where D = (−1, 1)× (−1, 1) , f(x, y) is a given Hölder continuous function in D, and φ(x, y) is an unknown function. The equation (1) has applications in the theory of aeroelasticity [1]. Note that the equation without logarithmic singularities was many times considered in different classes of functions. In the literature the solutions of the equation (1) in bounded domains [2, 5, 6, 9] as well...

To study the interaction of a vibrating shallow shell with three-dimensional subsonic gas flow, we deduce system hypersingular integral equations for aerodynamic derivatives pressure drop. This is convenient solution problems aeroelasticity. We solve by using numerical approach based on discrete vortex method. model vibrations shells, ordinary differential help assumed-mode also perform investi...

Tapering is a common morphological modification to ensure the stability of civil structures, especially as more and high-rise buildings push skyline modern cities. However, aerodynamics, aeroelasticity, fluid-structure-interaction tapering remain far from been fully understood. Through wind tunnel tests, present work offers some notable observations on effects tapering, specifically considering...

In this study, a revised version of some numerical methods for class hybrid integro-differential equations with weakly singular kernels (Abel types) is presented. These were developed from first kind originating an aeroelasticity problem. By manipulating the bounds initial conditions random variations, study numerically demonstrated well-posedness properties equations. Finally, assumption separ...

This paper numerically investigates the effect of chordwise flexibility on the dynamic stability of compliant airfoils. A classical two-dimensional aeroelastic model is expanded with an additional degree of freedom to capture time-varying camber deformations, defined by a parabolic bending profile of the mean aerodynamic chord. Aerodynamic forces are obtained from unsteady thin airfoil theory a...

Motivated by modeling blood flow in human arteries, we study a fluid-structure interaction problem in which the structure is composed of multiple layers, each with possibly different mechanical characteristics and thickness. In the problem presented in this manuscript the structure is composed of two layers: a thin layer modeled by the 1D wave equation, and a thick layer modeled by the 2D equat...

Blade-to-blade variations, known as mistuning, significantly affect the turbomachinery aeroelastic performance. Typically mistuning is observed to be beneficial for flutter stability but detrimental forced response. In some unconventional cases however, may even result in a benefit response reported by researchers. Many previous studies indicated that neglecting mistuning-induced changes aerody...