On non-ideal and non-linear portal frame dynamics analysis using bogoliubov averaging method

We apply the Bogoliubov Averaging Method to the study of the vibrations of an elastic foundation, forced by a Non-ideal energy source. The considered model consists of a portal plane frame with quadratic nonlinearities, with internal resonance 1:2, supporting a direct current motor with limited power. The non-ideal excitation is in primary resonance in the order of one-half with the second mode frequency. The results of the averaging method, plotted in time evolution curve and phase diagrams are compared to those obtained by numerically integrating of the original differential equations. The presence of the saturation phenomenon is verified by analytical procedures.

BEM/FEM non-linear model applied to transient analysis with viscous damping

In this article a two-dimensional transient boundary element formulation based on the mass matrix approach is discussed. The implicit formulation of the method to deal with elastoplastic analysis is considered, as well as the way to deal with viscous damping effects. The time integration processes are based on the Newmark rhoand Houbolt methods, while the domain integrals for mass, elastoplastic and damping effects are carried out by the well known cell approximation technique. The boundary element algebraic relations are also coupled with finite element frame relations to solve stiffened domains. Some examples to illustrate the accuracy and efficiency of the proposed formulation are also presented.

Non-linear analysis of laminated metal matrix composites by an integrated micro/macro-mechanical model

The present paper describes an integrated micro/macro mechanical study of the elastic-viscoplastic behavior of unidirectional metal matrix composites (MMC). The micromechanical analysis of the elastic moduli is based on the Composites Cylinder Assemblage model (CCA) with comparisons also draw with a Representative Unit Cell (RUC) technique. These "homogenization" techniques are later incorporated into the Vanishing Fiber Diameter (VFD) model and a new formulation is proposed. The concept of a smeared element procedure is employed in conjunction with two different versions of the Bodner and Partom elastic-viscoplastic constitutive model for the associated macroscopic analysis. The formulations developed are also compared against experimental and analytical results available in the literature.

Numerical study of Petrov-Galerkin formulations for the shallow water wave equations

The behavior of Petrov-Galerkin formulations for shallow water wave equations is evaluated numerically considering typical one-dimensional propagation problems. The formulations considered here use stabilizing operators to improve classical Galerkin approaches. Their advantages and disadvantages are pointed out according to the intrinsic time scale (free parameter) which has a particular importance in this kind of problem. The influence of the Courant number and the performance of the formulation in dealing with spurious oscillations are adressed.

Non-Linear Unsteady Aerodynamic Response Approximation Using Multi-Layer Functionals

Non-linear functional representation of the aerodynamic response provides a convenient mathematical model for motion-induced unsteady transonic aerodynamic loads response, that accounts for both complex non-linearities and time-history effects. A recent development, based on functional approximation theory, has established a novel functional form; namely, the multi-layer functional. For a large class of non-linear dynamic systems, such multi-layer functional representations can be realised via finite impulse response (FIR) neural networks. Identification of an appropriate FIR neural network model is facilitated by means of a supervised training process in which a limited sample of system input-output data sets is presented to the temporal neural network. The present work describes a procedure for the systematic identification of parameterised neural network models of motion-induced unsteady transonic aerodynamic loads response. The training process is based on a conventional genetic algorithm to optimise the network architecture, combined with a simplified random search algorithm to update weight and bias values. Application of the scheme to representative transonic aerodynamic loads response data for a bidimensional airfoil executing finite-amplitude motion in transonic flow is used to demonstrate the feasibility of the approach. The approach is shown to furnish a satisfactory generalisation property to different motion histories over a range of Mach numbers in the transonic regime.

Control of Structures with Cubic and Quadratic Non-Linearities with Time Delay Consideration

This paper studies the effect of time delay on the active non-linear control of dynamically loaded flexible structures. The behavior of non-linear systems under state feedback control, considering a fixed time delay for the control force, is investigated. A control method based on non-linear optimal control, using a tensorial formulation and state feedback control is used. The state equations and the control forces are expressed in polynomial form and a performance index, quadratic in both state vector and control forces, is used. General polynomial representations of the non-linear control law are obtained and implemented for control algorithms up to the fifth order. This methodology is applied to systems with quadratic and cubic non-linearities. Strongly non-linear systems are tested and the effectiveness of the control system including a delay for the application of control forces is discussed. Numerical results indicate that the adopted control algorithm can be efficient for non-linear systems, chiefly in the presence of strong non-linearities but increasing time delay reduces the efficiency of the control system. Numerical results emphasize the importance of considering time delay in the project of active structural control systems.

Analysis of Regular and Irregular Dynamics of a Non Ideal Gear Rattling Problem

This paper presents a study on the dynamics of the rattling problem in gearboxes under non-ideal excitation. The subject has being analyzed by a number of authors such as Karagiannis and Pfeiffer (1991), for the ideal excitation case. An interesting model of the same problem by Moon (1992) has been recently used by Souza and Caldas (1999) to detect chaotic behavior. We consider two spur gears with different diameters and gaps between the teeth. Suppose the motion of one gear to be given while the motion of the other is governed by its dynamics. In the ideal case, the driving wheel is supposed to undergo a sinusoidal motion with given constant amplitude and frequency. In this paper, we consider the motion to be a function of the system response and a limited energy source is adopted. Thus an extra degree of freedom is introduced in the problem. The equations of motion are obtained via a Lagrangian approach with some assumed characteristic torque curves. Next, extensive numerical integration is used to detect some interesting geometrical aspects of regular and irregular motions of the system response.

O ajuste de funções matemáticas a dados experimentais

The least square method is analyzed. The basic aspects of the method are discussed. Emphasis is given in procedures that allow a simple memorization of the basic equations associated with the linear and non linear least square method, polinomial regression and multilinear method.

Thermodynamic study of the solubility of sodium naproxen in some ethanol + water mixtures

By using the van't Hoff and Gibbs equations the apparent thermodynamic functions Gibbs energy, enthalpy, and entropy of solution for sodium naproxen in ethanol + water cosolvent mixtures, were evaluated from solubility data determined at temperatures from (278.15 to 308.15) K. The drug solubility was greatest in neat water and lowest in neat ethanol at all the temperatures studied. By means of non-linear enthalpy-entropy compensation analysis, it follows that the dissolution process of this drug in ethanol-rich mixtures is entropy-driven, whereas, in water-rich mixtures the process is enthalpy-driven.

Thermodynamic study of the solubility of triclocarban in ethanol + propylene glycol mixtures

By using the van't Hoff and Gibbs equations the apparent thermodynamic functions Gibbs energy, enthalpy, and entropy of solution for triclocarban in ethanol + propylene glycol mixtures were evaluated from solubility data determined at temperatures from (293.15 to 313.15) K. The drug solubility was greatest in the mixture with 0.60 in mass fraction of ethanol and lowest in neat propylene glycol at almost all the temperatures studied. Non-linear enthalpy-entropy compensation is found indicating apparently different mechanisms of the solution process according to the mixtures composition.

The transcendence of time in the epistemology of observation from a phenomenological standpoint

In this article I deal with time as a notion of epistemological content associated though with the notion of a subjective consciousness co-constitutive of physical reality. In this phenomenologically grounded approach I attempt to establish a 'metaphysical' aspect of time, within a strictly epistemological context, in the sense of an underlying absolute subjectivity which is non-objectifiable within objective temporality and thus non-susceptible of any ontological designation. My arguments stem, on the one hand, from a version of quantum-mechanical theory (History Projection Operator theory, HPO theory) in view of its formal treatment of two different aspects of time within a quantum context. The discrete, partial-ordering properties (the notions of before and after) and the dynamical-parameter properties reflected in the wave equations of motion. On the other hand, to strengthen my arguments for a transcendental factor of temporality, I attempt an interpretation of some relevant conclusions in the work of J. Eccles ([5]) and of certain results of experimental research of S. Deahaene et al. ([2]) and others.

Substitution-Newton-Raphson method applied to the modeling of a vapour compression refrigeration system using different representations of the thermodynamic properties of R-134a

This paper gives a detailed presentation of the Substitution-Newton-Raphson method, suitable for large sparse non-linear systems. It combines the Successive Substitution method and the Newton-Raphson method in such way as to take the best advantages of both, keeping the convergence features of the Newton-Raphson with the low requirements of memory and time of the Successive Substitution schemes. The large system is solved employing few effective variables, using the greatest possible part of the model equations in substitution fashion to fix the remaining variables, but maintaining the convergence characteristics of the Newton-Raphson. The methodology is exemplified through a simple algebraic system, and applied to a simple thermodynamic, mechanical and heat transfer modeling of a single-stage vapor compression refrigeration system. Three distinct approaches for reproducing the thermodynamic properties of the refrigerant R-134a are compared: the linear interpolation from tabulated data, the use of polynomial fitted curves and the use of functions derived from the Helmholtz free energy.

Reference values for lung function tests: I. Static volumes

Static lung volume (LV) measurements have a number of clinical and research applications; however, no previous studies have provided reference values for such tests using a healthy sample of the adult Brazilian population. With this as our main purpose, we prospectively evaluated 100 non-smoking subjects (50 males and 50 females), 20 to 80 years old, randomly selected from more than 8,000 individuals. Gender-specific linear prediction equations were developed by multiple regression analysis with total lung capacity (TLC), functional residual capacity (FRC), residual volume (RV), RV/TLC ratio and inspiratory capacity (IC) as dependent variables, and with age, height, weight, lean body mass and indexes of physical fitness as independent ones. Simpler demographic and anthropometric variables were as useful as more complex measurements in predicting LV values, independent of gender and age (R2 values ranging from 0.49 to 0.78, P<0.001). Interestingly, prediction equations from North American and European studies overestimated the LV at low volumes and underestimated them at high volumes (P<0.05). Our results, therefore, provide a more appropriate frame of reference to evaluate the normalcy of static lung volume values in Brazilian males and females aged 20 to 80 years.

Reference values for lung function tests: II. Maximal respiratory pressures and voluntary ventilation

The strength of the respiratory muscles can be evaluated from static measurements (maximal inspiratory and expiratory pressures, MIP and MEP) or inferred from dynamic maneuvers (maximal voluntary ventilation, MVV). Although these data could be suitable for a number of clinical and research applications, no previous studies have provided reference values for such tests using a healthy, randomly selected sample of the adult Brazilian population. With this main purpose, we prospectively evaluated 100 non-smoking subjects (50 males and 50 females), 20 to 80 years old, selected from more than 8,000 individuals. Gender-specific linear prediction equations for MIP, MEP and MVV were developed by multiple regression analysis: age and, secondarily, anthropometric measurements explained up to 56% of the variability of the dependent variables. The most cited previous studies using either Caucasian or non-Caucasian samples systematically underestimated the observed values of MIP (P<0.05). Interestingly, the self-reported level of regular physical activity and maximum aerobic power correlates strongly with both respiratory and peripheral muscular strength (knee extensor peak torque) (P<0.01). Our results, therefore, provide a new frame of reference to evaluate the normalcy of some useful indexes of respiratory muscle strength in Brazilian males and females aged 20 to 80.

Reference values for lung function tests: III. Carbon monoxide diffusing capacity (transfer factor)

Carbon monoxide diffusing capacity (DLCO) or transfer factor (TLCO) is a particularly useful test of the appropriateness of gas exchange across the lung alveolocapillary membrane. With the purpose of establishing predictive equations for DLCO using a non-smoking sample of the adult Brazilian population, we prospectively evaluated 100 subjects (50 males and 50 females aged 20 to 80 years), randomly selected from more than 8,000 individuals. Gender-specific linear prediction equations were developed by multiple regression analysis with single breath (SB) absolute and volume-corrected (VA) DLCO values as dependent variables. In the prediction equations, age (years) and height (cm) had opposite effects on DLCOSB (ml min-1 mmHg-1), independent of gender (-0.13 (age) + 0.32 (height) - 13.07 in males and -0.075 (age) + 0.18 (height) + 0.20 in females). On the other hand, height had a positive effect on DLCOSB but a negative one on DLCOSB/VA (P<0.01). We found that the predictive values from the most cited studies using predominantly Caucasian samples were significantly different from the actually measured values (P<0.05). Furthermore, oxygen uptake at maximal exercise (VO2max) correlated highly to DLCOSB (R = 0.71, P<0.001); this variable, however, did not maintain an independent role to explain the VO2max variability in the multiple regression analysis (P>0.05). Our results therefore provide an original frame of reference for either DLCOSB or DLCOSB/VA in Brazilian males and females aged 20 to 80 years, obtained from the standardized single-breath technique.