A novel nonlinear approach to suppress resonant vibrations

A novel approach to suppress resonant vibration is presented by employing a single degree of freedom transmissibility system which utilizes a nonlinear damping element. Studies have shown that the nonlinear damping element can reduce the output energy at the driving frequency and at the same time spread the output signal energy over a wider range of harmonics. It will also be shown that the reduction becomes larger as the nonlinear damping characteristic gets stronger and in most cases, the power at the harmonics in the output spectrum will be much less if the nonlinear damping characteristic is an odd function. Hence, an odd polynomial nonlinear damping element can be introduced between the incoming signal and the structure of interest to suppress resonant vibration. An expression is derived to express the transmitted force spectrum in terms of the nonlinear generalized frequency response functions, to clearly show how the energy, at the excitation frequency, is modified by the nonlinearity

Comparisons between harmonic balance and nonlinear output frequency response function in nonlinear system analysis

By using the Duffing oscillator as a case study, this paper shows that the harmonic components in the nonlinear system response to a sinusoidal input calculated using the Nonlinear Output Frequency Response Functions (NOFRFs) are one of the solutions obtained using the Harmonic Balance Method (HBM). A comparison of the performances of the two methods shows that the HBM can capture the well-known jump phenomenon, but is restricted by computational limits for some strongly nonlinear systems and can fail to provide accurate predictions for some harmonic components. Although the NOFRFs cannot capture the jump phenomenon, the method has few computational restrictions. For the nonlinear damping systems, the NOFRFs can give better predictions for all the harmonic components in the system response than the HBM even when the damping system is strongly nonlinear

The parametric characteristics of frequency response functions for nonlinear systems

The characteristics of the frequency response functions of nonlinear systems can be revealed and analyzed through the analysis of the parametric characteristics of these functions. To achieve these objectives, a new operator is defined, and several fundamental and important results about the parametric characteristics of the frequency response functions of nonlinear systems are developed. These theoretical results provide a significant and novel insight into the frequency domain characteristics of nonlinear systems and circumvent a large amount of complicated integral and symbolic calculations which have previously been required to perform nonlinear system frequency domain analysis. Several new results for the analysis and synthesis of nonlinear systems are also developed. Examples are included to illustrate potential applications of the new results

Analytical study of the frequency response function of a nonlinear spring damper system

A spring damper system with a nonlinear damping element is investigated using the Volterra series method to study the system frequency response function (FRF) characteristics. The relationship between the FRF and the characteristic parameters of the nonlinear damper is determined to produce an analytical description for the system FRF. Simulation studies are used to verify the theoretical analysis. These results provide an important basis for the FRF based analysis and design of nonlinear spring damper systems in the frequency domain

A new approach to nonlinear feedback control for suppressing periodic disturbances: Part 2. A Case Study

In part 1 of this paper some fundamental theoretical results for the design of a nonlinear feedback controller to suppress periodic exogenous disturbances were developed based on the frequency domain theory of nonlinear systems, and a general procedure for the controller design was proposed. In this study, Part 2 of the paper, the new approach and the theoretical results in Part 1 are demonstrated using a case study based on the design of an active vibration control system. Simulation results are given to illustrate the effectiveness of the new method and the advantage of the nonlinear feedback controller

Suppressing resonant vibrations using nonlinear springs and dampers

The energy entering the resonant region of a system can be significantly reduced by introducing designed nonlinearities into the system. The basic choice of the nonlinearity can be either a nonlinear spring element or a nonlinear damping element. A numerical algorithm to compute and compare the energy reduction produced by these two types of designed elements is proposed in this study. Analytical results are used to demonstrate the procedure. The numerical results indicate that the designed nonlinear damping element produces low levels of energy at the higher order harmonics and no bifurcations in the system output response. In contrast the nonlinear spring based designs induce significant energy at the harmonics and can produce bifurcation behaviour. The conclusions provide an important basis for the design of nonlinear materials and nonlinear engineering systems

A new approach to nonlinear feedback control for suppressing periodic disturbances: Part 1. Fundamental Theory

A new nonlinear feedback control approach is proposed in the present study to suppress periodic exogenous disturbances based on a frequency domain theory of nonlinear systems. In Part 1 of this paper, a series of fundamental theoretical results and techniques are established. It is shown that a low order nonlinear feedback may be sufficient for some control problems. A general procedure is then proposed for controller design. The new approach is demonstrated by a case study on the design of an active vibration control system in Part 2. Theoretical analysis and simulation results verify the effectiveness of the new results

A Guide to the Zygotic Embryo Culture of Coconut Palms (Cocos nucifera L.)

Crop Production/Industries,

Model structure detection and system identification of metal rubber devices

Metal rubber (MR) devices, a new wire mesh material, have been extensively used in recent years due to several unique properties especially in adverse environments. Although many practical studies have been completed, the related theoretical research on metal rubber is still in its infancy. In this paper, a semi-constitutive dynamic model that involves nonlinear elastic stiffness, nonlinear viscous damping and bilinear hysteresis Coulomb damping is adopted to model MR devices. After approximating the bilinear hysteresis damping using Chebyshev polynomials of the first kind, a very efficient procedure based on the orthogonal least squares (OLS) algorithm and the adjustable prediction error sum of squares (APRESS) criterion is proposed for model structure detection and parameter estimation of an MR device for the first time. The OLS algorithm provides a powerful tool to effectively select the significant model terms step by step, one at a time, by orthogonalizing the associated terms and maximizing the error reduction ratio, in a forward stepwise procedure. The APRESS statistic regularizes the OLS algorithm to facilitate the determination of the optimal number of model terms that should be included into the dynamic model. Because of the orthogonal property of the OLS algorithm, the approach leads to a parsimonious model. Numerical ill-conditioning problems confronted by the conventional least squares algorithm can also be avoided by the new approach. Finally by utilising the transient response of a MR specimen, it is shown how the model structure can be detected in a practical application. The identified model agrees with the experimental measurements very well

The dynamic characterisation of disk geometry particle dampers

Particle dampers (PDs) have the advantages of being simple in geometry, small in volume and applicable in extreme temperature environments. Experimental studies have shown that PDs can offer considerable potential for suppressing structural resonant conditions over a wide frequency range. In this paper, the nonlinear characteristics of PDs are studied experimentally in a series of response-level-controlled tests. The effect of the geometry is studied and a method is developed to model the nonlinear damping of PDs as equivalent viscous dampers that can be applied directly to engineering structures at the design stage