and separation) is proposed, which is effective under both bolt looseness and non-looseness (stick) conditions. The bi-linear hysteretic model combined with the piecewise linear model is used to simultaneously consider different interface states. The Kirchhoff plate theory, the Sanders’ shell theory, and the Euler-Bernoulli beam theory are used to derive the energy functions of the disk, drum, and flange, respectively. Then, the Lagrange equations are employed to derive the governing equations of BFJDDSs. Modal and nonlinear forced vibration experiments are carried out on a BFJDDS to prove the correctness of the proposed mathematical model. Research results show that the proposed mathematical model is able to achieve good predictions of nonlinear dynamic properties of BFJDDSs under both bolt looseness and non-looseness conditions. This model is also able to well predict the jumping phenomenon observed in the experiment.

Existing analytic solutions for the free vibration of functionally graded carbon nanotube reinforced doubly-curved panels primarily address the cases with two parallel simply supported boundaries, known as Lévy-type boundary conditions (BCs). However, doubly-curved panels with non-Lévy-type BCs are more commonly encountered in practical engineering applications, yet their analytic solutions are rarely available due to significant mathematical challenges. This gap motivates us to develop new analytic free vibration solutions under these more complex BCs. The nanocomposites’ material properties are first computed according to the rule of mixture. The Hamiltonian-system governing equation for the free vibration of doubly-curved panels is then formulated from the Donnell-Mushtari theory, and is solved by adopting the analytic symplectic superposition method. The obtained analytic solutions are derived without requiring predefined solution forms, and have been thoroughly validated by comparison with the results from the finite element method. By utilizing the accurate analytic solutions, the effects of aspect ratios, BCs, types of CNT distributions, and volume fractions of CNT on the free vibration behaviors are further analyzed. The present solution procedure and the resulting analytic solutions are expected to be useful for dynamic modeling of composite shell panels, supporting both future research and practical applications.