The escape factor in plasma spectroscopy—III. Two case studies

This paper contains two case studies, involving two contrasting approaches to the evaluation of the escape factor. These include the case usually associated with Zanstra, Osterbrock and Hearn, and a case where an approximation to the escape factor Λ(=1?Ψ) is obtained via an approximation to the complementary quantity Ψ.     

Artificial cochlea and acoustic black hole travelling waves observation: Model and experimental results

An inhomogeneous fluid structure waveguide reproducing passive behaviour of the inner ear is modelled with the help of the Wentzel–Kramers–Brillouin method. A physical setup is designed and built. Experimental results are compared with a good correlation to theoretical ones. The experimental setup is a varying width plate immersed in fluid and terminated with an acoustic black hole. The varying width plate provides a spatial repartition of the vibration depending on the excitation frequency. The acoustic black hole is made by decreasing the plate?s thickness with a quadratic profile and by covering this region with a thin film of viscoelastic material. Such a termination attenuates the flexural wave reflection at the end of the waveguide, turning standing waves into travelling waves.     

Modeling and analysis of nonlinear rotordynamics due to higher order deformations in bending

A mathematical model incorporating the higher order deformations in bending is developed and analyzed to investigate the nonlinear dynamics of rotors. The rotor system considered for the present work consists of a flexible shaft and a rigid disk. The shaft is modeled as a beam with a circular cross section and the Euler Bernoulli beam theory is applied with added effects such as rotary inertia, gyroscopic effect, higher order large deformations, rotor mass unbalance and dynamic axial force. The kinetic and strain (deformation) energies of the rotor system are derived and the Rayleigh–Ritz method is used to discretize these energy expressions. Hamilton’s principle is then applied to obtain the mathematical model consisting of second order coupled nonlinear differential equations of motion. In order to solve these equations and hence obtain the nonlinear dynamic response of the rotor system, the method of multiple scales is applied. Furthermore, this response is examined for different possible resonant conditions and resonant curves are plotted and discussed. It is concluded that nonlinearity due to higher order deformations significantly affects the dynamic behavior of the rotor system leading to resonant hard spring type curves. It is also observed that variations in the values of different parameters like mass unbalance and shaft diameter greatly influence dynamic response. These influences are also presented graphically and discussed.