The Treatment of Damping Forces in Vibration Theory
TL;DR: In this article, it is shown that free vibration cannot be treated satisfactorily unless the definition of hysteretic damping is widened in some way to cover nonharmonic motion.
Abstract: This paper is the first of a series of three which are concerned with the subject of “ hysteretic damping.” This type of damping, in a simple system with one degree of freedom, is like the familiar “ viscous damping ” in that it implies a resisting force which is in phase with velocity; but it is unlike viscous damping in that the magnitude of the force is not proportional to the velocity but to the displacement. When a system has n degrees of freedom, hysteretic damping implies that damping forces exist which are proportional to relative displacement but which are in phase with relative velocity. From a physical standpoint, hysteretic damping may give a better representation of the facts when the damping arises from the internal friction of solid materials. On the side of theory, it raises considerations which it is the purpose of these three papers to elucidate. It may be said, at the outset, that the notion of hysteretic damping raises no great mathematical difficulty; on the contrary, a main reason for presenting the theory is that it appears to allow of a much simpler discussion (than does viscous damping) of the nature of steady damped oscillation of systems having n degrees of freedom. In the first paper, the purpose is discussed of mathematical theories of damping in vibration theory. It is concluded that the theory of “ hysteretic damping ” is a useful one since it provides an alternative to the fiction of “ viscous ” damping while retaining the mathematical linearity of equations of motion. The word “ hysteretic” is proposed for use in this sense instead of the previously used adjective, namely “ structural.” “ Complex damping ” is related to hysteretic damping in a way which is explained. The theory is given for forced oscillations of a system with one degree of freedom. It is shown that free vibration cannot be treated satisfactorily unless the definition of hysteretic damping is widened in some way to cover non-harmonic motion.
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TL;DR: In this article, the authors discussed the nature of damping mechanisms and how the damping depends on the amplitude and frequency of the cyclic motion of the system. But they did not consider the effect of the frequency and amplitude on damping.
384 citations
TL;DR: A review of micro resonant force gauges is presented in this article, where a theoretical description is given of gauges operating in a flexural mode of vibration, including a discussion of non-linear effects.
Abstract: A review of micro resonant force gauges is presented. A theoretical description is given of gauges operating in a flexural mode of vibration, including a discussion of non-linear effects. Gauge factor and quality factor are defined and their relevance is discussed. Performance issues such as sensitivity, stability and resolution are addressed. Design aspects, including the means for excitation and detection of the vibration, and examples of silicon microfabrication technologies are described.
272 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
TL;DR: In this article, a consistent time-domain representation for linear hysteretic damping is presented using the Hilbert transform, which is a mathe-matically correct way to replace the complex stiffness parameters or frequency-dependent damping coefficients commonly used in differential equations.
Abstract: Experimental observations have shown that the dissipation per cycle in many materials does not depend on the deformation frequency over a wide frequency range. A linear model used frequently to represent this type of mechanical behavior is the concept of linear hysteretic damping. Also referred to as structural damping and complex stiffness in the literature, this noncausal model is characterized by storage and loss moduli independent of frequency. In the present paper, a consistent time-domain representation for linear hysteretic damping is presented using the Hilbert transform. This time-domain representation is a mathe matically correct way to replace the complex-stiffness parameters or frequency-dependent damping coefficients commonly used in differential equations that model the dynamics of structures with linear hysteretic damping. A technique is proposed for the computation of the response of structures containing linear hysteretic elements in the time domain; the convergence of the iterative technique is analyzed; and simple numerical examples are developed to illustrate the application of the method.
143 citations
01 Jan 2010
TL;DR: Vasques et al. as discussed by the authors developed mathematical descriptions of material damping to represent the linear viscoelastic constitutive behavior, their implementation into finite element (FE) formulations and the use of the underlying different solution methods.
Abstract: This is the first of two companion articles addressing an integrated study on the mathematical modeling and assessment of the efficiency of surface mounted or embedded viscoelastic damping treatments, typically used to reduce structural vibration and/or noise radi- ation from structures, incorporating the adequate use and development of viscoelastic (arbitrary frequency dependent) damping models, along with their finite element (FE) implementation, and the experimental identification of the constitutive behavior of viscoelastic materials. This first article (Part I) is devoted to the development of mathematical descriptions of material damping to represent the linear viscoelastic constitutive behavior, their implementation into FE formulations and the use of the underlying different solution methods. To this end, internal variables models, such as the Golla-Hughes-McTavish (GHM) and anelastic displacement fields (ADF) models, and other methods such as the direct frequency response (DFR), based on the complex modulus approach (CMA), iterative modal strain energy (IMSE) and an approach based on an iterative complex eigensolution (ICE) are described and implemented at the global FE model level. The experimental identification of viscoelastic materials properties and the aforementioned viscoelastically damped FE modeling approaches are assessed and validated in the companion article (Vasques, C.M.A. et al., Viscoelastic damping technologies-Part II: Experimental identification procedure and validation, Journal of Advanced Research in Mechanical Engineering 1(2): 96-110 (2010)).
80 citations
Cites background from "The Treatment of Damping Forces in ..."
...The interested readers are referred to some textbooks and articles on general damping theory [Bishop (1955), Crandall (1970), Ewins (2000), Lesieutre (2001), Inman (2001), Cremer et al....
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Book•
01 Jan 1951
TL;DR: This book, although having the same title as the 1938 edition, is an entirely new text, in which the whole subject matter is brought up to date and the theoretical foundations of chain reactions are well set out.
Abstract: This book, although having the same title as the 1938 edition, is an entirely new text, in which the whole subject matter is brought up to date. It is divided into four parts. Part I describes the chemistry and kinetics of the reactions of fuel gases with oxygen, and in detail with hydrogen, carbon monoxide and various hydrocarbon gases. The theoretical foundations of chain reactions are well set out in an initial chapter and the authors have not been shy of using mathematics to give precision to the subject. The hydrocarbon chapter ends with an account of recent work on engine knock.
205 citations
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...Recently a book on the flutter of aircraft has appeared((2)) in which extensive use is made of the concept....
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TL;DR: In this paper, the structural damping factor g in vibration problems implies that the damped free vibration frequency of the structure increases with damping, and relations are derived comparing the natural frequencies and logarithmic decrements for viscous and structural dampings.
Abstract: The use of the structural damping factor g in vibration problems implies tha t the damped free vibration frequency of the structure increases with damping. Relations are derived comparing the natural frequencies and logarithmic decrements for viscous and structural damping. For low values of damping (up to g — 0.20), the two concepts give nearly the same results when g is taken as twice the critical viscous damping ratio.
59 citations