Optimal parameters of viscoelastic tuned-mass dampers

A vibration absorber, also known as a tuned mass damper (TMD), is a passive vibration control device. This is achieved by attaching a secondary oscillator to a primary oscillator. In general, the aim is to reduce the vibration of the primary oscillator by suitably choosing the parameters of the secondary oscillator. The effectiveness of a TMD depends on (a) optimised the value of the tuned parameters, and (b) the nature of ambient damping of the absorber. They theory of TMD when the secondary and the primary oscillators are undamped or viscously damped is well developed. This paper presents an analytical approach to obtain optimal parameters of a TMD when the vibration absorber is viscoelastically damped. Classical results on viscously damped vibration absorbers can be obtained as a special case of the general results reduced in the paper. It is shown that by using a viscoelastically damped TMD, it is possible to obtain superior vibration absorption compared to an equivalent viscously damped TMD

An approximate Itô-SDE based simulated annealing algorithm for multivariate design optimization problems

This research concerns design optimization problems involving numerous design parameters and large computational models. These problems generally consist in non-convex constrained optimization problems in large and sometimes complex search spaces. The classical simulated annealing algorithm rapidly loses its efficiency in high search space dimension. In this paper a variant of the classical simulated annealing algorithm is constructed by incorporating (1) an It\^o stochastic differential equation generator (ISDE) for the transition probability and (2) a polyharmonic splines interpolation of the cost function. The control points are selected iteratively during the research of the optimum. The proposed algorithm explores efficiently the design search space to find the global optimum of the cost function as the best control point. The algorithm is illustrated on two applications. The first application consists in a simple function in relatively high dimension. The second is related to a Finite Element model

Identification of Stochastic Loads Applied to a Nonlinear Dynamical System Using an Uncertain Computational Model

This paper deals with the identification of stochastic loads applied to a nonlinear dynamical system for which a few experimental responses are available using an uncertain computational model. Uncertainties are induced by the use of a simplified computational model to predict the responses of the real system. A nonparametric probabilistic approach of both parameter uncertainties and model uncertainties is implemented in the simplified computational model in order to take into account uncertainties. The level of uncertainties is identified using the maximum likelihood method. The identified stochastic simplified computational model which is obtained is then used to perform the identification of the stochastic loads applied to the real nonlinear dynamical system. A numerical validation of the complete methodology is presented

Frequency domain homogenization for the viscoelastic properties of spatially correlated quasi-periodic lattices

An analytical framework is developed for investigating the effect of viscoelasticity on irregular hexagonal lattices. At room temperature many polymers are found to be near their glass temperature. Elastic moduli of honeycombs made of such materials are not constant, but changes in the time or frequency domain. Thus consideration of viscoelastic properties are essential for such honeycombs. Irregularity in lattice structures being inevitable from practical point of view, analysis of the compound effect considering both irregularity and viscoelasticty is crucial for such structural forms. On the basis of a mechanics based bottom-up approach, computationally efficient closed-form formulae are derived in frequency domain. The spatially correlated structural and material attributes are obtained based on Karhunen-Loève expansion, which is integrated with the developed analytical approach to quantify the viscoelastic effect for irregular lattices. Consideration of such spatially correlated behaviour can simulate the practical stochastic system more closely. The two effective complex Young’s moduli and shear modulus are found to be dependent on the viscoelastic parameters, while the two in-plane effective Poisson’s ratios are found to be independent of viscoelastic parameters and frequency. Results are presented in both deterministic and stochastic regime, wherein it is observed that the amplitude of Young’s moduli and shear modulus are significantly amplified in the frequency domain. The response bounds are quantified considering two different forms of irregularity, randomly inhomogeneous irregularity and randomly homogeneous irregularity. The computationally efficient analytical approach presented in this study can be quite attractive for practical purposes to analyse and design lattices with predominantly viscoelastic behaviour along with consideration of structural and material irregularity

Stochastic modeling for hysteretic bit–rock interaction of a drill string under torsional vibrations

© The Author(s) 2019. This paper aims at constructing a stochastic model for the hysteretic behavior of the nonlinear bit–rock interaction of a drill string under torsional vibrations. The proposed model takes into account the fluctuations of the stick–slip oscillations observed during the drilling process. These fluctuations are modeled by introducing a stochastic process associated with the variations of the torque on bit, which is a function of the bit speed. The parameters of the stochastic model are calibrated with field data. The response of the proposed stochastic model, considering the random bit–rock interaction, is analyzed, and statistics related to the stability of the drill string are estimated

Hysteretic bit/rock interaction model to analyze the torsional dynamics of a drill string

The present paper proposes a novel hysteretic (non-reversible) bit/rock interaction model for the torsional dynamics of a drill string. Non-reversible means that the torque-on-bit depends not only on the bit speed, but also on the bit acceleration, producing a type of hysteretic cycle. The continuous drill string system is discretized by means of the finite element method and a reduced-order model is constructed using the normal modes of the associated conservative system. The parameters of the proposed hysteretic bit/rock interaction model is fitted with field data. The non-linear torsional vibration and the stability map of the drill string system are analyzed employing the proposed bit/rock interaction model and also a commonly used reversible model (without hysteresis). It turns out that the hysteretic model affects the stability region of the system

The minimum norm multi-input multi-output receptance method for partial pole placement

A closed-form analytical solution is developed for the first time that fully addresses the problem of choosing feedback gains that minimize the control effort required for partial pole placement in multi-input, multi-output systems. The norm of the feedback gain matrix is shown to take the form of an inverse Rayleigh quotient, such that the optimal closed-loop system eigenvectors are given as a function of the dominant (highest)eigenvectors of the matrix in the quotient. The feedback gains that deliver the required pole placement with minimum effort may then be determined using standard procedures. The original formulation by the receptance method proposed an arbitrary choice of the closed loop eigenvectors that assigned the poles exactly but was generally wasteful of control effort that might otherwise be conserved or put to good use in satisfying additional control objectives. The analytical solution is validated against a set of numerical examples

A sensitivity-based one-parameter-at-a-time model updating method

International audienceThis paper is interested in model updating problems which consists in identifying optimal values of model parameters by comparing the model outputs with the experimental outputs. Such a problem generally yields a challenging multivariate inverse problem to be solved in high dimension. The high-dimensionality requires the use of a global optimization algorithm in order the explore efficiently the parameters space. In this paper we propose an alternative algorithm which allows each model parameters to be identified separately and sequentially by solving separated univariate inverse problems. For each parameter, a devoted inverse problem is introduced by identifying an output which is sensitive to this parameter only, the sensitivity being quantified using Sobol indices. The proposed method is illustrated through a three-storey structure for which experimental measurements are collected

Model updating in structural dynamics — Uncertainties on the position and orientation of sensors and actuators

This research concerns the updating of computational models in presence of uncertainties related to the position and the orientation of the sensors and actuators. Such uncertainties yield uncertainties in the correspondence between the experimental dynamical responses and the dynamical responses calculated using the computational model. These uncertainties in the response increase with frequency and have to be taken into account when updating the parameters of the computational model in order to obtain a robust estimation of these parameters. This paper provides a complete methodology to take into account and analyse such uncertainties. Furthermore, an optimal sensor placement method is proposed so that (1) the measured data are as sensitive as possible with respect to updating parameters and (2) the measured data are as robust as possible with respect to position/orientation uncertainties. The methodologies developed here are illustrated through two numerical applications