Precise Prediction on Pull-In Instability of a Deformable Micro-Plate Actuated by Distributed Electrostatic Force and Approximate Closed-Form Solutions

2005 ◽  
Author(s):  
Paul C.-P. Chao ◽  
Chi-Wei Chiu
Keyword(s):  
Residual Stress ◽  
Thin Plate ◽  
Electrostatic Force ◽  
Capacitive Sensor ◽  
External Pressure ◽  
Discrete Models ◽  
Parallel Plates ◽  
Restoring Force ◽  
Closed Form Solutions ◽  
Sensor Actuator

This study is dedicated to perform nonlinear asymptotic analysis based on the continuous thin plate model of MEMS capacitive sensor/actuator in order to predict the pull-in voltages/positions more precisely than past works. In these past studies, only discrete models without residual stress were considered. A sensor/actuator is considered in structure of two parallel electrostatically-charged flexible square plates — one thin plate in persistent vibrations to reflect external pressure and another thick plate in relative still as the backplate. The dynamic model in the form of the partial differential equation for the parallel plates is first established based on the balance among plate flexibility, residual stress and electrostatic forces. Assuming harmonic deflection for the vibrating plate clamped on boundaries, Galerkin method is used to decompose the established system p.d.e. into discrete modal equations. Solving the discrete modal equations, plate deflection can be obtained. The pull-in position is next solved from the condition that as the pull-in occurs the electrostatic attraction force on the deflected plate exceeds the elastic restoring force by the deflected plate. It is found from analysis results for some case study that the pull-in position is 1.66 μm with air gap of 3.75 μm. This predicted pull-in position is smaller than the predict position from past works, two-thirds of the gap. In addition to theoretical analysis, experiments are also conducted to verify the correctness of the established model.

Investigation on residual stress distribution in thin plate subjected to two sided laser shock processing

2019 ◽  
Vol 111 ◽  
pp. 146-155 ◽  
Author(s):  
Xingquan Zhang ◽  
Zhiwei Huang ◽  
Bin Chen ◽  
Yiwei Zhang ◽  
Jinyu Tong ◽  
...  
Keyword(s):  
Residual Stress ◽  
Stress Distribution ◽  
Thin Plate ◽  
Residual Stress Distribution ◽  
Laser Shock ◽  
Laser Shock Processing ◽  
Shock Processing

Research of Reinforce Stress on the Pressure Structure of Submersible Vehicle

2014 ◽  
Vol 496-500 ◽  
pp. 590-593
Author(s):  
Guan Nan Chu ◽  
Qing Yong Zhang ◽  
Guo Chun Lu
Keyword(s):  
Residual Stress ◽  
Finite Element ◽  
Stress Distribution ◽  
Hoop Stress ◽  
External Pressure ◽  
Finite Element Models ◽  
Cylinder Pressure ◽  
Simulation Experiments ◽  
Element Analysis ◽  
Load Carrying

In order to improve the load-carrying properties of pressure structure, a new method to improve the external bearing limit is put forward and residual stress is used. Based on finite element analysis, finite element models of cylinder pressure structure of submersible vehicle are established to produce hoop residual stress in the process of outward expansion. According to a lot of data of simulation experiments, the result indicates that hoop residual stress is compressive on the outer surface of the pipe and the hoop stress keeps tensile on the inside surface. This kind of stress distribution is helpful to the cylinder structure and can improve its bearing capacity of external pressure. Moreover, the rules of the residual stress are got. The influences of physical dimension, yield strength of material and the expansion rate to the stress distribution are analyzed. The measures to produce the stress distribution are also presented.

A Model for Underfill Viscous Flow Considering the Resistance Induced by Solder Bumps

2004 ◽  
Vol 126 (2) ◽  
pp. 186-194 ◽  
Author(s):  
Chyi-Lang Lai ◽  
Wen-Bin Young
Keyword(s):  
Flip Chip ◽  
External Pressure ◽  
Good Prediction ◽  
Parallel Plates ◽  
Rectangular Array ◽  
Chip Technology ◽  
Solder Bumps ◽  
Proposed Model ◽  
Filling Time ◽  
Underfill Flow

During the underfill process, polymers driven by either capillary force or external pressure are filled at a low speed between the chip and substrate. Current methods treated the flow in the chip cavity as a laminar flow between parallel plates, which ignored the resistance induced by the solder bumps or other obstructions. In this study, the filling flow between solder bumps was simulated by a flow through a porous media. By using the superposition of flows through parallel plates and series of rectangular ducts, permeability of the underfill flow was fully characterized by the geometric arrangement of solder bumps and flat chips. The flow resistances caused by adjacent bumps were represented in its permeability. The model proposed in this study could provide a numerical approach to approximate and simulate the undefill process for flip-chip technology. Although the proposed model is applicable for any geometric arrangement of solder bumps, rectangular-array of solder bumps layout was used first for comparison with experimental results of other article. Comparisons of the flow-front shapes and filling time with the experimental data indicated that the flow simulation obtained from the proposed model gave a good prediction for the underfill flow.

Parameter Identification of a Nonlinear Beam Energy Harvester

2012 ◽  
Author(s):  
Dennis J. Tweten ◽  
Brian P. Mann
Keyword(s):  
Parameter Identification ◽  
Harmonic Balance ◽  
Beam Energy ◽  
Restoring Force ◽  
Nonlinear Beam ◽  
Weakly Nonlinear ◽  
Closed Form Solutions ◽  
Energy Harvesters ◽  
Identification Method ◽  
Balance Parameter

This paper describes the application of the harmonic balance parameter identification method to beam energy harvesters. The method is applied to weakly nonlinear and nonlinear, bistable fixed-free piezoelectric beams with tip masses. It is shown that only one measurement is required to identify parameters even though the systems are continuous. In addition, an experimental method of determining the number of restoring force coefficients required to accurately model the systems is presented. The harmonic balance parameter identification method is extended to account for multiple concurrent frequencies in order to identify parameters of weakly nonlinear systems. Finally, parameters are identified for two experimental energy harvesters. Good agreement is shown between the experimental data and the identified parameters using simulations and closed form solutions.

Neural Network Based Hybrid Adaptive Controller for an Autonomously Driving Car Using Thin Plate Spline Radial Basis Activation Function

2014 ◽  
Vol 592-594 ◽  
pp. 2184-2188 ◽  
Author(s):  
P. Suresh ◽  
P.V. Manivannan
Keyword(s):  
Neural Network ◽  
Thin Plate ◽  
Error Control ◽  
Adaptive Controller ◽  
Activation Function ◽  
Thin Plate Spline ◽  
Lateral Deviation ◽  
Closed Form Solutions ◽  
Radial Basis ◽  
Feed Forward Controller

– This paper presents a hybrid lateral and longitudinal controller for a self-driving passenger car. The controller comprises a Proportional Derivative (PD) controller as a closed loop controller and Neural Network (NN) based adaptive compensator as a feed forward controller. The activation function of the NN adaptive stage is based on a poly-harmonic Thin Plate Spline (TPS) Radial Basis Function (RBF), which promises better accuracy, smoother interpolation and closed form solutions. The controller development and testing has been performed using a non-linear vehicle dynamics model, which has been developed using the Matlab / Simulink tool. The Controller performance in terms of vehicle lane following (lateral deviation control) and safe cruising control (longitudinal spacing error control) have been verified through simulations. Reductions of lateral deviation error by 15% and longitudinal spacing error by 7% have been achieved.

Dent Imperfections in Shell Buckling: The Role of Geometry, Residual Stress, and Plasticity

2020 ◽  
Vol 88 (3) ◽  
Author(s):  
S. Gerasimidis ◽  
J. W. Hutchinson
Keyword(s):  
Residual Stress ◽  
Residual Stresses ◽  
Middle Surface ◽  
External Pressure ◽  
Second Step ◽  
Elastic Buckling ◽  
Spherical Shells ◽  
Shell Buckling ◽  
Cylindrical Metal

Abstract Departures of the geometry of the middle surface of a thin shell from the perfect shape have long been regarded as the most deleterious imperfections responsible for reducing a shell’s buckling capacity. Here, systematic simulations are conducted for both spherical and cylindrical metal shells whereby, in the first step, dimple-shaped dents are created by indenting a perfect shell into the plastic range. Then, in the second step, buckling of the dented shell is analyzed, under external pressure for the spherical shells and in axial compression for the cylindrical shells. Three distinct buckling analyses are carried out: (1) elastic buckling accounting only for the geometry of the dent, (2) elastic buckling accounting for both dent geometry and residual stresses, and (3) a full elastic–plastic buckling analysis accounting for both the dent geometry and residual stresses. The analyses reveal the relative importance of the geometry and the residual stress associated with the dent, and they also provide a clear indicator of whether plasticity is important in establishing the buckling load of the dented shells.

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