Adel Jilani

Transverse Vibrations of a Centrally Clamped Rotating Circular Disk

The transverse vibrations of a circular disk of uniform thickness rotatingabout its axis with constant angular velocity are analyzed. The resultsspecialized to the linear case of disks clamped at the center and free atthe periphery are in good agreement with those reported in the literature.The natural frequencies of spinning hard and floppy disks are obtained for various nodal diameters and nodal circles. Primary resonance is shown to occur at the critical rotational speed at which, in the linear analysis, the spinning disk is unable to support arbitraryspatially fixed transverse loads. Using the method of multiple scales, wedetermine a set of four nonlinear ordinary-differential equations governingthe modulation of the amplitudes and phases of two interacting modes. Thesymmetry of the system and the loading conditions are reflected in thesymmetry of the modulation equations. They are reduced to an equivalentset of two first-order equations whose equilibrium solutions aredetermined analytically. The stability characteristics of thesesolutions is studied; the qualitative behavior of the response isindependent of the mode being considered.

Deformation characteristics of circular RAINBOW actuators

Thin-plate theory, an energy-based Rayleigh-Ritz approach, which uses approximations to the deformation field, and the inclusion of geometric nonlinearities in the strain-displacement relations are used to develop an analysis to study the manufactured shape of circular piezoceramic RAINBOW actuators. The analysis predicts that the manufactured shape will be domelike or cylindrical. Which shape occurs is predicted to depend on the radius to thickness ratio of the original piezoceramic wafer used to make the actuator and the thickness of the reduced layer relative to the unreduced layer. The analysis is also used to predict the quasi-static (no inertia effects) shape change of the wafer due to actuation of the unreduced layer for voltages to 1.5 MV m-1. For these levels of voltage, the actuator response is very close to being linear with applied voltage, a factor that has advantages when dynamic effects are being considered.

Predicting the Axisymmetric Manufacturing Deformations of Disk-Style Benders

The thermally-induced deformations of multilayer disk-style benders that are consolidated at elevated temperature to cure the adhesives bonding the layers together and then cooled to room temperature are studied. Only axisymmetric deformations are considered, and hence the disks cool to a dome-like shape due to the different thermal expansion properties of the layers. The paper derives the equations governing the deformation and, since the out-of-plane deformations are often many times the disk thickness, geometrically nonlinear effects are considered in the derivation. As a comparison case, the equations are linearized and solved in closed form. The geometrically nonlinear case is solved by using the shooting method and the Rayleigh-Ritz method. A number of simple bender designs are studied to examine the influence of geometric nonlinearities, disk geometry, and layer material properties on the deformations. It is concluded that geometric nonlinearities lead to flattening of the dome relative to the geometrically linear case, and the thermally-induced deformations are sensitive to layer material properties, layer thickness, and disk radius.

MULTI-DISCIPLINARY SIMULATION OF PIEZOELECTRIC DRIVEN MICROFLUIDIC INKJET

Piezoelectric inkjet technology is critical to documentation, graphic arts and manufacturing applications. Physical modeling plays an essential role in the development of this technology. In this paper, we present a comprehensive, multi-level, inter-disciplinary simulation approach for piezoelectric inkjet design. This includes a high-fidelity, inter-disciplinary detailed simulation method for architecture investigation, and a much faster reduced-order modeling approach that enables interactive design of voltage waveforms. Simulation results are compared with experimental data. The multi-level inter-disciplinary simulation methodology presented here can be applied to designing MEMS and microfluidic devices and systems [1].Copyright

Manufactured Configurations of Piezoceramic Disk-Style Actuators

The thermally-induced deformations of disk-style actuators that are manufactured flat at an elevated temperature to cure the adhesives and are then cooled to room temperature for use are studied. These particular actuators are designed to deform out of plane as they are cooled. Though the intended deformed shape is dome-like, they sometimes cool to a near-cylindrical configuration. This issue is studied by developing an analysis and then using it to explore the influence of geometry, material properties, and fabrication temperature on whether the cooled configuration is dome-like or near-cylindrical. The analysis is based on using the total potential energy in combination with the Rayleigh-Ritz approach. Geometric nonlinearities are included, and as a result, stability of the cooled configurations is studied.

Manufactured Shapes of Rectangular RAINBOW Actuators

A model based on energy and variational methods is developed and used to predict the manufactured shape of square RAINBOW actuators. Due to the large out-of-plane deformations of the actuators as they are cooled from their elevated processing temperature, geometric nonlinearities are included in the model. It is shown there is a critical value of the ratio of actuator sidelength to thickness that determines whether the manufactured out-of-plane shape is a dome or a cylinder. Additionally, there is a critical value of the ratio of the reduced layer thickness to total thickness which determines which shape will occur. A simple extension to the model is used to predict the deformations due to application of an electric field. Despite the inclusion of geometric nonlinearities, the field strength vs. deformation relation is generally very nearly linear, which is an advantage when studying dynamic response. However, the response could be significantly nonlinear if the actuator was inadvertently designed to have geometric parameters near the critical values.