ABSTRACT
Progressive flexural waves can be generated only in finite structures by fine tuning the excitation and the boundary conditions. The tuning process eliminates the reflected waves arising from discontinuities and edge effects. This work presents and expands two new methods for the identification and tuning of traveling waves. One is a parametric method based on fitting an ellipse to the complex spatial amplitude distribution. The other is a nonparametric method based on the Hilbert transform providing a space-localized estimate. With these methods, an optimization-based tuning of transverse flexural waves in a one-dimensional structure, a vibrating beam, is developed. Existing methods are designed for a single frequency and are based on either combining two vibration modes or mechanical impedance matching. Such methods are limited to a designated excitation frequency determined by a specific configuration of the system. With the proposed methods, structural progressive waves can be generated for a wide range of frequencies under the same given system configuration and can be tuned in real time to accommodate changes in boundary conditions. An analytical study on the nature of the optimal excitation conditions has been carried out, revealing singular configurations. The experimental verification of the sensing and tuning methods is demonstrated on a dedicated laboratory prototype. The proposed methods are not confined to mechanical waves and present a comprehensive approach applicable for other physical wave phenomena.
ABSTRACT
This paper presents the theory describing the dynamical behavior of a noncontacting lateral transportation of planer objects by means of a gas squeeze film created by traveling flexural waves of a driving surface. An oscillating motion in the normal direction between two surfaces can generate a gas film with an average pressure higher than the surrounding. This load-carrying phenomenon arises from the fact that a viscous flow cannot be instantaneously squeezed; therefore, fast vibrations give rise to a cushioning effect. Equilibrium is established through a balance between viscous flow forces and compressibility forces. When the oscillatory motion between two surfaces creates traveling waves, lateral viscous forces are generated in addition to the normal levitation forces. These forces are produced as a result of nonuniform pressure gradients in the lateral direction between the surfaces. The combination of normal and lateral forces could be used for transporting objects without any direct contact with the driving surface. The numerical algorithm in this work couples the squeeze film phenomenon, which is represented by means of finite difference equations, to model a variant of the Reynolds equation, together with the equations describing the dynamics of the floating object. Numerical simulations are presented and investigated to highlight noteworthy topics.
