M. Rastgaar Aagaah

Linear static analysis and finite element modeling for laminated composite plates using third order shear deformation theory

In this paper, deformations of a laminated composite plate due to mechanical loads are presented. Third order shear deformation theory of plates, which is categorized in equivalent single layer theories, is used to derive linear dynamic equations of a rectangular multi-layered composite plate. Moreover, derivation of equations for FEM and numerical solutions for displacements and stress distributions of different points of the plate with a sinusoidal distributed mechanical load for Navier type boundary conditions are presented.

Comparison of Exact and Approximate Frequency Response of a Piecewise Linear Vibration Isolator

In this paper an investigation is carried out to classify the steady state responses of asymmetric piecewise linear vibration isolators as double hitting, single hitting, and no hitting. In each class, the analysis has been carried out using a set of coupled nonlinear algebraic equations following Natsiavas and Gonzalez [1]. Applying perturbation technique, a closed form analytic expression of the frequency response is also derived for symmetric conditions. The exact frequency response is utilized to validate the analytic results obtained by perturbation techniques. Direct comparison indicates the results obtained by averaging method are mathematically and practically close to the exact solution.Copyright

Frequency Response of Vibration Isolators With Saturating Spring Elements

An investigation using averaging method is carried out to obtain the frequency response of a class of vibration isolators with saturation spring. The saturation characteristics are modeled using a hyperbolic-tangent function. The hyperbolic-tangent saturation function is compared with other popular saturation functions, using piecewise nonlinear approximation. A parameteric study indicates that piecewise linear approximation of saturating functions provide results that are close enough to the results of hyperbolic tangent approximation. A sensitivity analysis of frequency response of the system is also investigated based on the piecewise linear approximation.Copyright

Time Response Dynamics of Linear Model of Microcantilever-MEMS

This paper presents analytic derivation of dynamic behavior of a liniearized micro-electro-mechanical resonator. The parametric oscillation results from a displacement-dependent electrostatic force generated by oscillation of a microbeam. The utilized device is a MEMS with a time-varying capacitor. The stability and steady state dynamic behavior of the MEMS has been analyzed without polarization voltage. The main characteristic of the no-polarization model is effects of parameters in stability of the system. A set of stability charts is provided for prediction of the boundary between the stable and unstable domains for the principal resonance. Applying perturbation method, analytical equations are derived to describe both the steady state and time response of the system.Copyright

Distribution of Sub and Super Harmonic Solution of Mathieu Equation Within Stable Zones

The third stable region of the Mathieu stability chart, surrounded by one π-transition and one 2π-transition curve is investigated. It is known that the solution of Mathieu equation is either periodic or quasi-periodic when its parameters are within stable regions. Periodic responses occur when they are on a “splitting curve”. Splitting curves are within stable regions and are corresponding to coexisting of periodic curves where an instability tongue closes. Distributions of sub and super-harmonics, as well as quasi-periodic solutions are analyzed using power spectral density method.Copyright

Stability Analysis of a Linearized MEMS

This paper presents the stability theory and dynamic behavior of a micro-mechanical parametric-effect resonator. The device is a MEMS time-varying capacitor. The nonlinear dynamics of the MEMS are investigated analytically, and numerically. Applying perturbation methods, and deriving an analytical equation to describe the frequency response of the system enables the designer to study the effect of changes in the system parameters that can be used for design and optimization of the system.Copyright

Design of Applied Reentry Guidance Algorithms for Low Cost Vehicles

Simple guidance methods for Reentry Vehicles (RV) with low lift to drag ratio (L/D) during the reentry phase is investigated. Proposed algorithms, based on nominal trajectory method, permit the vehicle to experience the aerodynamic force, which is needed to keep the actual trajectory close to the desired one and increase landing accuracy. Simulation results for a conceptual RV are provided to demonstrate the performance of the trajectory guidance laws under a variety of non-nominal conditions.Copyright

VEHICLES AND NONLINEAR SUSPENSIONS

An independent suspension for conventional vehicles has been modeled as a nonlinear vibration absorber with a nonlinear third-order ordinary differential equation. In order to obtain conditions that guarantee existence of periodic solutions and stable responses, the Schauder’s fixed-point theorem has been implemented to prove a third-order solution existence theorem for general third-order differential equations. A numerical method has been developed for rapid convergence, and applied for a sample model. The correctness of sufficient conditions and solution algorithm has been shown with appropriate figures.Copyright

ANALYSIS OF SOLITARY WAVES IN ARTERIES

Solitary waves are coincided with separaterices, which surrounds an equilibrium point with characteristics like a center, a sink, or a source. The existence of closed or spiral orbits in phase plane predicts the existence of such an equilibrium point. If there exists another saddle point near that equilibrium point, separatrix orbit appears. In order to prove the existence of solution for any kind of boundary value problem, we need to apply a fixed-point theorem. We have used the Schauder’s fixed-point theorem to show that there exists at least one nontrivial solution for equation of wave motion in arteries, which has a spiral characteristic. The equation of wave motion in arteries has a nonlinear character. Thus, the amplitude of the wave depends on the wave velocity. There is no general analytical or straightforward method for prediction of the amplitude of the solitary wave. Therefore, it must be found by numerical or nonstraightforward methods. We introduce and analyse three methods: saddle point trajectory, escape moving time, and escape moving energy. We apply these methods and show that the results of them are in agreement, and the amplitude of a solitary wave is predictable.Copyright