José Manoel Balthazar

NONLINEAR VIBRATIONS OF CANTILEVER TIMOSHENKO BEAMS: A HOMOTOPY ANALYSIS

THIS STUDY ANALYZES THE FOURTH-ORDER NONLINEAR FREE VIBRATION OF A TIMOSHENKO BEAM. WE DISCRETIZE THE GOVERNING DIFFERENTIAL EQUATION BY GALERKINÂx80x99S PROCEDURE AND THEN APPLY THE HOMOTOPY ANALYSIS METHOD (HAM) TO THE OBTAINED ORDINARY DIFFERENTIAL EQUATION OF THE GENERALIZED COORDINATE. WE DERIVE NOVEL ANALYTICAL SOLUTIONS FOR THE NONLINEAR NATURAL FREQUENCY AND DISPLACEMENT TO INVESTIGATE THE EFFECTS OF ROTARY INERTIA, SHEAR DEFORMATION, PRE-TENSILE LOADS AND SLENDERNESS RATIOS ON THE BEAM. IN COMPARISON TO RESULTS ACHIEVED BY PERTURBATION TECHNIQUES, THIS STUDY DEMONSTRATES THAT A FIRST-ORDER APPROXIMATION OF HAM LEADS TO HIGHLY ACCURATE SOLUTIONS, VALID FOR A WIDE RANGE OF AMPLITUDE VIBRATIONS, OF A HIGH-ORDER STRONGLY NONLIN-EAR PROBLEM.

On Nonlinear Dynamics and Flight Control at High Angles of Attack With Uncertain Aerodynamics

In this paper we consider the flight dynamics of fighter aircraft at high angles of attack with uncertain aerodynamic coefficients. Stochastic parametric uncertainty is dealt with by employing spectral decomposition of the random variables by means of the generalized polynomial chaos expansion. We propose an optimal linear feedback strategy for the automatic pilot system to recover the aircraft from stall and provide acceptable dynamic response. Optimality of the proposed control law is proved by solving the Hamilton-Jacobi-Bellman equation and asymptotically stability of the controlled nonlinear aircraft model is guaranteed in the Lyapunov sense. Numerical results are verified with Monte-Carlo simulations.Copyright

Exploring the Nonlinear Stochastic Dynamics of an Orchard Sprayer Tower Moving Through an Irregular Terrain

In agricultural industry, the process of orchards spraying is of extreme importance to avoid losses and reduction of quality in the products. In orchards spraying process an equipment called sprayer tower is used. It consists of a reservoir and fans mounted over an articulated tower, which is supported by a vehicle suspension. Due to soil irregularities this equipment is subject to random loads, which may hamper the proper dispersion of the spraying fluid. This work presents the construction of a consistent stochastic model of uncertainties to describe the non-linear dynamics of an orchard sprayer tower. In this model, the mechanical system is described by as a multi-body with three degrees of freedom, and random loadings as a harmonic random process. Uncertainties are taken into account through a parametric probabilistic approach , where maximum entropy principle is used to specify random parameters distributions. The propagation of uncertainties through the model is computed via Monte Carlo method.

Experimental evaluation of HJB optimal controllers for the attitude dynamics of a multirotor aerial vehicle

The present paper is concerned with the design and experimental evaluation of optimal control laws for the nonlinear attitude dynamics of a multirotor aerial vehicle. Three design methods based on Hamilton-Jacobi-Bellman equation are taken into account. The first one is a linear control with guarantee of stability for nonlinear systems. The second and third are a nonlinear suboptimal control techniques. These techniques are based on an optimal control design approach that takes into account the nonlinearities present in the vehicle dynamics. The stability Proof of the closed-loop system is presented. The performance of the control system designed is evaluated via simulations and also via an experimental scheme using the Quanser 3-DOF Hover. The experiments show the effectiveness of the linear control method over the nonlinear strategy.

Method of Direct Separation of Motions Applied to a Non-ideal Electromechanical Pendulum System

This paper uses the approach of Vibrational Mechanics (VM) performing the Method of Direct Separation of Motions (MDSM) for the analysis of a non-ideal rotor mechanism with a limited power source. We employ a modification of the method to study the governing equations of a non-ideally excited electromechanical pendulum system consisting of three masses (block, rotating, pendulum) and a DC motor. The mechanism has three degrees of freedom and we derive the main equations of the slow component of motion from the initial governing equations to allow for a derivation of analytical solutions in the stability domain. The paper focuses on a purely analytical approach.

Nonlinear Identification Using Polynomial NARMAX Model and a Stability Analysis of an Aeroelastic System

This work describes the nonlinear identification applied to an aeroelastic pitch-plunge system using polynomial NARMAX model and a stability analysis. The apparatus is available and consists of a wing typical section with pitch and plunge degrees of freedom. The identification procedure aims to obtain the parameters for the mathematical model including the torsional stiffness as a quadratic polynomial function. The candidate structure to the polynomial model is obtained from discretization of a continuous-time state-space model and the predictions are obtained via the identification procedure using simulated data. The simulation is performed considering the aerodynamics with free stream velocity increased within an established velocity range which includes the flutter phenomenon. In future work, a data acquisition from the experimental apparatus will be performed. The NARMAX model indicates a polynomial function of fourth order for the nonlinearity and a stability analysis, discussed in this work, mapping the nonlinear regions.

Polynomial Chaos-based analysis of Multirotor Aerial Vehicles Model Subjected to Uncertainties

Abstract: Uncertainties are ubiquitous in mathematical equations that represent physical models and may come from unknown plant parameters or from the purposeful choice of a simplified representation of the system dynamics. In case of Multirotor Aerial Vehicles (MAVs), which have become interesting for applications where manned operations are considered inefficient and dangerous for humans, uncertainties such as inaccurate parameters, neglect of gyroscopic effect, blade flapping, as well as, wind gusts can have strong adverse effects on the system behavior. This paper uses the Polynomial Chaos Expansion method to propagate uncertainties in the multirotor model and characterize the effects over the vehicle trajectory, considering constraints on both the total thrust magnitude and the inclination of the rotor plane in the design of the position control. The Polynomial Chaos method constructs meta-models that accurately mimic the behavior of systems with uncertainty about the mean of stochastic inputs. The uncertainties are described in terms of normal distribution. The results are compared with Monte Carlo simulations.

On Chaotic Dynamics of a Double Pendulum Arm Excited by a Nonlinear Shaker Based RLC Circuit

The chaotic dynamics of a double pendulum arm coupled to a nonlinear shaker based RLC circuit through a magnetic field is studied numerically. The nonlinear term, in the circuit, is introduced by considering that the voltage of the capacitor is a nonlinear function of the instantaneous electric charge. For the identification of the response of the system various techniques, including chaos techniques as bifurcation diagrams and time histories, power spectral densities (FFT), Poincare maps and exponents of Lyapunov are used. This electromechanical system will represent a basic subsystem of any robot.Copyright