In this study we describe an FEM-based methodology to solve the coupled fluid-structure problem due to squeeze film effects present in vibratory MEMS devices, such as resonators, gyroscopes, and acoustic transducers. ...In this study we describe an FEM-based methodology to solve the coupled fluid-structure problem due to squeeze film effects present in vibratory MEMS devices, such as resonators, gyroscopes, and acoustic transducers. The aforementioned devices often consist of a plate-like structure that vibrates normal to a fixed substrate, and is generally not perfectly vacuum packed. This results in a thin film of air being sandwiched between the moving plate and the fixed substrate, which behaves like a squeeze film offering both stiffness and damping. Typically, such structures are actuated electro-statically, necessitating the thin air gap for improving the efficiency of actuation and the sensitivity of detection. To accurately model these devices the squeeze film effect must be incorporated. Extensive literature is present on mod- eling squeeze film effects for rigid motion for both perforated as well as non-perforated plates. Studies which model the plate elasticity often use approximate mode shapes as input to the 2D Reynolds Equation. Recent works which try to solve the coupled fluid elasticity problem, report iterative FEM-based solution strategies for the 2D Reynolds Equation coupled with the 3D elasticity Equation. In this work we present a FEM-based single step solution for the coupled problem at hand, using only one type of element (27 node 3D brick). The structure is modeled with 27 node brick elements of which the lowest layer of nodes is also treated as the fluid domain (2D) and the integrals over fluid domain are evaluated for these nodes only. We also apply an electrostatic loading to our model by considering an equivalent electro-static pressure load on the top surface of the structure. Thus we solve the coupled 2D-fluid-3D-structure problem in a single step, using only one element type. The FEM results show good agreement with both existing analytical solutions and published experimental data.展开更多
A locking-free rectangular Mindlin plate element with a new multi-resolution analysis (MRA) is proposed and a new finite element method is hence presented. The MRA framework is formulated out of a mutually nesting dis...A locking-free rectangular Mindlin plate element with a new multi-resolution analysis (MRA) is proposed and a new finite element method is hence presented. The MRA framework is formulated out of a mutually nesting displacement subspace sequence whose basis functions are constructed of scaling and shifting on the element domain of basic full node shape function. The basic full node shape function is constructed by extending the split node shape function of a traditional Mindlin plate element to other three quadrants around the coordinate zero point. As a result, a new rational MRA concept together with the resolution level (RL) is constituted for the element. The traditional 4-node rectangular Mindlin plate element and method is a mono-resolution one and also a special case of the proposed element and method. The meshing for the monoresolution plate element model is based on the empiricism while the RL adjusting for the multiresolution is laid on the rigorous mathematical basis. The analysis clarity of a plate structure is actually determined by the RL, not by the mesh. Thus, the accuracy of a plate structural analysis is replaced by the clarity, the irrational MRA by the rational and the mesh model by the RL that is the discretized model by the integrated.展开更多
文摘In this study we describe an FEM-based methodology to solve the coupled fluid-structure problem due to squeeze film effects present in vibratory MEMS devices, such as resonators, gyroscopes, and acoustic transducers. The aforementioned devices often consist of a plate-like structure that vibrates normal to a fixed substrate, and is generally not perfectly vacuum packed. This results in a thin film of air being sandwiched between the moving plate and the fixed substrate, which behaves like a squeeze film offering both stiffness and damping. Typically, such structures are actuated electro-statically, necessitating the thin air gap for improving the efficiency of actuation and the sensitivity of detection. To accurately model these devices the squeeze film effect must be incorporated. Extensive literature is present on mod- eling squeeze film effects for rigid motion for both perforated as well as non-perforated plates. Studies which model the plate elasticity often use approximate mode shapes as input to the 2D Reynolds Equation. Recent works which try to solve the coupled fluid elasticity problem, report iterative FEM-based solution strategies for the 2D Reynolds Equation coupled with the 3D elasticity Equation. In this work we present a FEM-based single step solution for the coupled problem at hand, using only one type of element (27 node 3D brick). The structure is modeled with 27 node brick elements of which the lowest layer of nodes is also treated as the fluid domain (2D) and the integrals over fluid domain are evaluated for these nodes only. We also apply an electrostatic loading to our model by considering an equivalent electro-static pressure load on the top surface of the structure. Thus we solve the coupled 2D-fluid-3D-structure problem in a single step, using only one element type. The FEM results show good agreement with both existing analytical solutions and published experimental data.
文摘A locking-free rectangular Mindlin plate element with a new multi-resolution analysis (MRA) is proposed and a new finite element method is hence presented. The MRA framework is formulated out of a mutually nesting displacement subspace sequence whose basis functions are constructed of scaling and shifting on the element domain of basic full node shape function. The basic full node shape function is constructed by extending the split node shape function of a traditional Mindlin plate element to other three quadrants around the coordinate zero point. As a result, a new rational MRA concept together with the resolution level (RL) is constituted for the element. The traditional 4-node rectangular Mindlin plate element and method is a mono-resolution one and also a special case of the proposed element and method. The meshing for the monoresolution plate element model is based on the empiricism while the RL adjusting for the multiresolution is laid on the rigorous mathematical basis. The analysis clarity of a plate structure is actually determined by the RL, not by the mesh. Thus, the accuracy of a plate structural analysis is replaced by the clarity, the irrational MRA by the rational and the mesh model by the RL that is the discretized model by the integrated.
