Loss Factors Of Beams Research Articles

Novel dynamic model for calculating the equivalent Young's modulus and loss factor of layered beams

Accurate and efficient models of the dynamics of a laminated transformer core structure are essential for the design of quiet power transformers. However, owing to the complex structure of the transformer core, the dynamic response of the core has not yet been accurately modelled. In this paper, the strains in different laminas and the strain differences between them are included as key parameters in the derivation of the equivalent bending stiffness of a beam subject to transverse vibration. As a result, the equivalent stiffness and loss factor of the beam are obtained as functions of the number of layers and strain difference ratio due to the inter-layer friction factor and the clamping force. The equivalent material properties are then used to determine the frequency response functions of laminated beams using the finite element method. Two sets of frequency response functions produced by different numbers of layers and different clamping forces are measured experimentally. A comparison between the simulated and measured frequency response functions shows good agreement with the relative error of the natural frequencies less than 6% for the first four natural frequencies.

Vibration and Sound Radiation of Visco-Elastically Damped Plates. Acoustic Power Radiation of Point-Excited Beams.

The effects of structural damping and wavenuwmber ratio on the acoustic power radiated by point-excited damped infinite beams and simply supported finite beams with same cross sections have been studied. The numerical calculations of the acoustic power were carried out using Keltie's equations based on the Heckl's power integral. The acoustic medium is assumed to be air, and the effect of the back reaction of the sound field is neglected in the beam response equation. Non-dimensional acoustic power, sound radiation efficiency, and acoustic power conversion efficiencies are presented as functions of wavenumber ratio and beam loss factors. It is shown that the power conversion efficiency of the infinite beam is inversely proportional to the wavenumber ratio and independent of the loss factor below coincidence, and is approximately proportional in inverse to the loss factor above coincidence. The power conversion efficiency of the finite beam has dull peaks with values roughly inverse-proportional to the loss factor at nonresonant frequencies. The similarity of acoustic power radiation between infinite beams and finite beams has been observed when the length and loss factor of beams is increased.

The loss factor of beams with thick constrained layers

A constrained layer beam, consisting of a base beam, viscoelastic layer, and cover plate, is analyzed with each layer modeled using the two‐dimensional equations of viscoelasticity. The (three) layers are ‘‘cascaded,’’ enforcing appropriate equations of continuity. A shape factor is invoked to account for the effect of the beam’s finite width on the dilatational wave speed of the constrained layer. Composite loss factors are first defined solely for the freely propagating (modified) flexural wave‐number component of the response and then in terms of the overall drive point response of the beam to a mid‐span load. At low frequencies results are compared to values obtained from Kerwin’s [1959] classic thin layer model. At the other end, high frequency asymptotic limits are obtained by viewing the constrained layer as being semi‐infinite and/or ‘‘fuzzy.’’ Finally, predictions are compared to measurements performed on a steel‐Nitrile‐steel beam [Junger et al., 1986].

Vibration analysis of a partially covered beam with a constrained viscoelastic layer. In the case of different boundary conditions for base layer and constraining layer.

This paper presents an analytical method of flexural vibration of a beam with partial coverage of a constrained viscoelastic layer. The problem of discontinuity of the neutral axis at the connecting point between the multi-layer and homogeneous parts which arises in the method used so far, is solved by treating the axial displacement of a base layer and that of a constraining layer as being independent, and by taking the axial force and displacement of a homogeneous part into consideration. Frequencies and loss factors of beams whose base layers are clamped at both ends are calculated numerically by use of the present method and the usual method. Experimental values are also presented and compared with calculated results. An a results, damping properties of partially covered beams are clarified, and it is found that the usual method can be used practically in many cases.

Vibration and Damping Analysis of Curved Multilayered Beams

Governing equations of motion for a general curved multilayered beam with alternate elastic and viscoelastic layers, subjected to harmonic excitation are derived using an energy method. A solution for simply supported end conditions has been obtained, to determine the resonant frequencies and associated system loss factors of beams with 3, 5 and 7 layers. Both constant size and constant weight criteria have been used for comparison.