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nonlinear-mathieu-equation
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Non-linear Effects on "linear point" through Analytical Methods
, M.Sc. Thesis Sharif University of Technology ; Abolhassani, Aliakbar (Supervisor)
Abstract
By studying of simulations, it can be seen that the linear point (LP), a point lies midway between the scales associated with the peak and the dip in the correlation function on BAO scales, is a useful window into cosmology and large scale structures rather than baryonic echo peak. Some fundamental features of the LP, been unaffected by redshift space distortions and gravitational non-linear effects, has made it important. I want to find evidences to stability of the LP by utilizing Standard Perturbation Theory through my thesis
Nonlinear Analysis and Design of Estimation and Filtering System for a MEMS Gyroscope with Parametric Excitation
, M.Sc. Thesis Sharif University of Technology ; Salarieh, Hassan (Supervisor) ; Alasti, Aria (Co-Advisor)
Abstract
Recently, parametric excitation has been proposed and experimentally proven to provide micro gyroscopes with robustness to parameter variations and enhancement of sensitivity [L.A. Oropeza-Ramos, C.B. Burgner, K.L. Turner, Robust micro-rate sensor actuated by parametric resonance, Sensors and Actuators A: Physical, 152 (2009) 80-87].The first part of this thesis aims at investigating the nonlinear dynamics of MEMS vibratory gyroscopes with parametric excitation which can be represented by a minor variation of nonlinear Mathieu equation coupled to a Duffing oscillator. Our approach is based on analytical frequency response derivation via method of multiple time scales. Stability of responses,...