Abstract
A novel procedure based on the Sturm’s theorem for real-valued polynomials is developed to predict and identify periodic and non-periodic solutions for a graphene-based MEMS lumped parameter model with general initial conditions. It is demonstrated that under specific conditions on the lumped parameters and the initial conditions, the model has certain periodic solutions and otherwise there are no such solutions. This theoretical procedure is made practical by numerical implementations with Python scripts to verify the predicted behaviour of the solutions. Numerical simulations are performed with sample data to justify by this procedure the analytically predicted existence of periodic solutions.
Original language | English |
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Pages (from-to) | 59-72 |
Number of pages | 14 |
Journal | Applied and Computational Mechanics |
Volume | 12 |
Issue number | 1 |
DOIs | |
Publication status | Published - Jan 1 2018 |
Keywords
- Existence of solutions
- Graphene
- MEMS
- Periodic solutions
- Pull-in
- Singularity
- Sturm’s theorem
ASJC Scopus subject areas
- Biophysics
- Computational Mechanics
- Civil and Structural Engineering
- Fluid Flow and Transfer Processes
- Computational Mathematics