Frequency Response Of Nonlinear System Research Articles

Surface and nonlocal effects on response of linear and nonlinear NEMS devices

Nonlocal and surface effects become important for nanoscale devices. To model these effects on frequency response of linear and nonlinear nanobeam subjected to electrostatic excitation, we use Eringen’s nonlocal elastic theory and surface elastic theory proposed by Gurtin and Murdoch to modify the governing equation. Subsequently, we apply Galerkin’s method with exact mode shape including nonlocal and surface effects to get static and dynamic modal equations. After validating the procedure with the available results, we analyze the variation of pull-in voltage and frequency resonance by varying surface and nonlocal parameters. To do frequency analysis of nonlinear system, we solve nonlinear dynamic equation using the method of multiple scale. We found that the frequency response of nonlinear system reduces for fixed excitation as the surface and nonlocal effects increase. Also, we found that the nature of nonlinearity can be tuned from hardening to softening by increasing the nonlocal effects.

The effects of nonlinearity on the output frequency response of a passive engine mount

In this paper, the new concept of output frequency-response function (OFRF) that was derived recently by the authors from the Volterra-series theory of nonlinear systems is briefly introduced. An effective algorithm is proposed to determine the monomials in the OFRF-based representation of the output frequency response of nonlinear systems. The results are then used to analyze the output frequency response of a passive engine mount. Important conclusions regarding the effects of system nonlinearity on the output frequency-response behaviors of the engine mount are reached via theoretical analysis and verified by simulation studies. These conclusions are of significant importance for the analysis and design of vibration isolators such as engine mounts in practice.

Frequency Response of Nonlinear Systems

Frequency Response of Nonlinear Systems

The Frequency Response and Jump-resonance Criteria of Non-linear Control Systems

In this paper a simple graphical method of obtaining the frequency response of nonlinear systems along with a criterion for jump resonance is presented when the frequency of the sinusoidal input is varied. The method is applicable whether the system considered contains a non-linearity with a real or complex describing function. As an example a system with saturation non-linearity is considered.

Closed-loop frequency response of nonlinear systems

WHEN A NONLINEAR feedback control system includes saturation, the output of the system may oscillate with either the input frequency or the l/n order subharmonic of the input frequency, where n is a positive integer greater than l. When the frequency of the output is l/n times that of the input, the output oscillation is called the l/n order pure subharmonic oscillation. The possibility of the occurrence of pure subharmonic oscillations as the response of a nonlinear feedback control system may be predicted from an accurate closed-loop attenuation-frequency curve for a given input amplitude. That is, if the maximum ratio of the system output amplitude to the system input amplitude is large (about 3 db or more), there is a possibility that the output of the system may oscillate with a subharmonic of the input frequency. However, if the maximum ratio of the output amplitude to the input amplitude is small (about 2 db or less), the possibility of the occurrence of pure subharmonic oscillations is very small, if any. Because of the fact that the wave form of the output of a nonlinear element is often extremely nonsinusoidal and it is difficult, in general, to handle nonlinear differential equations, graphical techniques are usually employed for finding the closed-loop frequency response of nonlinear feedback control systems.

A generalized method for determining the closed-loop frequency response of nonlinear systems

One of the formidable problems in the area of feedback control concerns the analysis and synthesis of nonlinear systems. Of the several methods available for treating nonlinear systems, one of the more widely used is the sinusoidal response method. Valuable information about the characteristics of nonlinear systems can be obtained from the open-loop frequency response, but the full potential of this method has not been exploited because apparently there is no widely accepted procedure for determining the closed-loop frequency response. This paper describes a method whereby the closed-loop frequency response of an important class of nonlinear systems can be determined easily. Development of this method is dependent upon representing the nonlinear element as a so-called equivalent gain. The method is described and illustrated by analytically determining the closed-loop frequency response of an acceleration-limited system and an error-limited system. The results of the use of this method compare favorably with solutions of the two problems as obtained from an analogue computer. A few of the nonlinear phenomena which can be reasonably approximated by this method are saturation, limiting, backlash, and dead space.

Open-loop frequency response method

SERVOMECHANISM DESIGN and test procedures which are based upon the assumption of system linearity are not satisfactory for many servos. This problem has been summarized in a recent article in this magazine. <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">1</sup> A method for representing the open-loop frequency response of nonlinear systems will be considered which indicates the presence of most nonlinear phenomena of closed-loop systems.