Towards identification of a general model of damping
01 Jan 2000-Vol. 4062, pp 377
TL;DR: In this paper, the authors developed methodologies for identification of general damping models responsible for energy dissipation in a vibrating structure using experimentally identified complex modes and complex natural frequencies.
Abstract: Characterization of damping forces in a vibrating structure has long been an active area of research in structural dynamics. In spite of a large amount of research, understanding of damping mechanisms is not well developed. A major reason for this is that unlike inertia and stiffness forces it is not in general clear what are the state variables that govern the damping forces. The most common approach is to use `viscous damping' where the instantaneous generalized velocities are the only relevant state variables. However, viscous damping by no means the only damping model within the scope of linear analysis. Any model which makes the energy dissipation functional non-negative is a possible candidate for a valid damping model. This paper is devoted to develop methodologies for identification of such general damping models responsible for energy dissipation in a vibrating structure. The method uses experimentally identified complex modes and complex natural frequencies and does not a-priori assume any fixed damping model (eg., viscous damping) but seeks to determine parameters of a general damping model described by the so called `relaxation function'. The proposed method and several related issues are discussed by considering a numerical example of a linear array of damped spring-mass oscillators.
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TL;DR: In this article, the authors extend classical modal analysis to non-viscously damped linear dynamic systems and derive the transfer function matrix of the system in terms of the right and left eigenvectors of the second-order system.
Abstract: This paper is aimed at extending classical modal analysis to treat lumped-parameter nonviscously damped linear dynamic systems. It is supposed that the damping forces depend on the past history of velocities via convolution integrals over some kernel functions. The traditional restriction of symmetry has not been imposed on the system matrices. The nature of the eigenvalues and eigenvectors is discussed under certain simplified but physically realistic assumptions concerning the system matrices and kernel functions. A numerical method for calculation of the right and left eigenvectors is suggested. The transfer function matrix of the system is derived in terms of the right and left eigenvectors of the second-order system. Exact closed-form expressions for the dynamic response due to general forces and initial conditions are presented. The proposed method uses neither the state-space approach nor additional dissipation coordinates. Suitable examples are given to illustrate the derived results.
114 citations
TL;DR: In this article, an adaptive triaxial angular rate (AR) sensor is proposed to detect rotation in three orthogonal axes using a single vibrating mass, and the output of the device is simply an estimate of input rotation, removing the need for additional demodulation.
Abstract: This paper presents a novel concept for an adaptively controlled triaxial angular rate (AR) sensor device that is able to detect rotation in three orthogonal axes, using a single vibrating mass. Pedestrian navigation is presented as an example demonstrating the suitability of the proposed device to the requirements of emerging applications. The adaptive controller performs various functions. It updates estimates of all stiffness error, damping and input rotation parameters in real time, removing the need for any offline calibration stages. The parameter estimates are used in feedforward control to cancel out their otherwise erroneous effects, including zero-rate output. The controller also drives the mass along a controlled oscillation trajectory, removing the need for additional drive control. Finally, the output of the device is simply an estimate of input rotation, removing the need for additional demodulation normally used for vibratory AR sensors. To enable all unknown parameter estimates to converge to their true values, the necessary model trajectory is shown to be a three-dimensional Lissajous pattern. A modified trajectory algorithm is presented that aims to reduce errors due to discretization of the continuous time system. Simulation results are presented to verify the operation of the adaptive controller. A finite-element modal analysis of a preliminary structural design is presented. It shows a micro electro mechanical systems realizable design having modal shapes and frequencies suitable for implementing the presented adaptive controller
69 citations
TL;DR: In this paper, the theory of direct experimental identification of damping matrix based on the dynamic stiffness matrix (DSM) method is further developed in order to find the frequency range in which such a hybrid model is valid.
11 citations
TL;DR: An improved experimental procedure is developed to reduce the effect of these errors in order to make the DSM-based damping identification method a practical option.
7 citations
01 Jan 2006
TL;DR: In this paper, the authors describe the use of MEMS technology in the last two decades to enable angular rate sensors to be fabricated that can be used for large scale aeronautical applications.
Abstract: Prohibitive cost and large size of conventional angular rate sensors have limited their use to large scale aeronautical applications. However, the emergence of MEMS technology in the last two decades has enabled angular rate sensors to be fabricated that
6 citations
References
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TL;DR: In this article, the necessary and sufficient conditions under which both discrete and continuous damped linear dynamic systems possess classical normal modes were determined for both continuous and discrete linear systems, respectively.
Abstract: The purpose of this paper is to determine necessary and sufficient conditions under which both discrete and continuous damped linear dynamic systems possess classical normal modes.
884 citations
TL;DR: In this article, the authors examined the implications of various damping models for the interpretation of measured transfer functions, especially in the context of experimental modal analysis, and showed that in the case of a dissipation-matrix model, it is possible in principle to determine all the model parameters from measurements.
254 citations
TL;DR: In this paper, a discussion of various mathematical models which have been proposed to represent the damping behavior of solid materials, with emphasis on their usefulness in structural dynamic analyses is presented, along with derivations of interrelationships which exist among them.
245 citations
01 Jan 1958
TL;DR: In this article, the authors presented a new and synthetic approach to the linear mechanics of deformation of solids, which includes as particular cases the classical theory of Elasticity, Thermoelasticity, and ViscoELasticity.
Abstract: The Thermodynamics of linear irreversible processes is presented from a unified viewpoint. This provides a new and synthetic approach to the linear mechanics of deformation of solids, which includes as particular cases the classical theory of Elasticity, Thermoelasticity and Viscoelasticity. The first two sections constitute an introduction to the general concepts and principles of linear Thermodynamics as developed in the writer’s earlier work and presented in somewhat more detail. This is followed by the application of the general thermodynamic theory to Thermoelasticity which combines the theories of Elasticity, Heat Transfer, and their coupled effects into a single treatment. Some immediate consequences are derived such as the property of diffusion of entropy and certain fundamental relations with reference to thermal stresses. The introduction of inertia forces leads to a general formulation of thermoelastic dissipation of dynamical systems by Lagrangian methods. The second order heat produced by the dissipation is evaluated. Linear Viscoelasticity and Relaxation Phenomena are also a particular case of the thermodynamic theory. The resulting stress-strain relations with heredity properties are discussed. The operational formulation of these relations leads naturally to a formal correspondence with the theory of Elasticity and to an operational-variational principle. The latter provides a generalization of Lagrange’s equations in integro-differential form to the dynamics and stress analysis of viscoelastic structures. Some specific applications of these principles are presented.
213 citations