Dissipation Effect on Local and Global Fluid-Elastic Instabilities

This chapter presents a joint local/global stability analysis of a model problem of fluid-elastic instabilities: the fluid-conveying pipe. The fluid-conveying pipe may be seen as a model problem for many physical systems, where a slender structure is coupled to an axial flow, and has applications in many fields, such as paper and nuclear industries, aeronautics, musical acoustics and biomechanics. The chapter briefly describes the local and global analyses. It presents the linear equations governing the dynamics of a fluid-conveying pipe. Effect of damping on the local and global stability of the fluid-conveying pipe is analyzed. The chapter discusses an application to energy harvesting. Various harvesting systems have been considered theoretically or experimentally, such as the simple Kelvin-Voigt-type dampers, electromagnetic coupling and piezoelectric coupling. The chapter summarizes the study of a clamped-free plate equipped with a continuous distribution of piezoelectric patches.