The governing equations of the reduced-order model are derived fr

The governing equations of the reduced-order model are derived from the equation governing the transverse motion of the microplate. The model is specialized to the case where a single basis function for the transverse displacement is used to yield manageable solutions. In the static analysis, pull-in parameters are found by solving a system of two nonlinear algebraic equations for the transverse displacement amplitude and the load parameter. The eigenvalue problem corresponding to linear vibrations of the system about its statically deflected position is solved for the fundamental frequency. We show that the fundamental frequency goes to zero as pull-in conditions are approached. The pull-in parameters found from the eigenvalue analysis agree well with those derived from the static analysis. We investigate effects of nanoscale forces and thermal stresses on pull-in parameters and small vibrations of electrostatically actuated microplates.The rest of the paper is organized as follows. In section 2, we present the governing nonlinear equations of motion for a von K��rm��n microplate under the simultaneous effects of thermal loading, electrostatic force, and nanoscale forces. We present expressions of the distributed loads due to either the Casimir or the van der Waals forces. In section 3, we introduce a reduced-order model for the considered device that is capable of accurately predicting its dynamics. The derivation of the reduced-order model read more follows a procedure typically used for studying deformations of thin two-dimensional structures. That is, in-plane inertial effects are neglected, and the resulting equation is solved for in-plane displacements in terms of transverse deflections which are then substituted in the equation governing the evolution of transverse deflection. Once transverse deflections have been computed, in-plane displacements can be found. In section 3, we also briefly outline the technique used to solve equations for the reduced order model. In section 4, we present our results, that include the pull-in parameters and the fundamental frequencies for rectangular microplates. We specia
Remote sensing and GIS technology is increasingly integrated with hydrological modelling. Digital elevation models (DEMs), digital data of soil type and land use, as well as powerful GIS tools have opened new possibilities for hydrological research leading to a more data driven modelling and understanding of the fundamental physical processes underlying the hydrological cycle. Recently, many hydrological models with a flood prediction component have been developed or have been updated to use DEMs, such as SWAT [1], CASC2D [2], DWSM [3], HYDROTEL [4], whereas models like SHE and TOPMODEL were adapted to benefit from GIS data [5, 6]. These models are either loosely or tightly coupled with GIS and remotely sensed data.

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