2021/03/11 by Katerina Nik, Nik, Katerina
Computer Science · Engineering · #Advanced Mathematical Modeling in Engineering #Vibration and Dynamic Analysis #Numerical methods in engineering
paper · pdf · doi:10.48550/arxiv.2103.06772
A stationary free boundary problem modeling a three-dimensional electrostatic\nMEMS device is investigated. The device is made of a rigid ground plate and an\nelastic top plate which is hinged at its boundary, the plates being held at\ndifferent voltages. The model couples a nonlocal fourth-order equation for the\ndeformation of the top plate to a Laplace equation for the electrostatic\npotential in the free domain between the two plates. The strength of the\ncoupling is tuned by a parameter \λ which is proportional to the square\nof the applied voltage difference. Existence of a stable stationary solution is\nestablished for small values of \λ. Nonexistence of stationary solutions\nis obtained when \λ is large enough.\n