Under the effects of uncertain parameters and external disturbances, the attitude and trajectory tracking accuracy will be reduced and the response will be slowed down in the flight control of quadrotor unmanned air vehicles (UAVs). To solve this problem, the extended Kalman filter method was used given its excellent adaptability and noise suppression ability for nonlinear systems, to preliminarily estimate the quadrotor state information and suppress the high-frequency signal disturbance to reduce the estimation burden on the extended state observer. Moreover, the extended Kalman filter combined with the expanded state observer was applied to estimate the total disturbance composed of the system uncertainty parameters and external disturbances to reduce system reliance on precise models, and the differential values of the perturbation estimates were used for feedforward compensation to improve the tracking accuracy under abrupt disturbances and to overcome the phase lag caused by abrupt disturbances. The joint state observer, the linear extended state observer with feedforward compensation and the PD controller with error compensation were integrated to form an improved active disturbance rejection controller to jointly observe disturbances while suppressing high-frequency noises and abrupt disturbances to a relatively large extent, by means of the extended Kalman filter and the extended state observer with feedforward compensation. Simulation and experiment results show that, the joint observer can effectively reduce the observation error amplitude, correct the observation phase lag in advance and obtain more accurate state information, and the improved active disturbance rejection controller can better meet requirements of quadrotor UAVs for fast responses and stable control, and accurately and efficiently fulfill complex trajectory tracking tasks.

The dynamic responses of bridges with uncertain parameters under moving loads were analyzed, and a polynomial dimensional decomposition method for the analysis of structural responses induced by moving loads was proposed for the first time. The uncertain parameters were regarded as independent random variables, and the random response function about these uncertain parameters was constructed. The dimensional decomposition of the function was further performed with a group of component functions with a gradually increasing number of variables, and the approximate expressions of the component functions were derived through the Fourier polynomial expansion. Then, the expansion coefficients were efficiently calculated through the introduction of the dimension-reduction integration method. The numerical examples give response estimation of bridges with uncertain parameters under moving loads, which in comparison with those from the Monte-Carlo simulation, verify the accuracy and efficiency of the proposed method.

Based on the Davenport wind speed spectrum, the responses of 6-parameter practical viscoelastic damping energy dissipation structures were studied systematically. Firstly, the differential constitutive relation of the 6-parameter viscoelastic damper was used to establish the motion equation of the energy dissipation structure under the Davenport wind spectrum excitation. Then, the motion equation was transformed from the 2nd-order differential equation to the 1st-order one by means of the complex mode method, and the frequency-domain solution and the power spectral density function expression of the energy dissipation structure system under wind excitation were obtained. Finally, based on the random vibration theory, the analytical solutions of the response of the energy dissipation structure system under the Davenport wind spectrum excitation and the force response of the damper, were obtained with the mathematical identity. This method not only contains the results of the all-vibration-mode expansion of the structure system under wind excitation, but also has more simple and efficient expressions than existing methods, and applies to nonclassical structures.

A closed-form solution of responses of SDOF structures with SPIS-Ⅱ dampers under seismic excitation modeled with the Clough-Pezien spectrum was proposed, and the shock absorption performance and influential factors of this system were studied based on the proposed method. Firstly, the motion equation for the SPIS-Ⅱ damper was established, and the unified expressions of frequency domain solutions of structural responses, such as the structural displacement and the inerter force, were obtained. Secondly, based on the rational expression decomposition and the residue theorem, the quadratic orthogonal equations of the frequency response eigenvalue function and the Clough-Pezien spectrum were obtained respectively, and in turn the quadratic orthogonal equation of the structural response power spectrum was deduced. Thirdly, the concise closed-form solutions of the 0~2nd-order spectral moments of the structural responses were acquired. The proposed method and the virtual excitation method were used to analyze a case respectively, which verifies the correctness of the proposed method. Finally, the proposed method was used to analyze the effects of the inerter parameters on the seismic performances of the structure. The research shows that, the proposed method gives closed-form solutions better than those given by the virtual excitation method in terms of computation efficiency and accuracy. The damping performance will improve with the increase of μ_m and μ_ξ for a constant μ_ω and the damping performance will reach the optimum for μ_ω=1.

Functionally graded piezoelectric materials (FGPMs), combining the properties of functionally graded materials and piezoelectric materials, provides a new idea for multi-functional and intelligent lightweight components, and has broad application prospects in electronic devices. Based on the elastic and electric equilibrium equations, the Mian and Spencer functionally graded plate theory was extended from elastic materials to piezoelectric materials to study the cylindrical bending of FGPM plates, where the material elastic constants, piezoelectric and dielectric parameters were assumed to vary continuously and arbitrarily along the thickness direction. Accordingly, the elasticity solutions for cylindrical bending of FGPMs plates under the uniform transverse loading were obtained. Numerical examples were given to demonstrate the piezoelectric effects on the static responses of the presented FGPMs plates.

In view of the contact problem of functionally graded piezoelectric material (FGPM) coating under different kinds of conducting indenters, effects of the gradient index on the contact mechanical behavior of the FGPM coating were investigated. A model for the multilayer FGPM coating was established. The contact problem of the FGPM coating was transformed into singular integral equations by means of the Fourier integral transform technology and the transfer matrix method. The Gauss-Chebyshev quadrature formula was used to obtain the surface stress distribution and the charge distribution in the FGPM coating-substrate system under a rigid conducting flat indenter and a conducting cylindrical indenter. According to the numerical results, the effects of variations of the FGPM coating parameters on the indentation and electrical potential were analyzed. The distributions of stress and electrical displacement in the FGPM coating were obtained. The results show that, the variations of the FGPM coating parameters have an important influence on the contact behavior of the system.

The contact angle hysteresis is defined as the difference between the advancing and receding contact angles, and is an important phenomenon in the two-phase flow on the wet surface. An improved pseudo-potential lattice Boltzmann (LB) multiphase flow model, combined with geometric wetting boundary condition, was employed to study the motion behavior of dual droplets in microchannels with contact angle hysteresis. The effects of the capillary number, the wettability, the contact angle hysteresis window width, the initial distance between the two droplets and the relative size of the droplets on the dynamic behavior of the droplets in the microchannel, were investigated. The research results show that, the increase of the capillary number is conducive to the movement of droplets, but not conducive to the discharge of droplets from the microchannel, and the influence of the capillary number on the upstream droplet is greater than that on the downstream droplet. On the other hand, the larger the contact angle hysteresis window is, the slower the droplet motion and deformation will be, but the more obvious the deformation will be, and the earlier the two droplets will merge but the later they will discharge from the microchannel. In addition, with the increase of the initial distance between the two droplets, the droplet motion mode will differ among different stages, but the duration of the droplet discharge will extend. Correspondingly, the larger the relative size difference between upstream and downstream droplets is, the more difficultly the droplets will discharge from the microchannel.

Based on the theoretical framework of adaptive dynamics, the evolution of the predator-prey model with functional response of group defense effect on the predator handling time, was investigated. Firstly, in view of the interaction of predator populations with interspecific competition, the evolutionary conditions for a single predator population to split into 2 populations with different strategies through evolutionary branching were given. Secondly, when the ecological equilibrium of the model is unstable and the system has a limit cycle, the population will have strong coexistence under large mutation, but this coexistence will be evolutionarily unstable. Finally, the conclusions for the model with Holling-Ⅱ type functional response were compared. The results indicate that, with a sufficiently large prey carrying capacity, group defense effects can evolutionarily lead to the extinction of predators.

A dynamical model for infectious disease with media coverage effects and limited medical resources was established and analyzed. The basic reproduction number of the disease was defined, the existence and stability of the equilibria were analyzed, and the conditions for the forward bifurcation, the backward bifurcation and the Hopf bifurcation to occur in the system were given. Numerical simulation results show that, increasing the media coverage rate or the maximum hospital capacity can significantly reduce the number of infections at the peak or in the steady state of the epidemic. With the variations of parameters, the system will exhibit dynamic behaviors including not only the backward bifurcation or the forward bifurcation, but also the saddle node bifurcation, the Hopf bifurcation, or the change of the endemic equilibrium point stability with parameters.

In order to explore the combined effects of seasonality, vector-bias and human diffusion on malaria transmission, a partially degenerate periodic reaction-diffusion model was considered. With the persistence theory for dynamical systems, the threshold dynamics for the system was established in terms of basic reproduction number

. That is, the disease will go extinct if

$\mathcal{R}_0<1$

, while the disease will be uniformly persistent and break out seasonally for

$\mathcal{R}_0>1$

. Numerical results show that, the neglect of spatial heterogeneity and vector-bias will lead to underestimation of the risk of disease spread.

In view of the density dependence of mature individuals, a two-stage cannibalistic model with the egg-to-maturity stage was established. The dynamic behaviors of the model were discussed from two aspects. In the case without cannibalism, the global asymptotic stability of the equilibrium points was proved through construction of the Lyapunov function, while in the case with cannibalism, the existence of saddle-node bifurcation due to cannibalism was proved with the center manifold theorem. Through construction of the Dulac function, nonexistence of the limit cycle in the two-dimensional autonomous system was elucidated, and therefore, the global stability of the equilibrium points was obtained. Finally, the theoretical results were verified through numerical simulation.