1. Stochastic processes and random fields 2. Continuous semimartingales and stochastic integrals 3. Semimartingales with spatial parameter and stochastic integrals 4. Stochastic flows 5. Convergence of stochastic flows 6. Stochastic partial differential equations.

Stochastic flows and stochastic differential equations

Aeroelastic energy harvesting: A review

In this von Karman lecture, a subject is addressed whose foundations were significantly influenced by the work of Theodore von Karman. A classic paper by von Karman and Sears first considered the determination of aerodynamic forces on an airfoil undergoing general time-dependent motion. Also, early in his career, von Karman investigated fundamental issues in structural mechanics and derived the celebrated von Karman plate equations for determining the large (nonlinear) deflections of an elastic plate under a distributed force. Finally, he authored a widely cited paper on the importance of nonlinearities for engineers and engineering. In this lecture, these themes are recalled and the current state of the art in nonlinear aeroelasticity and unsteady aerodynamics is discussed. Several of the most significant nonlinearities arising in a structure or in an aerodynamic flow field are identified. Recent and relevant theoretical and experimental studies are reviewed and future developments are projected that are expected to have a significant impact on our ability to understand and beneficially use nonlinear dynamic aeroelastic behavior

Nonlinear Aeroelasticity and Unsteady Aerodynamics

From last few decades, piezoelectric materials have played a vital role as a mechanism of energy harvesting, as they have the tendency to absorb energy from the environment and transform it to electrical energy that can be used to drive electronic devices directly or indirectly. The power of electronic circuits has been cut down to nano or micro watts, which leads towards the development of self-designed piezoelectric transducers that can overcome power generation problems and can be self-powered. Moreover, piezoelectric energy harvesters (PEHs) can reduce the need for batteries, resulting in optimization of the weight of structures. These mechanisms are of great interest for many researchers, as piezoelectric transducers are capable of generating electric voltage in response to thermal, electrical, mechanical and electromagnetic input. In this review paper, Fluid Structure Interaction-based, human-based, and vibration-based energy harvesting mechanisms were studied. Moreover, qualitative and quantitative analysis of existing PEH mechanisms has been carried out.

https://www.mdpi.com/1996-1073/11/7/1850/pdf

A Review on Mechanisms for Piezoelectric-Based Energy Harvesters

This work investigates the influence of structural and aerodynamic nonlinearities on the dynamic behavior of a piezoaeroelastic system. The system is composed of a rigid airfoil supported by nonlinear torsional and flexural springs in the pitch and plunge motions, respectively, with a piezoelectric coupling attached to the plunge degree of freedom. The analysis shows that the effect of the electrical load resistance on the flutter speed is negligible in comparison to the effects of the linear spring coefficients. The effects of aerodynamic nonlinearities and nonlinear plunge and pitch spring coefficients on the system’s stability near the bifurcation are determined from the nonlinear normal form. This is useful to characterize the effects of different parameters on the system’s output and ensure that subcritical or “catastrophic” bifurcation does not take place. Numerical solutions of the coupled equations for two different configurations are then performed to determine the effects of varying the load resistance and the nonlinear spring coefficients on the limit-cycle oscillations (LCO) in the pitch and plunge motions, the voltage output and the harvested power.

Modeling and analysis of piezoaeroelastic energy harvesters

Application of the centre manifold theory in non-linear aeroelasticity

Non-linear aeroelastic analysis using the point transformation method, part 1: freeplay model

The construction of symplectic numerical schemes for stochastic Hamiltonian systems is studied. An approach based on generating functions method is proposed to generate the stochastic symplectic integration of any desired order. In general the proposed symplectic schemes are fully implicit, and they become computationally expensive for mean square orders greater than two. However, for stochastic Hamiltonian systems preserving Hamiltonian functions, the high-order symplectic methods have simpler forms than the explicit Taylor expansion schemes. A theoretical analysis of the convergence and numerical simulations are reported for several symplectic integrators. The numerical case studies confirm that the symplectic methods are efficient computational tools for long-term simulations.

High-Order Symplectic Schemes for Stochastic Hamiltonian Systems

This paper presents new finite difference schemes for solving the Helmholtz equation in the polar and spherical coordinates. The most important result presented in this study is that the developed difference schemes are pollution free, and their convergence orders are independent of the wave number k. Let h denote the step size, it will be demonstrated that when solving the Helmholtz equation at large wave numbers and considering kh is fixed, the errors of the proposed new schemes decrease as h decreases even when k is increasing and kh > 1.

Yau Shu Wong

Papers

Application of the centre manifold theory in non-linear aeroelasticity

Non-linear aeroelastic analysis using the point transformation method, part 1: freeplay model

High-Order Symplectic Schemes for Stochastic Hamiltonian Systems

Efficient and Accurate Numerical Solutions for Helmholtz Equation in Polar and Spherical Coordinates

Non-linear aeroelastic analysis using the point transformation method, part 2: hysteresis model