Evolution of the resonance vibrations of an oscillator with dry friction

We study the problem of free and forced vibrations of a mechanical system modeling the functioning of seismic isolation systems of “kinematic foundation” type in the case when the sliding friction damper is not centrally located. We determine the damping characteristics in the case of free vibrations and the critical values of the damping parameter for the case of forced vibrations. For the case of resonance vibrations with one degree of freedom we establish the relation of the increase in the amplitude of the vibrations to time at subcritical values of the friction. Translated fromDinamicheskie Sistemy, Vol. 11, 1992.     

Subharmonic and bursting oscillations of a ferromagnetic mass fixed on a spring and subjected to an AC electromagnet

This paper considers the dynamics of an electromechanical system consisting of a ferromagnetic mass fixed on a spring and subjected to an AC electromagnet. Subharmonic and bursting oscillations are found and their shape analyzed when one varies the viscous damping coefficient, the number of turns of the coil, the frequency and amplitude of the AC voltage. Pulse packages patterns and sharp burstings are observed in the motion of the mechanical part.     

A tuning criterion for the inertial tuned damper. Design using phasors in the Argand–Gauss plane

A new approach to the design of a dynamic damper for a monomass oscillator is presented; the design procedure is then applied to control a multimodal oscillator. This new dynamics emerged from an analysis by means of phasors (rotating vectors in the Argand–Gauss plane) which revealed the phase relations between the damper and main oscillator. In particular this work introduces a geometric formalism, based on the use of phasors in the complex plane, for the sizing of inertial dampers applied to multimodal structural oscillators. Their damping effect depends on the fact that the response of the secondary oscillator (the damper) delays the response of the primary mass by 90°, so that the elastic force transmitted by the damper becomes a viscous force on the controlled oscillator. When such condition occurs we say that the damper is “tuned” to the main oscillator; the damping induced by the damper serves to limit the displacement of main oscillator. Our geometrical approach provides a method whose language is close to that of structural mechanics, thus paving the way to the professionals for: (i) sizing the damper parameters and (ii) evaluating the stability to the damped system and its performance limits. The aim of the development is that of exploring the use of dampers to control the response of buildings under horizontal seismic and aerodynamic loads.     

Residual saturated porous media – from oscillating water blobs to waves in ground earth

A model for wave propagation in residual saturated porous media is presented distinguishing enclosed fluid clusters with respect to their eigenfrequency and damping properties. The additional micro-structure information of cluster specific damping is preserved during the formal upscaling process and allows a stronger coupling between micro- and macro-scale than characterisation via eigenfrequencies alone. A numerical example of sandstone filled with air and liquid clusters of different eigenfrequency and damping distributions is given. If energy dissipation due to viscous damping dominates energy storage due to cluster oscillations, the damping distribution is more influential than the eigenfrequency distribution and vice versa. Spreading the damping distribution around a constant mean value supported the effect of capillary forces and spreading the eigenfrequency distribution around a constant mean value supported the effect of viscous damping in the investigated samples. For a wide distribution of the liquid clusters' damping properties, two damping mechanisms of propagating waves occur at the same time: damping due to viscous effects (for highly damped clusters) and energy storage by cluster oscillations (for underdamped clusters). (© 2013 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Dynamics of an electromechanical damping device with magnetic coupling

In this paper, we analyze the dynamics of an electromechanical damping device, which consist of an electrical system coupled magnetically to a mechanical structure, and that works by transferring the vibration energy of the mechanical system to the electrical system. We study the instability issues which limit the performance of the device. An analysis of the effective range of the coupling parameter for which a good reduction of the amplitude of the mechanical system occurs is presented. The effects of the coupling parameter on the bifurcation structures are found and it appears that with the appropriate choosing coupling parameter, the quenching of mechanical chaotic vibrations takes place.     

Shaking table tests of a model-scale building with 2DOF pendulum mass damper

In this paper, the numerical and experimental studies of a tall building's model with 2DOF pendulum mass damper (PMD) are considered. It is assumed that the model excitation is in the form of horizontal and/or torsional motion of the ground caused by earthquake. The construction consists of the main system (tall building's model) and a double pendulum mass damper, which is attuned to the first (bending) and the second (torsional) eigenfrequencies of the main structure. The analysis focuses on reduction of structure vibration caused by horizontal or torsional component of ground motions. Therefore, results presented in this work show efficiency of 2DOF PMD for vibration reduction. The numerical analysis of the problem is performed with using COSMOS/M system (a FEM numerical model is defined), while experimental analysis is carried out on a physical model-scale building with 2DOF PMD. Model consists of twenty five recurrent storeys (height 2.5m) with a PMD located on the highest one. Shaking table device is used to simulate an earthquake excitation in horizontal and torsional component, independently. (© 2012 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

On the characteristics of a quasi-zero-stiffness vibration isolator with viscoelastic damper

Quasi-zero-stiffness (QZS) vibration isolators have been widely studied in previous literature, in which the viscous damping was adopted. In this paper, the QZS isolator with viscoelastic damper is studied, to seek an approach for further improving the isolation performance. The governing equation of the QZS isolator with viscoelastic damper (QZS-VED isolator) is formulated. The dynamic response is analyzed analytically and numerically. The transmissibility characteristics with varying key parameters are investigated, accompanied by comparison with the conventional QZS isolator, to demonstrate the advantages of the QZS-VED isolator. It is revealed that the damping ratio can be optimized to attain the lowest peak transmissibility and meanwhile the roll-off rate of high frequency transmissibility is twice that of the conventional QZS isolator, which implies superior isolation performance both around the resonant frequency and at high frequencies.     

Frequency response and damping analyses of structures with different damping models

The behavior of structures with different damping models has been investigated using finite element and frequency response analyses. As an example, systems with hysteretic and viscous damping were examined. The damped eigenfrequencies and the corresponding loss factors were computed based on frequency response analysis and then compared to the results obtained from free vibration analysis using the method of complex eigenvalues. Recommendations are given for a more effective employment of frequency response and damping analyses in the structures considered.Institute of Computer Analysis of Structures, Riga Technical University, Kalku, St. 1, Riga, LV-1658 Latvia. Published in Mekhanika Kompozitnykh Materialov, Vol. 33, No. 2, pp. 226–234, March–April, 1997.     

Nonlinear resonances of a semi-infinite cable on a nonlinear elastic foundation

The Multiple Time Scale (MTS) method is applied to the study of nonlinear resonances of a semi-infinite cable resting on a nonlinear elastic foundation, subject to a constant uniformly distributed load and to a linear viscous damping force. The zero order solution provides the static displacement, which is governed by a nonlinear equation which has been solved in closed form. The first order solution provides the linear resonances, which are seen to be functions of the nonlinearity parameter and of the static displacement at the finite boundary only. Although the first-order governing equation is linear, it has non constant coefficients and cannot be solved in closed form, so that a numerical solution is considered; the eigenfrequencies obtained in this way are also compared with the approximate eigenvalues obtained by the WKB method. At the second order of the MTS expansion, we see that the solution is independent of the intermediate time scale; some additional terms are present, including a time-independent shift of the average position of the oscillations. Finally, the nonlinear frequency–amplitude response curves, which are investigated in detail and which represent the main result of this work, are obtained from the solvability condition at the third order.     

On the stability of swelling porous elastic soils with fluid saturation by one internal damping

^** Email: wangjc{at}graduate.hku.hk^*** Email: bzguo{at}iss.ac.cn This article addressed the stabilization of a system of 1D swellingporous elastic soils with fluid saturation. The system is describedby strongly coupled vibrating fluid and solid elastic materials.Using Riesz basis approach, we show that the whole system canbe exponentially stabilized by only one internal viscous dampingwith variable feedback gain imposed in the fluid part, whichis sharp contrast with the same effect by two dampings in existingliterature. Moreover, the explicit asymptotic expressions ofhigh eigenfrequencies exhibit clearly how this one damping canaffect the another part of solid vibration.     

A vertically acting tuned liquid column damper

The U-shaped tuned liquid column damper (TLCD) increases the effective structural damping of horizontal vibrations similar to the classical tuned mechanical pendulum type damper (TMD). The pipe-in-pipe TLCD applies to vertical vibrations, likewise to the spring-mass-dashpot TMD. When sealed, the gas-spring effect extends the frequency range of application to about five Hertz. The geometric analogy between the novel TLCD and the TMD still exists, making the first step in the tuning procedure “classical”. Subsequent fine tuning in state space when the TLCD is split into smaller ones in parallel action, renders an even more robust passive action. The experimentally observed averaged turbulent damping of the relative fluid flow and the weakly nonlinear gas-spring render the TLCD insensitive to overloads and parametric forcing. (© 2006 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Investigation of Damping of Vibrations in a System With Two‐Disc Inseparable Clutch

This paper presents the results of tests on free and forced harmonic torsional vibrations in a system with a two‐disc inseparable clutch, with structural friction taken into account. Nonlinear histeresis loop describing the frictional‐elastic properties of the system was introduced into the model. The mathematical model of the vibrating system containing two disks inseparable clutch was built. During free vibrations of the system, its damping characteristics were tested by a digital simulation method. The vibration damping decrement as a function of amplitude torsional displacement was determined. When vibrations were harmonically forced, the amplitude ‐ frequency characteristics of the system were determined numerically. The system was used as a nonlinear torsional vibration damper in a linear system with a harmonic force. (© 2004 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

Exponential Decay Rates for Structural Acoustic Model with an Overdamping on the Interface and Boundary Layer Dissipation

We study uniform stability properties of a strongly coupled system of Partial Differential Equations of hyperbolic/parabolic type, which arises from the analysis and control of acoustic models with structural damping on an interface. A challenging feature of the present model is the presence of additional strong boundary damping which is responsible for lack of uniform stability of the free system ( overdamping phenomenon). It has been shown recently that by applying full viscous damping in the interior of the domain and suitable static damping on the interface, then the corresponding feedback system is uniformly stable. In this article we prove that uniform decay rates of solutions to the system can be achieved even if viscous damping is active just in an arbitrary thin layer near the interface.     

弱粘性流体中垂直激励表面波的阻尼效应

在竖直振动的圆柱形容器中,将Navier-Stokes方程线性化,利用两时间尺度奇异摄动展开法研究了弱粘性流体的单一自由面驻波运动．整个流场被分为外部势流区和内部边界层区两部分,对两部分区域分别求解,得到包含阻尼项和外驱动影响的线性振幅方程．利用稳定性分析,得到形成稳定表面波的条件,给出了临界曲线．此外,还获得了阻尼系数的解析表达式．最后,将线性阻尼加到理想流体条件下所得到的色散关系中对其进行修正,理论结果证明修正后的驱动频率更加接近实验的结果．通过计算发现,当驱动的频率较低时,流体的粘性对表面波模式选择有重要影响,而表面张力的影响不明显;但当驱动频率较高时,流体的表面张力起主要作用,而流体的粘性影响甚小．     

Paradox of Nicolai and related effects

The paper presents a general approach to the paradox of Nicolai and related effects analyzed as a singularity of the stability boundary. We study potential systems with arbitrary degrees of freedom and two coincident eigenfrequencies disturbed by small non-conservative positional and damping forces. The instability region is obtained in the form of a cone having a finite discontinuous increase in the general case when arbitrarily small damping is introduced. This is a new destabilization phenomenon, which is similar to well-known Ziegler’s paradox or the effect of the discontinuous increase of the combination resonance region due to addition of infinitesimal damping. It is shown that only for specific ratios of damping coefficients, the system is stabilized due to presence of small damping. Then, we consider the paradox of Nicolai: the instability of a uniform axisymmetric elastic column loaded by axial force and a tangential torque of arbitrarily small magnitude. We extend the results of Nicolai showing that the column is stabilized by general small geometric imperfections and internal and external damping forces. It is shown that the paradox of Nicolai is related to the conical singularity of the stability boundary which transforms to a hyperboloid with the addition of small dissipation. As a specific example of imperfections, we study the case when cross-section of the column is changed from a circular to elliptic form.     

Computational analysis of rates of energy decay in elastic beams

This paper is concerned with the damping of elastic beams of two different kinds. The first model involves the application of viscous damping at a single point either in the interior or at the boundary. The second involves a thermoelastic beam model in which mechanical damping is applied at a boundary. Since the second model is known to be uniformly stabilized via thermal effects alone, an analysis of the relative importance of the thermal and applied mechanical damping is presented. A careful analysis of the effects of rotational forces is also included using realistic model parameters.     

Damping of Vibrations in a SystemWith Two Beams by Structural Friction

This paper presents the results of tests on free and forced harmonic vibrations in a system with two beams with structural friction taken into account. The beams are clamped together with uniform unitary pressure. The hysteresis loop describing the frictional-elastic properties of the system has a form of a parallelogram. The autor created a mathematical model of the vibrating system with two beams. During free vibrations of the system, its damping characteristics were tested by a digital simulation method. The vibration damping decrement as a function of amplitude displacement was determined. When vibrations were harmonically forced, the amplitude - frequency characteristics of the system were determined numerically. The system was used as a nonlinear vibration damper in a linear system with a harmonic force. The equations of motion of the nonlinear two-degree of freedom system were solved by means of a digital simulation method. (© 2005 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Symmetric and Asymmetric Underplatform Dampers for Turbine Blades

Friction damping devices like underplatform dampers are widely used in turbomachinery applications to reduce vibration amplitudes and to increase lifetime and reliability of the bladed disk. Nowadays, in practical applications, a variety of different underplatform damper geometries is applied. Nevertheless, a detailed study of the in.uence of the geometric and dynamic properties of the damper is still not available. Within this paper the most frequently applied damper types like cylindrical and wedge as well as asymmetrical dampers are investigated and compared to each other with respect to their effectiveness. Especially the in.uence of the damper geometry on the resonance frequency and vibration amplitude is pointed out. (© 2006 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Resonance frequencies of a cavity containing a compressible viscous fluid

The aim of this paper is to study the resonance spectrum of a cavity containing a compressible viscous fluid. This system admits a discrete infinite sequence of eigenvalues whose real parts are negative, which is interpreted as the damping effect introduced by viscosity. Only a finite number of them have non-zero imaginary parts and this number depends on viscosity; a simple criterion is given for their position in the complex plane. The case of a cavity containing an elastic mechanical system immersed in the fluid is also examined; from a qualitative point of view, the nature of the resonance spectrum remains unchanged.     

Low-damping slow modes of orientational nonlinear vibrations in liquid crystals in the presence of destabilizing magnetic fields

For nor linear inertial torsion vibrations of the structure of a nematic liquid crystal in a destabilizing magnetic field, there exist low-frequency modes with anomalously weak damping. The corresponding solution of a sine-Gordon-type equation, accounting for viscous rotational friction, describes the transitions between two equilibrium states separated by a potential barrier. We show that when the vibration amplitude is large enough to overcome the barrier, the ratio of the damping time to the vibration period diverges logarithmically. Translated from Teoreticheskaya i Matematicheskaya Fizika. Vol. 111, No. 1, pp. 132–143, April, 1997.