Eduardo Márcio de Oliveira Lopes

On the passive control of vibrations with viscoelastic dynamic absorbers of ordinary and pendulum types

Abstract Dynamic vibration absorbers (DVA) provide a cheap and efficient means for vibration abatement in many complex systems, ranging from crankshafts of internal combustion engines, overhead transmission lines, machine casings, structural panels and large turbo machinery sets, to quote a few examples. One can provide a simple classification for them by considering the nature of the resilient material it contains as a form of “spring”: it may be viscous (CDVA), hysteretic (HDVA) or viscoelastic (VDVA). Viscous DVAs are the largely studied devices and one of their most remarkable applications is in mitigating crankshafts torsional vibrations and in very tall buildings. The most well known hysteretic DVA is the Stockbridge damper, largely applied in overhead electric power transmission lines. With modern use of fractional calculus, modelling viscoelastic materials became a routine work. The experimental identification of four fractional parameter models for viscoelastic material has become a standard technique amongst the authors of this work. Modelling viscoelastic materials by four fractional parameters has made advanced analysis of structures and systems where it is applied much more straightforward than it was before. This is true also for structures with VDVA and HDVA attached to it. In this paper it is shown that a hysteretic material model can be derived from a viscoelastic material model based on four fractional parameters. Generalized quantities of ordinary and pendulum type absorbers and for both viscoelastic and hysteretic materials are derived and their nature discussed. The performances of a system with absorbers of viscoelastic and hysteretic nature are compared. Input energy and dissipated energy by the absorbers of both natures and types are computed and compared, using the concept of generalized damping parameter of the absorbers. Conclusions are drawn from the comparisons. One of the ideas behind these computations is to check the validity of some international recommendations for the experimental assessment of Stockbridge dampers, which implicitly neglects the effect of the generalized mass parameter.

Design of Optimum Systems of Viscoelastic Vibration Absorbers for a Given Material Based on the Fractional Calculus Model

So-called vibration absorbers, which might more appropriately be called vibration neutralizers, are mechanical devices designed to be attached to another mechanical system, or structure, called the primary system, for the purpose of controlling, or reducing, the vibration (and consequent sound production) of machines, structural surfaces and panels. The cheapest and easiest way to construct a vibration absorber is by incorporating a viscoelastic material, functioning as both the resilient and the energy dissipating component. The viscoelastic material acts as a damped spring. This article sets out to describe how to design an optimal system of viscoelastic absorbers for a known material, through a model using four fractional parameters. A real example, of the design of a system of six viscoelastic vibration absorbers for mitigation of the response to fluid-structure instability in a hydroelectric generator system, is presented and discussed.

Modeling of dynamic rotors with flexible bearings due to the use of viscoelastic materials

Nowadays rotating machines produce or absorb large amounts of power in relatively small physical packages. The fact that those machines work with large density of energy and flows is associated to the high speeds of rotation of the axis, implying high inertia loads, shaft deformations, vibrations and dynamic instabilities. Viscoelastic materials are broadly employed in vibration and noise control of dynamic rotors to increase the area of stability, due to their high capacity of vibratory energy dissipation. A widespread model, used to describe the real dynamic behavior of this class of materials, is the fractional derivative model. Resorting to the finite element method it is possible to carry out the modeling of dynamic rotors with flexible bearings due to the use of viscoelastic materials. In general, the stiffness matrix is comprised of the stiffnesses of the shaft and bearings. As considered herein, this matrix is complex and frequency dependent because of the characteristics of the viscoelastic material contained in the bearings. Despite of that, a clear and simple numerical methodology is offered to calculate the modal parameters of a simple rotor mounted on viscoelastic bearings. A procedure for generating the Campbell diagram (natural frequency versus rotation frequency) is presented. It requires the embedded use of an auxiliary (internal) Campbell diagram (natural frequency versus variable frequency), in which the stiffness matrix as a frequency function is dealt with. A simplified version of that procedure, applicable to unbalance excitations, is also presented. A numerical example, for two different bearing models, is produced and discussed.

Design of optimum system of viscoelastic vibration absorbers with a Frobenius norm objective function

Vibration absorbers, also called vibration neutralizers, are mechanical systems to be attached to another mechanical system, or structure, called the primary system, with the purpose of reducing vibration and sound radiation. The simplest form of a vibration absorber is that of a single degree of freedom system, where the “spring” is made of a viscoelastic material, perhaps with some metallic inserts. This paper sets out to describe how to design a best possible system of viscoelastic vibration absorbers for an available viscoelastic material, known by its four fractional parameter model, by using a novel objective function, defined through a Frobenius norm. A real example is presented and discussed. Keywords : vibration absorber, vibration neutralizer, viscoelastic material, vibration abatement, vibration control

Experimental Validation of Angular Viscoelastic Dynamic Neutralizers Designed for Flexural Vibration Control in Rotating Machines

The installation of micro hydroelectric power plants has recently been growing in Brazil, where small hydraulic generators are combined with hydraulic turbines. Some technical solutions require different runaway factors, from 1.2 up to 3.0 times the synchronous speed of the generator, so that the mechanical design of them must be reinforced or changed to support this critical dynamic condition, affecting costs and reducing competitiveness. An effective technique to control vibration is the use of simple devices called ‘dynamic vibration neutralizers’. These devices can contain viscoelastic material to introduce high mechanical impedance onto the system to reduce its vibration levels. There is a special kind of neutralizer, called ‘angular viscoelastic dynamic neutralizer’ (angular VDN), which acts indirectly in slope degree of freedom controlling flexural vibration. They have the predicted ability to control more than one single mode once the device is assembled where the maximum slope happens. The aim of the current work is to present a methodology to design angular VDNs and validate it by using a simplified experimental rotor exploring two different geometries. The results show that, if well-tuned, this kind of control is effective not only for the frequency band of interest, but also over higher modes.