On the use of the transmissibility concept for the evaluation of frequency response functions

A Review of Structural Health Monitoring Techniques as Applied to Composite Structures

In this paper, a new transmissibility analysis method is proposed for the detection and location of damage via nonlinear features in multidegree-of-freedom (MDOF) structural systems. The method is derived based on the transmissibility of nonlinear output frequency response functions (NOFRFs), a concept recently proposed to extend the traditional transmissibility concept to the nonlinear case. The implementation of the method is only based on measured system output responses and by evaluating and analyzing the transmissibility of these system responses at super-harmonics. This overcomes the problems with available techniques, which assume there is one damaged component with nonlinear features in the system and/or require loading on inspected structural systems is measurable. Both numerical simulation studies and experimental data analysis have been conducted to verify the effectiveness and demonstrate the potential practical applications of the new method.

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A New Transmissibility Analysis Method for Detection and Location of Damage via Nonlinear Features in MDOF Structural Systems

The present chapter draws a general overview on the concept of transmissibility and on its potentialities, virtues, limitations and possible applications. The notion of transmissibility has, for a long time, been limited to the single degree-of-freedom (SDOF) system; it is only in the last ten years that the concept has evolved in a consistent manner to a generalized definition applicable to a multiple degree-of-freedom (MDOF) system. Such a generalization can be and has been not only developed in terms of a relation between two sets of harmonic responses for a given loading, but also between applied harmonic forces and corresponding reactions. Extensions to comply with random motions and random forces have also been achieved. From the establishment of the various formulations it was possible to deduce and understand several important properties, which allow for diverse applications that have been envisaged, such as evaluation of unmeasured frequency response functions (FRFs), estimation of reaction forces and detection of damage in a structure. All these aspects are reviewed and described in a logical sequence along this chapter. The notion of transmissibility is presented in every classic textbook on vibrations, associated to the single degree-of-freedom system, when its basis is moving harmonically; it is defined as the ratio between the modulus of the response amplitude and the modulus of the imposed amplitude of motion. Its study enhances some interesting aspects, namely the fact that beyond a certain imposed frequency there is an attenuation in the response amplitude, compared to the input one, i.e., one enters into an isolated region of the spectrum. This enables the design of modifications on the dynamic properties so that the system becomes “more isolated” than before, as its transmissibility has decreased. Usually, the transmissibility of forces, defined as the ratio between the modulus of the transmitted force magnitude to the ground and the modulus of the imposed force magnitude, is also deduced and the conclusion is that the mathematical formula of the transmissibility of forces is exactly the same as for the transmissibility of displacements. As it will be explained, this is not the case for multiple degree of freedom systems. The question that arises is how to extend the idea of transmissibility to a system with N degrees-of-freedom, i.e., how to relate a set of unknown responses to another set of known responses, for a given set of applied forces, or how to evaluate a set of reaction forces from a set of applied ones. Some initial attempts were given by Vakakis et al. (Paipetis & Vakakis, 1985; Vakakis, 1985; Vakakis & Paipetis, 1985; 1986), although that generalization was still

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Whys and Wherefores of Transmissibility

Condition or health monitoring techniques and methods have been widely used for engineering systems fault detection and diagnosis. However, there is a major challenge with monitoring the systems operating under time varying loadings especially when the system loads are unknown or hard to measure. To address this problem, a new concept, wavelet energy transmissibility function, is proposed in this paper. The main advantage of this new method is that it can remove the impact of varying loadings but it does not require any loading information. Further, the proposed method is robust to noise and is sensitive to system property changes. The effectiveness of the proposed method has been well demonstrated by a numerical example, the theoretical study, and the analysis of the field vibration data from bearings of operating wind turbines.

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Wavelet Energy Transmissibility Function and Its Application to Wind Turbine Bearing Condition Monitoring

This article uses frequency domain transmissibility functions for detecting and locating damage in operational con- ditions. In recent articles numerical and experimental examples were presented and the possibility to use the transmissibility concept for damage detection seemed quite promising. In the work discussed so far, it was assumed that the operational conditions were constant, the structure was excited by a single input in a fixed location. Transmissibility functions, defined as a simple ratio between two measured responses, do depend on the amplitudes or locations of the operational forces. The current techniques fail in the case of changing operational conditions. A suitable operational damage detection method should however be able to detect damage in a very early stage even in the case of changing operational conditions. It will be demonstrated in this paper that, by using only a small frequency band around the resonance frequencies of the structure, the existing methods can still be used in a more robust way. The idea is based on the specific property that the transmissibility functions become independent of the loading condition in the system poles. A numerical and experimental validation will be given.

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Kathy Vanbrabant

Papers

Structural health monitoring in changing operational conditions using tranmissibility measurements