具有局部非线性元件的结构动力分析

谐波增量平衡法在描述非线性力时计及多谐分量,是处理强非线性的一个有效方法.在本文中,此法被推广于分析局部非线性结构的稳态响应.被分析的结构分解为若干子结构,所有非线性元件均位于子结构的分界面上.系统的响应用谐波增量平衡法(Incremental Harmonic Balance Method,简称I.H.B法)结合F.F.T.(快速福里哀变换)技术与状态空间的模态综合法分析之.

Internal resonance of an L-shaped beam with a limit stop .1. Free vibration

Real-life structures often possess piecewise stiffness because of clearances or interference between subassemblies. Such an aspect can alter a system's fundamental free vibration response and leads to complex mode interaction. The free vibration behaviour of an L-shaped beam with a limit stop is analyzed by using the frequency response function and the incremental harmonic balance method. The presence of multiple internal resonances, which involve interactions among the first five modes and are extremely complex, have been discovered by including higher harmonics in the analysis. The results show that mode interaction may occur if the higher harmonics of a vibration mode are close to the natural frequency of a higher mode. The conditions for the existence of internal resonance are explored, and it is shown that a prerequisite is the presence of bifurcation points in the form of intersecting backbone curves. A method to compute such intersections by using only one harmonic in the free vibration solution is proposed. (C) 1996 Academic Press Limited

Nonlinear Dynamic Responses of the Tensioned Tether under Parametric Excitations

The nonlinear dynamic responses of the tensioned tether subjected to combined surge and heave motions of floating platform are investigated using 2-D nonlinear beam model. It is shown that if the transverse-axial coupling of nonlinear beam model and the combined surge-heave motions of platform are considered, the governing equation is not Mathieu equation any more, it becomes nonlinear Hill equation. The Hill stability chart is obtained by using the Hill's infinite determinant and harmonic balance method. A parameter M, which is the function of tether length, the surge and heave amplitude of platform, is defined. The Hill stability chart is obviously different from Mathieu stability chart which is the specific case as M=0. Some case studies are performed by employing linear and nonlinear beam model respectively. It can be found that the results differences between nonlinear and linear model are apparent.

Propriedade rural, posse e meio ambiente: uma ponderação harmoniosa

A presente tese tem por objetivo defender, sob a visão do direito civil-constitucional e da função promocional do direito, a inter-relação entre os direitos de posse, propriedade e do meio ambiente e a possibilidade de uma ponderação harmoniosa em caso de desequilíbrio entre esses direitos. Utiliza-se para tanto a dimensão analítica, empírica e normativa. A dimensão analítica tem por objetivo investigar os conceitos jurídicos envolvidos na pesquisa, especialmente em relação à propriedade e à sua função socioambiental. A relação entre tais conceitos sobressai através da análise da função socioambiental da propriedade, da posse enfatizando-se os aspectos da legislação ambiental. O direito fundamental ao meio ambiente é estudado como direito e dever de todos conforme disposto no art. 225 da Constituição de 1988, e, nesse ponto, diretamente eficaz nas relações interprivadas. Aborda-se, na dimensão empírica e normativa essencialmente aspectos práticos, com foco na jurisprudência, especialmente do Supremo Tribunal Federal (STF) e do Superior Tribunal de Justiça (STJ). A ponderação harmoniosa entre a propriedade, a posse e o meio ambiente, busca o equilíbrio na efetivação desses direitos, inclusive mediante a aplicação dos princípios do direito econômico. Por meio da ponderação, é possível alcançar, de forma mais eficiente do que o modelo tradicional de subsunção, uma resposta adequada e fundamentada para os casos difíceis, especialmente na efetivação e na restauração do equilíbrio entre a posse, a propriedade e o meio ambiente quando esses princípios, no caso concreto, colidem uns com os outros. Sobretudo, pretende-se concretizar os direitos fundamentais segundo exigências do pós-positivismo, por meio da aproximação entre o Direito e a Ética, com o fim de se alcançar a Justiça para o caso concreto.

Range of validity of the method of averaging

Sufficient conditions are derived for the validity of approximate periodic solutions of a class of second order ordinary nonlinear differential equations. An approximate solution is defined to be valid if an exact solution exists in a neighborhood of the approximation.

Two classes of validity criteria are developed. Existence is obtained using the contraction mapping principle in one case, and the Schauder-Leray fixed point theorem in the other. Both classes of validity criteria make use of symmetry properties of periodic functions, and both classes yield an upper bound on a norm of the difference between the approximate and exact solution. This bound is used in a procedure which establishes sufficient stability conditions for the approximated solution.

Application to a system with piecewise linear restoring force (bilinear system) reveals that the approximate solution obtained by the method of averaging is valid away from regions where the response exhibits vertical tangents. A narrow instability region is obtained near one-half the natural frequency of the equivalent linear system. Sufficient conditions for the validity of resonant solutions are also derived, and two term harmonic balance approximate solutions which exhibit ultraharmonic and subharmonic resonances are studied.

A new low-power highly linear mixer design using differential derivative superposition

This paper presents the analysis and design of a new low power and highly linear mixer topology based on a newly reported differential derivative superposition method. Volterra series and harmonic balance are employed to investigate its linearisation mechanism and to optimise the design. A prototype mixer has been designed and is being implemented in 0.18μm CMOS technology. Simulation shows this mixer achieves 19.7dBm IIP3 with 10.5dB conversion gain, 13.2dB noise figure at 2.4GHz and only 3.8mW power consumption. This performance is competitive with already reported mixers.

Nonlinear piezoelectricity in electroelastic energy harvesters: Modeling and experimental identification

We propose and experimentally validate a first-principles based model for the nonlinear piezoelectric response of an electroelastic energy harvester. The analysis herein highlights the importance of modeling inherent piezoelectric nonlinearities that are not limited to higher order elastic effects but also include nonlinear coupling to a power harvesting circuit. Furthermore, a nonlinear damping mechanism is shown to accurately restrict the amplitude and bandwidth of the frequency response. The linear piezoelectric modeling framework widely accepted for theoretical investigations is demonstrated to be a weak presumption for near-resonant excitation amplitudes as low as 0.5 g in a prefabricated bimorph whose oscillation amplitudes remain geometrically linear for the full range of experimental tests performed (never exceeding 0.25% of the cantilever overhang length). Nonlinear coefficients are identified via a nonlinear least-squares optimization algorithm that utilizes an approximate analytic solution obtained by the method of harmonic balance. For lead zirconate titanate (PZT-5H), we obtained a fourth order elastic tensor component of c1111p =-3.6673× 1017 N/m2 and a fourth order electroelastic tensor value of e3111 =1.7212× 108 m/V. © 2010 American Institute of Physics.

Exploring figures of merit associated with the suboptimum operation of class-E power amplifiers

Closed-form design equations for the operation of a class-E amplifier for zero switch voltage slope and arbitrary duty cycle are derived. This approach allows an additional degree of freedom in the design of class-E amplifiers which are normally designed for 50 duty ratio. The analysis developed permits the selection of non-unique solutions where amplifier efficiency is theoretically 100 but power output capability is less than that the 50 duty ratio case would permit. To facilitate comparison between 50 (optimal) and non-50 (suboptimal) duty ratio cases, each important amplifier parameter is normalised to its corresponding optimum operation value. It is shown that by choosing a non-50 suboptimal solution, the operating frequency of a class-E amplifier can be extended. In addition, it is shown that by operating the amplifier in the suboptimal regime, other amplifier parameters, for example, transistor output capacitance or peak switch voltage, can be included along with the standard specification criteria of output power, DC supply voltage and operating frequency as additional input design specifications. Suboptimum class-E operation may have potential advantages for monolithic microwave integrated circuit realisation as lower inductance values (lower series resistance, higher self-resonance frequency, less area) may be required when compared with the results obtained for optimal class-E amplifier synthesis. The theoretical analysis conducted here was verified by harmonic balance simulation, with excellent agreement between both methods. © The Institution of Engineering and Technology 2007.

Convergence acceleration of the doubly periodic Green's function for the analysis of thin wire arrays

A method is proposed to accelerate the evaluation of the Green's function of an infinite double periodic array of thin wire antennas. The method is based on the expansion of the Green's function into series corresponding to the propagating and evanescent waves and the use of Poisson and Kummer transformations enhanced with the analytic summation of the slowly convergent asymptotic terms. Unlike existing techniques the procedure reported here provides uniform convergence regardless of the geometrical parameters of the problem or plane wave excitation wavelength. In addition, it is numerically stable and does not require numerical integration or internal tuning parameters, since all necessary series are directly calculated in terms of analytical functions. This means that for nonlinear problem scenarios that the algorithm can be deployed without run time intervention or recursive adjustment within a harmonic balance engine. Numerical examples are provided to illustrate the efficiency and accuracy of the developed approach as compared with the Ewald method for which these classes of problems requires run time splitting parameter adaptation.

Analysis and Design of Class-E3F and Transmission-Line Class-E3F2 Power Amplifiers

In this paper, analysis and synthesis approach for two new variants within the Class-EF power amplifier (PA) family is elaborated. These amplifiers are classified here as Class-E3 F2 and transmission-line (TL) Class-E3 F 2. The proposed circuits offer means to alleviate some of the major issues faced by existing topologies such as substantial power losses due to the parasitic resistance of the large inductor in the Class-EF load network and deviation from ideal Class-EF operation due to the effect of device output inductance at high frequencies. Both lumped-element and transmission-line load networks for the Class-E 3 F PA are described. The load networks of the Class-E3 F and TL Class-E 3 F2amplifier topologies developed in this paper simultaneously satisfy the Class-EF optimum impedance requirements at fundamental frequency, second, and third harmonics as well as simultaneously providing matching to the circuit optimum load resistance for any prescribed system load resistance. Optimum circuit component values are analytically derived and validated by harmonic balance simulations. Trade-offs between circuit figures of merit and component values with some practical limitations being considered are discussed. © 2010 IEEE.

On Passive Intermodulation Test of Analog and Digital Systems

This paper presents initial results of evaluating suitability of the conventional two-tone CW passive intermodulation (PIM) test for characterization of modulated signal distortion by passive nonlinearities in base station antennas and RF front-end. A comprehensive analysis of analog and digitally modulated waveforms in the transmission lines with weak distributed nonlinearity has been performed using the harmonic balance analysis and X-parameters in Advanced Design System (ADS) simulator. The nonlinear distortion metrics used in the conventional two-tone CW PIM test have been compared with the respective spectral metrics applied to the modulated waveforms, such as adjacent channel power ratio (ACPR) and error vector magnitude (EVM). It is shown that the results of two-tone CW PIM tests are consistent with the metrics used for assessment of signal integrity of both analog and digitally modulated waveforms.

Analysis of multirate behavior in electronic systems

Esta tese insere-se na área da simulação de circuitos de RF e microondas, e visa o estudo de ferramentas computacionais inovadoras que consigam simular, de forma eficiente, circuitos não lineares e muito heterogéneos, contendo uma estrutura combinada de blocos analógicos de RF e de banda base e blocos digitais, a operar em múltiplas escalas de tempo. Os métodos numéricos propostos nesta tese baseiam-se em estratégias multi-dimensionais, as quais usam múltiplas variáveis temporais definidas em domínios de tempo deformados e não deformados, para lidar, de forma eficaz, com as disparidades existentes entre as diversas escalas de tempo. De modo a poder tirar proveito dos diferentes ritmos de evolução temporal existentes entre correntes e tensões com variação muito rápida (variáveis de estado activas) e correntes e tensões com variação lenta (variáveis de estado latentes), são utilizadas algumas técnicas numéricas avançadas para operar dentro dos espaços multi-dimensionais, como, por exemplo, os algoritmos multi-ritmo de Runge-Kutta, ou o método das linhas. São também apresentadas algumas estratégias de partição dos circuitos, as quais permitem dividir um circuito em sub-circuitos de uma forma completamente automática, em função dos ritmos de evolução das suas variáveis de estado. Para problemas acentuadamente não lineares, são propostos vários métodos inovadores de simulação a operar estritamente no domínio do tempo. Para problemas com não linearidades moderadas é proposto um novo método híbrido frequência-tempo, baseado numa combinação entre a integração passo a passo unidimensional e o método seguidor de envolvente com balanço harmónico. O desempenho dos métodos é testado na simulação de alguns exemplos ilustrativos, com resultados bastante promissores. Uma análise comparativa entre os métodos agora propostos e os métodos actualmente existentes para simulação RF, revela ganhos consideráveis em termos de rapidez de computação.

The characteristics of a nonlinear vibration neutralizer

This paper concerns an investigation into the use of cubic nonlinearity in a vibration neutralizer to improve its effectiveness. It is assumed that the frequency of the harmonic excitation is well above the resonance frequency of the machine to which the neutralizer is attached, and that the machine acts as a simple mass. It is also assumed that the response of the system is predominantly at the harmonic excitation frequency of the machine. The harmonic balance method is used to analyze the system. It is shown how the nonlinearity has the effect of shifting the resonant peak to a higher frequency away from the tuned frequency of the neutralizer so that the device is robust to mistune. In a linear neutralizer this can only be achieved by adding mass to the neutralizer, so the nonlinearity has a similar effect to that of adding mass. Some characteristic features are highlighted, and the effects of the system parameters on the performance are discussed. It is shown that, for a particular combination of the system parameters, the effect of the nonlinearity is also to increase the bandwidth of the device compared to the linear neutralizer with similar mass and damping. Some approximate expressions are derived, which facilitate insight into the parameters which influence the dynamics of the system. The results are validated by some experimental work. (c) 2012 Elsevier Ltd. All rights reserved.

On the undamped free vibration of a mass interacting with a Hertzian contact stiffness

Three methods are used to determine the natural frequency of undamped free vibration of a mass interacting with a Hertzian contact stiffness. The exact value is determined using the first integral of motion. The harmonic balance method is used on a transformed equation for an approximate solution, and the multiple scales method is used on an approximate equation. The maximum initial displacement avoiding contact loss is also determined, and the corresponding exact natural frequency is also obtained analytically. The methods are evaluated by studying the free vibration of an elastic sphere on a flat rigid surface. © 2011 Elsevier Ltd © 2011 Elsevier Ltd. All rights reserved.

On the Chaotic Suppression of Both Ideal and Non-ideal Duffing Based Vibrating Systems, Using a Magnetorheological Damper

In this paper the dynamics of the ideal and non-ideal Duffing oscillator with chaotic behavior is considered. In order to suppress the chaotic behavior and to control the system, a control signal is introduced in the system dynamics. The control strategy involves the application of two control signals, a nonlinear feedforward control to maintain the controlled system in a periodic orbit, obtained by the harmonic balance method, and a state feedback control, obtained by the state dependent Riccati equation, to bring the system trajectory into the desired periodic orbit. Additionally, the control strategy includes an active magnetorheological damper to actuate on the system. The control force of the damper is a function of the electric current applied in the coil of the damper, that is based on the force given by the controller and on the velocity of the damper piston displacement. Numerical simulations demonstrate the effectiveness of the control strategy in leading the system from any initial condition to a desired orbit, and considering the mathematical model of the damper (MR), it was possible to control the force of the shock absorber (MR), by controlling the applied electric current in the coils of the damper. © 2012 Foundation for Scientific Research and Technological Innovation.