Symplectic Elasticity Modeling for Miniaturized Crystalline Plate Structures Subject to Repulsive Casimir Forces and Surface Stresses

Description

The Casimir forces are known to originate from the quantum-mechanical vacuum zero-pointenergy and they belong to the generalized version of van der Waals forces. These forces arelong-ranged, and thus they are paramount to the design and operation of micro- and nano-scalesensoring/actuatoring devices. Majority of the previous studies were focused mainly on theeffects of the attractive Casimir forces including the adhesion between movable sensors and parts.Recent theoretical and experimental developments indicate that Casimir forces can also berepulsive, depending nontrivially on the shapes and compositions of the objects. This discoverynot only leads to new understanding of the forces, but also provides new ways to combatunwanted interactions in micro- and nano-electro-mechanical systems (NEMS/MEMS).However, the applications are largely complicated by the nonlinear nature of the force-distancedependence as well as the significant surface effects at minute scales. An efficient approachwhich can accurately predict the mechanical responses of a structural element in thesecircumstances is extremely desired.The principal investigator (PI) has published research papers on the effects of long-range,attractive CL forces in crystalline structures [83]. He has also conducted some preliminaryresearch on surface stress size effects [87,88]. The PI has conducted research on the newsymplectic elasticity approach that is capable of overcoming the bottlenecks of the classic platedynamics solution methodologies that do not apply to the classic Levy-like and Timoshenko-likesemi-inverse methods [45,75]. In this project, typical plate-like structures subject to Casimirforces and surface stresses are considered. The PI will (i) identify geometries and materials ofthe system for the transition from attractive to repulsive of the Casimir forces; (ii) develop a newsymplectic model and solution tools for the nonlinear mechanical responses of the plates to therepulsive Casimir forces and surface stresses; (iii) conduct experiments and atomistic simulationsto substantiate the model and solution approach, and (iv) further explore the potential engineeringapplications that applies the repulsive Casimir forces and surfaces stresses, including micro-,nano-switches, micro-, nano-actuating and sensing systems, nonlinear oscillators and quantumelectrodynamical floatation devices.The proposed project is expected to deliver the following research outcomes. In addition topublishing some technical papers in top, refereed international journals, the project will offer newunderstandings, insights, and experimental data and new solution tools for investigating therepulsive Casimir forces and surfaces stresses, as well as their engineering responses in microandnanocrystalline plate structures. One to two research students will receive in-depth trainingin the field. Last but not least, the successful completion of the project will provide a platformfor further research, which will also lead to engineering spin-offs, and, potentially, new designapplications in MEMS and NEMS.Keywords: actuator/sensor; nonlinear response; repulsive Casimir effect; surface stresses;symplectic elasticity?