Experimental travelling waves identification in mechanical structures

Abstract

Vibrations are often represented as a sum of standing waves in space, i.e. normal modes of vibration. While this can be mathematically accurate, the representation as travelling waves can be compact and more appropriate from a physical point of view, in particular when the energy flux along the structure is meaningful. The quantification of travelling waves assists in computing the energy being transferred and propagated along a structure. It can provide local as well as global information about the structure through which the mechanical energy flows. Presented in this paper is a new method to quantify the fraction of mechanical power being transmitted in a vibration cycle at a specific direction in space using measured data. It is shown that the method can detect local defects causing slight non-uniformity of the energy flux. Equivalence is being made with the electrical power factor and electromagnetic standing waves ratio, commonly employed in such cases. Other methods to perform experiment based wave identification in one-dimension are compared with the power flow based identification. Including a signal processing approach that fits an ellipse to the complex amplitude curve and Hilbert transform for obtaining the local phase and amplitude. A new representation of the active and reactive power flow is developed and its relationship to standing waves ratio is demonstrated analytically and experimentally.

Automatic traveling wave excitation of structures with imperfect cyclic symmetry

“…An estimation method of the response's TWR is derived for the optimization of 𝜃 and 𝜑, required for the TWR minimization. While other methods like calculating the power flow in the system [46] exist, the method presented here is preferred. The advantages of the described method are its ability to employ realtime filtering and handle multiple sensors.…”

Experimental multimode traveling waves identification in an acoustic waveguide

“…The traveling wave ratio is a scalar measure of the propagating versus circulating energies ratio [21]. It serves as a basis for quantifying these proportions on a realistic, physical model as outlined below.…”

“…4 The standing wave ratio (SWR) [17] and traveling wave ratio (TWR) [18,19] have been used to quantify the direction and purity of the propagating mode for the single-mode scenarios and to identify the acoustic impedance in a standing wave tube [20]. The power ratio and the TWR are closely related [21]; thus, either one can be used to quantify the fraction of propagating energy in each conveying mechanism. In a wave control application, TWR is preferred over SWR because the former is always finite and thus more suitable for real-time control [18].…”

“…As discussed in [18], the open-looped model is highly sensitive to model uncertainties; therefore, the traveling wave's experimental identification approach is crucial for reasonable control. The decomposition of a single traveling wave into its forward and backward components was done previously, both in a batch mode [18,24,33] and recursively [17,21], and is now a standard analysis tool. A multimode full wave decomposition was suggested in [34,35] when a rigid boundary tube was considered.…”

Nonlinear control of boundary impedance in an acoustic waveguide

“…Both the standing wave ratio (SWR) 13 and the traveling wave ratio (TWR) 14,15 can also be used to quantify the normalized amount and direction of energy transferred by each mechanism. It has been shown 16 that the power ratio and the TWR are equivalent descriptive parameters of the modal wave.…”