Alessandra Aimi

Vibration mitigation of moving flexible structures is a key issue in many applications. Examples include antennas, solar arrays, radar reflectors, and manipulator arms, especially in the aerospace sector. These structures typically consist of inter-connected slender and flexible elements moved by external actuators to reach specific configurations and positions. The movements excite vibrations, which lead to the risk of structural and fatigue failures; once in position, residual vibrations can be further amplified by structure lightness, causing bad performance and malfunctioning of onboard sensors. This paper proposes an effective technique to minimise the vibration of moving flexible structures by calculating the control points of a time-parametrised B-spline representing the shape of the motion law. A testing case of a rotating cantilever beam is considered. Validation using multi-flexible-body simulation software has shown the method’s effectiveness in minimising residual vibrations.

In this work, the Fourier-cosine series (COS) method has been combined with the Boundary Element Method (BEM) for a fast evaluation of barrier option prices. After a description of its use in the Black and Scholes (BS) model, the focus of the paper is on the application of the proposed methodology to the barrier option evaluation in the Heston model, where its contribution is fundamental to improve computational efficiency and to make BEM appealing among finance practitioners as a valid alternative to Monte Carlo (MC) or other more traditional approaches. An error analysis is provided on the number of terms used in the Fourier-cosine series expansion, where the error bound estimation is based on the characteristic function of the log-asset price process. A Matlab code implementing this technique is attached at the end of the paper.