Dynamic analysis for different finite element models of beams with viscoelastic damping layer

Many new viscoelastic materials have been developed recently to help improve noise and vibration levels in mechanical structures for applications in automobile and aeronautical industry. The viscoelastic layer treatment applied to solid metal structures modifies two main properties which are related to the mass distribution and the damping mechanism. The other property controlling the dynamics of a mechanical system is the stiffness that does not change much with the viscoelastic material. The model of such system is usually complex, because the viscoelastic material can exhibit nonlinear behavior, in contrast with the many available tools for linear dynamics. In this work, the dynamic behavior of sandwich beam is modeled by finite element method using different element types which are then compared with experimental results developed in the laboratory for various beams with different viscoelastic layer materials. The finite element model is them updated to help understand the effects in the damping for various natural frequencies and the trade-off between attenuation and the mass add to the structure.

Nonlinear angle control of a sectioned airfoil by using shape memory alloys

Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)

A virtual experiment for the detection of specific features in the frequency response of a coupled nonlinear and linear oscillator

This paper presents an investigation into some practical issues that may be present in a real experiment, when trying to validate the theoretical frequency response curve of a two degree-of-freedom nonlinear system consisting of coupled linear and nonlinear oscillators. Some specific features, such as detached resonance curves, have been theoretically predicted in multi degree-of-freedom nonlinear oscillators, when subject to harmonic excitation, and the system parameters have been shown to be fundamental in achieving such features. When based on a simplified model, approximate analytical expression for the frequency response curves may be derived, which may be validated by the numerical solutions. In a real experiment, however, the practical achievability of such features was previously shown to be greatly affected by small disturbances induced by gravity and inertia, which led to some solutions becoming unstable which had been predicted to be stable. In this work a practical system configuration is proposed where such effects are reduced so that the previous limitations are overcome. A virtual experiment is carried out where a detailed multi-body model of the oscillator is assembled and the effects on the system response are investigated.

On nonlinear dynamics and control of a robotic arm with chaos

Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)

Wave reflection at the end of a waveguide supported by a nonlinear spring

Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP)

Numerical and experimental investigation of a vibration system with non-ideal vibration source

An excitation force that is not influenced by the system's states is said to be an ideal energy source. In real situations, a direct and feedback coupling between the excitation source and the system must always exist. This manifestation of the law of conversation of energy is known as Sommerfeld Effect. In the case of obtaining a mathematical model for such system, additional equations are usually necessary to describe the vibration sources and their coupling with the mechanical system. In this work, a cantilever beam and a non-ideal electric DC motor that is fixed to the beam free end is analyzed. The motor has an unbalanced mass that provides excitation to the system proportional to the current applied to the motor. During the motor's coast up operation, as the excitation frequency gets closer to the beam first natural frequency and if the drive power increases further, the DC motor speed remains constant until it suddenly jumps to a much higher value (simultaneously the vibration amplitude jumps to a much lower value) upon exceeding a critical input power. It was found that the Sommerfeld effect depends on some system parameters and the motor operational procedures. These parameters are explored to avoid the resonance capture in Sommerfeld effect. Numerical simulations and experimental tests are used to help insight this dynamic behavior.

Scalar-bipolar asymptotic modules for solving (2+1)-dimensional nonlinear evolution equations with constraints

An infinite hierarchy of solvable systems of purely differential nonlinear equations is introduced within the framework of asymptotic modules. Eacy system consists of (2+1)-dimensional evolution equations for two complex functions and of quite strong differential constraints. It may be interpreted formally as an integro-differential equation in (1+1) dimensions. © 1988.

The use of nonlinear programming as a tool for maximum profit feed formulation of broilers

The purpose of this study was to compare linear and nonlinear programming models for feed formulation, for maximum profit, considering the real variation in the prices of the corn, soybean meal and broilers during the period from January of 2008 to October of 2009, in the São Paulo State, Brazil. For the nonlinear formulation model, it was considered the following scenarios of prices: a) the minimum broiler price and the maximum prices of the corn and soybean meal during the period, b) the mean prices of the broiler, corn and soybean meal in the period and c) the maximum broiler price and the minimum prices of the corn and soybean meal, in the considered period; while for the linear formulation model, it was considered just the prices of the corn and the soybean. It was used the Practical Program for Feed Formulation 2.0 for the diets establishment. A total of 300 Cobb male chicks were randomly assigned to the 4 dietary treatments with 5 replicate pens of 15 chicks each. The birds were fed with a starter diet until 21 d and a grower diet from 22 to 42 d of age, and they had ad libitum access to feed and water, on floor with wood shavings as litter. The broilers were raised in an environmentally-controlled house. Body weight, body weight gain, feed intake, feed conversion ratio and profitability (related to the prices variation of the broilers and ingredients) were obtained at 42 d of age. It was found that the broilers fed with the diet formulated with the linear model presented the lowest feed intake and feed conversion ratio as compared with the broilers fed with diets from nonlinear formulation models. There were no significant differences in body weight and body weight gain among the treatments. Nevertheless, the profitabilities of the diets from the nonlinear model were significantly higher than that one from the linear formulation model, when the corn and soybean meal prices were near or below their average values for the studied period, for any broiler chicken price.

Accuracy of nonlinear feed formulation for broiler chickens: maximising broiler profit

The modeling technique is simple, useful and practical to calculate optimum nutrient density to maximize profit margins, using nonlinear programming by predictive broiler performance. To demonstrate the influence of the broiler price could interact with nutrient density, the experiment aimed to define the quadratic equations for consumption and weight gain, based on modeling, to be applied to nonlinear programming, according to sex (male and female) in the starter (1 to 21 days), grower (22 to 42 days) and finisher phases (43 to 56 days). The experimental design was a randomized, totaling 6 treatments [energy levels of 2800, 2900, 3000, 3100, 3200 and 3300kcal AME/kg with constant nutrient : AME (Apparent Metabolizable Energy)] with 4 replicates and 10 birds per plot, using the program free download PPFR Excel workbook for feed formulation (http://www.foa.unesp.br/downloads/file_detalhes.asp?CatCod=4&SubCatCod=138&FileCod=1677). Data from this trial confirmed that there was a significant relationship between feed intake and total energy consumption of the diet, in which feed intake was increased or decreased simply to keep the amount of energy, with a constant rate of nutrient : AME. Therefore, the data support that if the essential dietary nutrients are kept in proportion to the energy density of the diet, according to the appropriate requirements (male / female) of broilers, the weight and feed conversion are significantly (P<0.05) favored by increasing the energy density of the diet. Thus, it enables the application of models for maximum profit (nonlinear formulation), to estimate the proportion of weight gain most appropriate according to the price paid by the market.

Caracterização experimental de sistemas mecânicos com comportamento não-linear

Pós-graduação em Engenharia Mecânica - FEIS

Monitoramento de integridade estrutural e de sistemas utilizando dispositivos de baixo custo

Pós-graduação em Engenharia Mecânica - FEB

Simulations of the Frequency Modulated Atomic Force Microscope (FM-AFM) nonlinear control system

The Frequency Modulated - Atomic Force Microscope (FM-AFM) is apowerful tool to perform surface investigation with true atomic resolution. The controlsystem of the FM-AFM must keep constant both the frequency and amplitude ofoscillation of the microcantilever during the scanning process of the sample. However,tip and sample interaction forces cause modulations in the microcantilever motion.A Phase-Locked Loop (PLL) is used as a demodulator and to generate feedback signalto the FM-AFM control system. The PLL performance is vital to the FM-AFMperformace since the image information is in the modulated microcantilever motion.Nevertheless, little attention is drawn to PLL performance in the FM-AFM literature.Here, the FM-AFM control system is simulated, comparing the performancefor di erent PLL designs.

Nonlinear ball and beam control system identification

The Ball and Beam system is a common didactical experiment in control laboratories that can be used to illustrate many different closed-loop control techniques. The plant itself is subjected to many nonlinear effects, which the most common comes from the relative motion between the ball and the beam. The modeling process normally uses the lagrangean formulation. However, many other nonlinear effects, such as non-viscous friction, beam flexibility, ball slip, actuator elasticity, collisions at the end of the beam, to name a few, are present. Besides that, the system is naturally unstable. In this work, we analyze a subset of these characteristics, in which the ball rolls with slipping and the friction force between the ball and the beam is non-viscous (Coulomb friction). Also, we consider collisions at the ends of the beam, the actuator consists of a (rubber made) belt attached at the free ends of the beam and connected to a DC motor. The model becomes, with those nonlinearities, a differential inclusion system. The elastic coefficients of the belt are experimentally identified, as well as the collision coefficients. The nonlinear behavior of the system is studied and a control strategy is proposed.