A Comparison of the Effects of Nonlinear Damping on the Free Vibration of a Single-Degree-of-Freedom System

This article concerns the free vibration of a single-degree-of-freedom (SDOF) system with three types of nonlinear damping. One system considered is where the spring and the damper are connected to the mass so that they are orthogonal, and the vibration is in the direction of the spring. It is shown that, provided the displacement is small, this system behaves in a similar way to the conventional SDOF system with cubic damping, in which the spring and the damper are connected so they act in the same direction. For completeness, these systems are compared with a conventional SDOF system with quadratic damping. By transforming all the equations of motion of the systems so that the damping force is proportional to the product of a displacement dependent term and velocity, then all the systems can be directly compared. It is seen that the system with cubic damping is worse than that with quadratic damping for the attenuation of free vibration. [DOI: 10.1115/1.4005010]

A simple method for choosing the parameters of a two degree-of-freedom tuned vibration absorber

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

Infrared degrees of freedom of Yang-Mills theory in the Schrodinger representation

We set up a new calculational framework for the Yang-Mills vacuum transition amplitude in the Schrodinger representation. After integrating out hard-mode contributions perturbatively and performing a gauge-invariant gradient expansion of the ensuing soft-mode action, a manageable saddle-point expansion for the vacuum overlap can be formulated. In combination with the squeezed approximation to the vacuum wave functional this allows for an essentially analytical treatment of physical amplitudes. Moreover, it leads to the identification of dominant and gauge-invariant classes of gauge field orbits which play the role of gluonic infrared (IR) degrees of freedom. The latter emerge as a diverse set of saddle-point solutions and are represented by unitary matrix fields. We discuss their scale stability, the associated virial theorem and other general properties including topological quantum numbers and action bounds. We then find important saddle-point solutions (most of them solitons) explicitly and examine their physical impact. While some are related to tunneling solutions of the classical Yang-Mills equation, i.e. to instantons and merons, others appear to play unprecedented roles. A remarkable new class of IR degrees of freedom consists of Faddeev-Niemi type link and knot solutions, potentially related to glueballs.

An overview on a nonideal system with three and a half degrees of freedom

The present paper studies a system comprised of two blocks connected by springs and dampers, and a DC motor with limited power supply fixed on a block, characterizing a non-ideal problem. This DC motor exciting the system causes interactions between the motor and the structure supporting it. Because of that, the non-ideal mathematical formulation of the problem has one and a half extra degree of freedom than the ideal one. A suitable choice of physical parameters leads to internal resonance conditions, that is, its natural frequencies are multiple of each other, by a known integer quantity. The purpose here is to study the dynamic behavior of the system using an analytical method based on perturbation techniques. The literature shows that the averaging method is the more flexible method concerning non-ideal problems. Summarizing, an steady state solution in amplitude and phase coordinates was obtained with averaging method showing the dependence of the structure amplitudes with the rotation frequency of the motor. Moreover, this solution shows that on of the amplitude coordinates has influence in the determination of the stationary rotation frequency. The analytical solution obtained shows the presence of the rotation frequency in expressions representing the oscillations of the structure, and the presence of amplitude coordinates in expressions describing the dynamic motion of the DC motor. These characteristics show the influence not only of the motor on structure but also of the response of the structure on dynamical behavior of the motor. Copyright © 2005 by ASME.

On the dynamic behaviour of a nonlinear system weakly connected to a linear single degree-of-freedom system

This paper discusses the dynamic behaviour of a nonlinear two degree-of-freedom system consisting of a harmonically excited linear oscillator weakly connected to a nonlinear attachment that behaves as a hardening Duffing oscillator. A system which behaves in this way could be a shaker (linear system) driving a nonlinear isolator. The mass of the nonlinear system is taken to be much less than that in the linear system and thus the nonlinear system has little effect on the dynamics of the linear system. Of particular interest is the situation when the linear natural frequency of the nonlinear system is less than the natural frequency of the linear system such that the frequency response curve of the nonlinear system bends to higher frequencies and thus interacts with the resonance frequency of the linear system. It is shown that for some values of the system parameters a complicated frequency response curve for the nonlinear system can occur; closed detached curves can appear as a part of the overall amplitude-frequency response. The reason why these detached curves appear is presented and approximate analytical expressions for the jump-up and jump-down frequencies of the system under investigation are given.

Control of Limit Cycle Oscillation in a Three Degrees of Freedom Airfoil Section Using Fuzzy Takagi-Sugeno Modeling

This work presents a strategy to control nonlinear responses of aeroelastic systems with control surface freeplay. The proposed methodology is developed for the three degrees of freedom typical section airfoil considering aerodynamic forces from Theodorsen's theory. The mathematical model is written in the state space representation using rational function approximation to write the aerodynamic forces in time domain. The control system is designed using the fuzzy Takagi-Sugeno modeling to compute a feedback control gain. It useds Lyapunov's stability function and linear matrix inequalities (LMIs) to solve a convex optimization problem. Time simulations with different initial conditions are performed using a modified Runge-Kutta algorithm to compare the system with and without control forces. It is shown that this approach can compute linear control gain able to stabilize aeroelastic systems with discontinuous nonlinearities.

Nonlinear dynamical analysis of an aeroelastic system with multi-segmented moment in the pitch degree-of-freedom

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

Compositional nutrient diagnosis of corn using the Mahalanobis distance as nutrient imbalance index

Parent, L. E., Natale, W. and Ziadi, N. 2009. Compositional nutrient diagnosis of corn using the Mahalanobis distance as nutrient imbalance index. Can. J. Soil Sci. 89: 383-390. Compositional nutrient diagnosis (CND) provides a plant nutrient imbalance index (CND - r(2)) with assumed chi(2) distribution. The Mahalanobis distance D(2), which detects outliers in compositional data sets, also has a chi(2) distribution. The objective of this paper was to compare D(2) and CND - r(2) nutrient imbalance indexes in corn (Zea mays L.). We measured grain yield as well as N, P, K, Ca, Mg, Cu, Fe, Mn, and Zn concentrations in the ear leaf at silk stage for 210 calibration sites in the St. Lawrence Lowlands [2300-2700 corn thermal units (CTU)] as well as 30 phosphorus (2300-2700 CTU; 10 sites) and 10 nitrogen (1900-2100 CTU; one site) replicated fertilizer treatments for validation. We derived CND norms as mean, standard deviation, and the inverse covariance matrix of centred log ratios (clr) for high yielding specimens (>= 9.0 Mg grain ha(-1) at 150 g H(2)O kg(-1) moisture content) in the 2300-2700 CTU zone. Using chi(2) = 17 (P < 0.05) with nine degrees of freedom (i.e., nine nutrients) as a rejection criterion for outliers and a yield threshold of 8.6 Mg ha(-1) after Cate-Nelson partitioning between low- and high-yielders in the P validation data set, D(2) misclassified two specimens compared with nine for CND -r(2). The D(2) classification was not significantly different from a chi(2) classification (P > 0.05), but the CND - r(2) classification differed significantly from chi(2) or D(2) (P < 0.001). A threshold value for nutrient imbalance could thus be derived probabilistically for conducting D(2) diagnosis, while the CND - r(2) nutrient imbalance threshold must be calibrated using fertilizer trials. In the proposed CND - D(2) procedure, D(2) is first computed to classify the specimen as possible outlier. Thereafter, nutrient indices are ranked in their order of limitation. The D(2) norms appeared less effective in the 1900-2100 CTU zone.

Notes on vibration control of a micro/macromanipulator mounted on a flexible structure

The objective of this study is to describe the design and the implementation of an experimental set-up used to study the dynamics, the experimental identification, and the active vibration control of a flexible structure mounted manipulator system. The system consists of a three-degree-of-freedom cylindrical manipulator system with a flexible link on its tip. A two-degree-of-freedom polar rigid manipulator is mounted on the flexible macromanipulator. The dynamic modelling and experimental modal analysis identification in the frequency domain are being applied to design active digital control strategies for the micro-manipulator system to damp the mechanical vibrations of the flexible structure on the tip of the macro-manipulator system.

Dual descriptions of spin-two massive particles in D=2+1 via master actions

Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)

BEM Formulations Based on Kirchhoff's Hypoyhesis to Perform Linear Bending Analysis of Plates Reinforced by Beams

In this work, are discussed two formulations of the boundary element method - BEM to perform linear bending analysis of plates reinforced by beams. Both formulations are based on the Kirchhoffs hypothesis and they are obtained from the reciprocity theorem applied to zoned plates, where each sub-region defines a beam or a stab. In the first model the problem values are defined along the interfaces and the external boundary. Then, in order to reduce the number of degrees of freedom kinematics hypothesis are assumed along the beam cross section, leading to a second formulation where the collocation points are defined along the beam skeleton, instead of being placed on interfaces. on these formulations no approximation of the generalized forces along the interface is required. Moreover, compatibility and equilibrium conditions along the interface are automatically imposed by the integral equation. Thus, these formulations require less approximation and the total number of the degrees of freedom is reduced. In the numerical examples are discussed the differences between these two BEM formulations, comparing as well the results to a well-known finite element code.

Analysis of the Coupled Stretching-Bending Problem of Stiffened Plates by a BEM Formulation Based on Reissner's Hypothesis

In this work, the plate bending formulation of the boundary element method - BEM, based on the Reissner's hypothesis, is extended to the analysis of plates reinforced by beams taking into account the membrane effects. The formulation is derived by assuming a zoned body where each sub-region defines a beam or a slab and all of them are represented by a chosen reference surface. Equilibrium and compatibility conditions are automatically imposed by the integral equations, which treat this composed structure as a single body. In order to reduce the number of degrees of freedom, the problem values defined on the interfaces are written in terms of their values on the beam axis. Initially are derived separated equations for the bending and stretching problems, but in the final system of equations the two problems are coupled and can not be treated separately. Finally are presented some numerical examples whose analytical results are known to show the accuracy of the proposed model.