Relative Index Method for Nonlinear Strain Analysis of Piezoceramic Sensored Structure

Abstract

In this paper, a relative index method is proposed to analyze the nonlinear Von Karman strain effects on the piezoceramic sensored rotor blades. Although other qualitative and quantitative methods are available for nonlinear strain analysis, these methods have inherent drawbacks. For qualitative method the fuzzy terms such as severe, negligible influence, etc., are usually used to describe the effect. The main disadvantage of using these terms is that to different people the same fuzzy word can be interpreted differently. This causes inconsistency which may lead to inaccurate analysis. For quantitative methods, the major disadvantage is that they are unable to delineate the whole picture of the nonlinear effects. However, the proposed relative index method circumvents the drawbacks of both qualitative and quantitative methods. Firstly, it measures the nonlinear effect and converts it into a numerical value. The value is in the range of zero to one in which zero is corresponding to negligible effects and one indicates the highest severity of the nonlinear effects. In addition, to generate the index value this method takes the whole picture of nonlinear effect response into consideration. The results of using the relative index method show that at any given mode of vibration the nonlinear effect on sensor is relatively negligible at high rate of rotation than that on lower ones. The results also indicate that the nonlinear effect is increasing at lower modes of vibration but its effect on sensor almost levels off at higher modes. Moreover, if comparing index value of a given modes of vibration with the index value of its preceding modes, the effect of nonlinearity is decreasing. In addition, the results also suggest that at any given instantaneous speed of rotation the level of the nonlinear effect is diminishing with the higher acceleration/deceleration rate of operation of the blade.