Modelling MEMS Resonators Past Pull-In

2008 ◽  
Author(s):  
Chandrika P. Vyasarayani ◽  
Eihab M. Abdel-Rahman ◽  
John McPhee ◽  
Stephen Birkett
Keyword(s):  
Differential Equation ◽  
Mathematical Model ◽  
Partial Differential Equation ◽  
Numerical Solution ◽  
Nonlinear Ordinary Differential Equations ◽  
Mems Resonators ◽  
Electrostatic Mems ◽  
Stationary Electrode ◽  
External Forces ◽  
The Galerkin Method

In this paper, we develop a mathematical model of an electrostatic MEMS beam undergoing impact with a stationary electrode subsequent to pull-in. We model the contact between the beam and the substrate using a nonlinear foundation of springs and dampers. The system partial differential equation (PDE) is converted into coupled nonlinear ordinary differential equations (ODEs) using the Galerkin method. A numerical solution is obtained by treating all nonlinear terms as external forces.

Modeling MEMS Resonators Past Pull-In

2011 ◽  
Vol 6 (3) ◽  
Author(s):  
Chandrika P. Vyasarayani ◽  
Eihab M. Abdel-Rahman ◽  
John McPhee ◽  
Stephen Birkett
Keyword(s):  
Natural Frequencies ◽  
Contact Length ◽  
Mode Shapes ◽  
Nonlinear Ordinary Differential Equations ◽  
Micro Electro Mechanical Systems ◽  
Mems Resonators ◽  
Electrostatic Mems ◽  
Stationary Electrode ◽  
External Forces ◽  
The Galerkin Method

In this paper, we develop a mathematical model of an electrostatic MEMS (Micro-Electro-Mechanical systems) beam undergoing impact with a stationary electrode subsequent to pull-in. We model the contact between the beam and the substrate using a nonlinear foundation of springs and dampers. The system partial differential equation is converted into coupled nonlinear ordinary differential equations using the Galerkin method. A numerical solution is obtained by treating all nonlinear terms as external forces. We use the model to predict the contact length, natural frequencies, and mode shapes of the beam past pull-in voltage as well as the dynamic response of a shunt switch in a closing and opening sequence.

A Meshless Method for Solving the Mathematical Model Associated the Leakage Problem in Gas Pipeline

2014 ◽  
Vol 986-987 ◽  
pp. 1418-1421
Author(s):  
Jun Shan Li
Keyword(s):  
Differential Equation ◽  
Mathematical Model ◽  
Partial Differential Equation ◽  
Inverse Problem ◽  
Basis Function ◽  
Meshless Method ◽  
Numerical Solutions ◽  
Basis Functions ◽  
Gas Pipeline ◽  
The Mathematical Model

In this paper, we propose a meshless method for solving the mathematical model concerning the leakage problem when the pressure is tested in the gas pipeline. The method of radial basis function (RBF) can be used for solving partial differential equation by writing the solution in the form of linear combination of radius basis functions, that is, when integrating the definite conditions, one can find the combination coefficients and then the numerical solution. The leak problem is a kind of inverse problem that is focused by many engineers or mathematical researchers. The strength of the leak can find easily by the additional conditions and the numerical solutions.

Numerical Simulation of Orientation Distribution on Fibers Suspensions in Planar Extensional Field

2013 ◽  
Vol 395-396 ◽  
pp. 1174-1178
Author(s):  
Pei Fang Luo ◽  
Zan Huang
Keyword(s):  
Differential Equation ◽  
Numerical Simulation ◽  
Mathematical Model ◽  
Partial Differential Equation ◽  
Fiber Orientation ◽  
Extensional Flow ◽  
Orientation Distribution ◽  
Specific Form ◽  
Fiber Orientation Distribution ◽  
Planar Extensional Flow

A mathematical model of evolution process is adopted to simulate orientation distribution of fibers suspensions in planar extensional flow, i.e., specific form of Fokker-Plank partial differential equation and Jeffery equation. The analytical solution of differential equation on forecast fiber orientation distribution is deduced.

A family of positivity preserving schemes for numerical solution of Black–Scholes equation

2016 ◽  
Vol 03 (04) ◽  
pp. 1650025
Author(s):  
M. Mehdizadeh Khalsaraei ◽  
R. Shokri Jahandizi
Keyword(s):  
Differential Equation ◽  
Partial Differential Equation ◽  
Exact Solution ◽  
Numerical Solution ◽  
Numerical Scheme ◽  
Initial Vector ◽  
Positivity Preserving ◽  
Fully Implicit ◽  
Black Scholes ◽  
Spurious Oscillations

When one solves the Black–Scholes partial differential equation, it is of great important that numerical scheme to be free of spurious oscillations and satisfy the positivity requirement. With positivity, we mean, the component non-negativity of the initial vector, is preserved in time for the exact solution. Numerically, such property for fully implicit scheme is not always satisfied by approximated solutions and they generate spurious oscillations in the presence of discontinuous payoff. In this paper, by using the nonstandard discretization strategy, we propose a new scheme that is free of spurious oscillations and satisfies the positivity requirement.

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