Loss factor

Abstract: For a number of years it has been known that flexural vibrations in a plate can be damped by the application of a layer of damping (viscoelastic) material that is in turn constrained by a backing layer or foil. A common example is the damping tape currently used in aircraft.This paper presents a quantitative analysis of the damping effectiveness of such a constrained layer. As in the work of H. Oberst the damping is characterized by the loss factor η, which is the normalized imaginary part of the complex bending stiffness of the damped plate.The calculated damping factor depends on the wavelength of bending waves in the damped plate, and on the thicknesses and elastic moduli of the plate, the damping layer, and the constraining layer. A complex shear modulus is assigned to the damping layer, where all of the energy dissipation is assumed to take place.Damping factors have been determined experimentally on laboratory test bars for a number of constrained‐damping‐layer applications for frequencies from abou...

Abstract: Systems that harvest or scavenge energy from their environments are of considerable interest for use in remote power supplies. A class of such systems exploits the motion or deformation associated with vibration, converting the mechanical energy to electrical, and storing it for later use; some of these systems use piezoelectric materials for the direct conversion of strain energy to electrical energy. The removal of mechanical energy from a vibrating structure necessarily results in damping. This research addresses the damping associated with a piezoelectric energy harvesting system that consists of a full-bridge rectifier, a filter capacitor, a switching DC–DC step-down converter, and a battery. Under conditions of harmonic forcing, the effective modal loss factor depends on: (1) the electromechanical coupling coefficient of the piezoelectric system; and (2) the ratio of the rectifier output voltage during operation to its maximum open-circuit value. When the DC–DC converter is maximizing power flow to the battery, this voltage ratio is very nearly 1/2, and the loss factor depends only on the coupling coefficient. Experiments on a base-driven piezoelectric cantilever, having a system coupling coefficient of 26%, yielded an effective loss factor for the fundamental vibration mode of 2.2%, in excellent agreement with theory.

Abstract: Fractional derivative models offer a powerful tool to describe the dynamic behaviour of real viscoelastic materials. A version of the fractional derivative models characterized by five parameters is presented and investigated in this paper in order to describe asymmetrical loss factor peak and the high-frequency behaviour of polymeric damping materials. The speculative derivation of the model constitutive equation containing time derivatives of stress and strain of different orders is given. The model behaviour is investigated in the frequency domain, the physical meaning of the model parameters is defined and constraints on the parameter values are made. It is shown that the asymmetry of loss peak and the high-frequency behaviour of the model are governed by the difference between the order of time derivatives of stress and strain. Moreover, it is shown that this difference is related to the high-frequency limit value of the loss factor. The model is fitted to experimental data on some polymeric damping materials to verify its behaviour.

Abstract: Vibrational energy distribution between two coupled plates is considered. Inversion of the linear power balance equations is used to determine the plate loss factors and the coupling loss factors in situ. To accomplish the determinations power was injected and measured sequentially at five points chosen at random on each plate to ensure effective statistical independence of modes. In each case the response of both plates was measured at ten randomly chosen points and mean values of response and injected power were determined. Good agreement is obtained between the predicted and measured coupling loss factors and between the in situ loss factors and loss factors determined for each plate separately also in steady state from power injection measurements. Loss factors determined by transient decay methods are consistently lower than those determined by either steady state method. It is suggested that the latter result may be true because the energy distribution among decaying modes is not the same as in steady state. During reverberant decay the more lightly damped modes predominate giving rise to an apparent loss factor which is significantly less than the steady state loss factor.

Abstract: An extensive study of the effects of frequency and strain amplitude as well as temperature on the damping behaviour of superelastic NiTi shape memory alloy wires was undertaken. A full factorial design taking into account the two-level interactions between these variables has been conducted. The dissipated energy and the loss factor were analyzed. Analysis shows that an increase in temperature has no effect on the dissipated energy while it decreases slightly the loss factor. Both however increase with the increase in strain amplitude. A maximum in dissipated energy and in the loss factor is observed around 0·1 Hz. Both factors then decrease as the frequency continues to increase. This behaviour is also strain amplitude dependent. A thermal analysis showed that the observed frequency and frequency–amplitude interaction effects are due to an important temperature variation produced by the energy generated during the transformation. Finally, a three harmonic Fourier sine series model is proposed to model the shape memory alloy dynamic behaviour. Frequency, amplitude and temperature effects are taken into account and dissipated energy and the loss factor can be determined from this model.