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)     

Damping Of Pedestrian‐Induced Bridge Vibrations By Tuned Liquid Column Dampers

The excessive lateral vibrations of Londons Millenium Bridge and the Toda Park Bridge in Japan due to a large number of crossing pedestrians have raised an unexpected problem in footbridge constructions. Secondary tuned structures, like the conventional tuned mass damper (TMD) or the tuned liquid damper (TLD) were installed to the bridge in order to suppress these vibrations. In the present investigation it is proposed to apply the more efficient and more economic tuned liquid column damper (TLCD), which relies on the motion of a liquid mass in a sealed tube to counteract the external motion, while a built‐in orifice plate induces turbulent damping forces that dissipate kinetic energy. For optimal tuning of TLCDs the natural frequency and equivalent linear damping coefficient have to be chosen suitable, likewise to the conventional TMDs, as given in Den Hartog [1]. The advantages of TLCDs are: simple tuning of natural frequency and damping, low cost of design and maintenance and a simple construction. A mathematical model of a three degree‐of‐freedom (DOF) bridge coupled with an optimal tuned TLCD is derived and analyzed numerically. Furthermore, a small scale experimental model set‐up has been constructed in the laboratory of the TU‐Insitute. The experimental results are in good agreement with the theoretical predictions and indicate that TLCDs are effective damping devices for the undesired pedestrian induced footbridge vibrations. (© 2004 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

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.     

On the oscillations of a thin-walled structure containing a fluid, in the presence of a hydrodynamic damper : PMM vol. 43, no. 6, 1979, pp. 1095–1101

A model of a hydrodynamic oscillation damper is proposed. The model is used to obtain the equations describing longitudinal oscillations of a structure which includes a shell partially filled with fluid, and contains a hydrodynamic damper. It is shown that the use of the damper leads to considerable increase in the damping of the oscillations of specified frequencies within the structure.

In modern technology one encounters various types of problems connected with restricting the amplitudes of the axisymmetric vibrations of shells and of the longitudinal oscillations of structures consisting of shells partially filled with fluid. Various devices have been proposed [1] for solving these problems. All these devices have a common feature, namely an elastic shell filled with gas and placed in the fluid. The natural frequency of oscillations of such a shell in a fluid can be tuned to required frequency. The effect of such a device is analogous to the effect of a dynamic vibration damper in mechanical systems [2]. A part of the fluid contained in the shell serves as the active mass of the dynamic damper, and for this reason we shall call such devices the hydrodynamic vibration dampers.     

Mechatronic system with shunted piezoelectric damper modelled with structural damping

Paper presents analysis of an one-dimension flexural vibrating mechatronic system. The considered system is a cantilever beam with a piezoelectric transducer bonded to the beam's surface. An external electric circuit is adjoined to the transducer's clamps in order to damp vibrations. System was analyzed on the basis of an approximate Galerkin method. Verification and assumptions of the approximate method were described in the previous papers where analysis of the mechatronic system with piezoelectric shunt damper was presented. Structural damping of all system's components was being taken into consideration. Rheological properties were introduced using Kelvin-Voigt model of materials. Influences of component's structural damping coefficients values on the system's dynamic flexibility were defined. Obtained results were presented on 3D graphs as dynamic flexibility dependence on the structural damping coefficient and frequency of an external force that was applied to the system. (© 2011 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Damping of structural vibrations using an electromotive eddy current damper

Structural vibrations are normally the cause for high cycle fatigue failure (HCF) in technical structures. For example, the blades of rotating bladed turbine disks are subjected to fluctuating gas forces during operation that cause blade vibrations. Therefore, one of the main tasks in the design of turbomachinery blading is the reduction of the vibration amplitudes of the blades and it is well known that the vibration amplitudes can be reduced significantly to a reasonable amount by means of friction damping devices such as underplatform dampers, tip shrouds and damping wires. If the temperature of the working fluid is not excessively high, the use of an electromotive eddy current damper can be a possible alternative to this well known classical friction damping devices. If a conducting material is moving in a stationary magnetic field, eddy currents are generated inside the conductor. These eddy currents cause an energy dissipation effect and damping forces are generated. This damping effect can be used to reduce the resonance amplitudes and therefore to decrease the risk of a HCF failure. (© 2008 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Active nonlinear saturation-based control for suppressing the free vibration of a self-excited plant

A nonlinear saturation-based control strategy for the suppression of the free vibration of a self-excited plant is presented. The self-excitation to have the classical form of that of the van der Pol oscillator is considered. The control technique is implemented by coupling the active absorber with the plant via a specific set of quadratic nonlinearities. The perturbation method of multiple scales is employed to find the first-order approximate solutions to the governing equations. Then a stability analysis is conducted for the response of the system and the performance of the control strategy is investigated. A parametric investigation is carried out to see the effects of changing the damping ratio of the absorber, and the value of the feedback gain on the responses of the plant and the absorber. Finally, the perturbation solutions are verified by numerical integration of the governing differential equations. It is demonstrated that the saturation-based control method is effective in reducing the vibration response of the self-excited plant when the absorber’s frequency is exactly tuned to one-half the natural frequency of the plant.     

The vibrational behaviour of bladed disks with multiple coupling devices

In turbomachinery applications turbine blades are subjected to high static and dynamic loads. Static loads are due to centrifugal stresses and thermal strains. Especially the dynamic excitation caused by fluctuating gas forces results in high vibration amplitudes which can lead to high cycle fatigue failures (HCF). Therefore, in practical applications, coupling devices like underplatform dampers, lacing wires and tip shrouds are installed to the structure. In case of blade vibrations the relative displacements between these coupling devices and the blades generate friction forces. The resulting energy dissipation provides additional damping to the structure. Furthermore, coupling devices, in particular tip shrouds, snubbers and lacing wires, increase the stiffness of the structure. Hence, they lead to a shift of the resonance frequencies. So far, only effects of single coupling devices and the influencing properties have been examined. Within this paper the effect of multiple couplings is determined and compared with single couplings. The forced response of turbine bladings with multiple couplings is calculated under consideration of geometrical and mechanical parameters of the blading and contacts, respectively. The results are compared with the single coupled blading. Furthermore, a multiple coupled device with under-platform damper and connecting pin is compared with respect to his effectiveness. Especially the influence on the resonance frequency and the achievable damping is analysed. The results of the simulation are verified by measurements at a two-blade non-rotating test rig with an underplatform damper and connecting pin. (© 2008 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)     

Structural vibration control by means of nonlinear pendulum dampers

This paper discusses the application of a nonlinear Pendulum Tuned Mass Damper (PTMD) for the reduction of structural vibrations. Pendulum dynamic absorbers are used extensively to reduce the vibration level of slender elastic structures such as towers. A PTMD is a device consisting of a suspended mass, and a damper that is attached to the tower in order to reduce its dynamic response. The primary eigenfrequency of the nonlinear damper is tuned to a particular structural frequency. Energy is dissipated by the damping force acting on the structure. Here, the PTMD is applied to a tower as a continuous system consisting of distributed mass and elasticity. The optimum values of PTMD parameters are found based on minimization of the response of the tower tip–point. Time history and frequency domain responses for the tower with PTMD in linear and nonlinear condition are compared. In addition, the equations of motion of active pendulum control are intruduced. (© 2008 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Design of an optimal tuned mass damper for a system with parametric uncertainty

Structural control is becoming an attractive alternative for enhanced performance of civil engineering structures subject to seismic and wind loads. However, in order to guarantee stability and performance of structures when implemented with a passive or active control technique, there is a need to include information of uncertainty in the structural models due to the fact that civil engineering structures are time variant and nonlinear. These variations in the structure are often due to parameters such as variable live loads and inelastic behavior and, in cases, may be modeled as parametric uncertainty. The design of an optimal tuned mass damper (TMD) for a one degree-of-freedom (SDOF) system with parametric uncertainty is presented in this paper. The optimization of the connection between the absorber and the primary structure is cast as a constant feedback problem which is solved using structured singular value, μ, synthesis with D-K iteration and decentralized H _∞ design. Results are presented of the TMD that minimize the harmonic response of the primary structure represented by a set of systems within an uncertainty set.     

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)     

约束阻尼悬臂梁瞬态响应近似解析解与实验分析

利用弹性悬臂梁模态叠加构造出约束阻尼悬臂梁的振动模态,基于Lagrange方程推导出了约束阻尼悬臂梁的控制方程,求解了在集中力突然卸载的情况下约束阻尼悬臂梁的动力响应．计算并测试了一系列铝合金约束阻尼悬臂梁模型的振动频率和瞬态响应,分析了阻尼层材料参数对铝合金约束悬臂梁瞬态响应时间的影响．采用了解析法以及实验法两种方法,结果表明,所采用的方法是可靠的．     

Mechanical model of a mistuned 2DOF-structure coupled by viscous damping

In this paper the vibration amplitude reduction of a mechanical system is investigated when applying a damper between different DOF of that structure. Thereby, an elementary mechanical model consisting of two mass-spring elements with slightly differing eigenfrequencies and which are connected via a viscous dashpot damper is regarded. To investigate the systems behavior, an analysis of the transfer function and its poles and zeros in the L APLACE domain is performed when varying the damping constant. This reveals that the achievable amplitude reduction depends on the mistuning of the system and that even ideal viscous damping leads to a coupling which results in a shift of eigenfrequencies. (© 2009 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Tuning of mass dampers for preventing brittle fracture by employing teaching learning based optimization

In design of reinforced concrete structures, a ductile design is needed, because the brittle fracture is sudden. Also, the energy absorbed by the structure is effective for ductile structures during earthquake excitations. In design regulations, especially for vertical supporters such as columns, the shear force and axial force capacity is limited, although the strength of the members is not at the limits. For that reason, the shear forces of structures excited by earthquakes can be reduced by adding a tuned mass damper (TMD), but TMD must be optimized and it must not be heavy. If the mass of the TMD is not optimized, the ductile behaviour constraint about the axial force capacity cannot be provided. The compressive strength of the concrete is a measure for the effective application of a TMD to a reinforced concrete structure. Since the mass is limited by the design constraint, the other design variables of TMD such as period and damping ratio are optimized. Using the formulas for frequency and damping ratio related to a preselected mass may not be sufficient and a precise optimum solution for preventing brittle fracture. Metaheuristic methods can be used by using a specific limit. In this study, Teaching Learning Based Optimization (TLBO) is employed to find optimum TMD parameters. Several earthquake excitations were used in the optimization process. A three storey RC frame structures with different compressive strength of concrete is investigated. Three stopping criteria have been used in the proposed methodology. The first criterion is the reduction of the maxi-mum shear force value for the most critical excitation to the ductile behaviour limit. The second criterion is the reduction of the ratio of maximum first storey displacements of structure with and without TMD. This value is reduced under a user defined value, but the user defined value can be entered as zero. This value can be iteratively increased for minimization. The last criterion is the reduction of the acceleration transfer function of the structure. The proposed method is feasible on finding optimum TMD ensuring ductility conditions. (© 2016 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

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.     

Vibration analysis of Nano-Rotor's Blade applying Eringen nonlocal elasticity and generalized differential quadrature method

This study investigates the small scale effect on the flapwise bending vibrations of a rotating nanoplate. The nanoplate is modeled with a classical plate theory and considering cantilever and propped cantilever boundary conditions. Due to the rotation, the axial forces are included in the model as true spatial variation. Hamilton's principle is used to derive the governing equation and boundary conditions of the classical plate theory based on Eringen's nonlocal elasticity theory. The generalized differential quadrature method is employed to solve the governing equation. The effect of small-scale parameter, non-dimensional angular velocity, non-dimensional hub radius, aspect ratio, and different boundary conditions in the first four non-dimensional frequencies is discussed. Due to considering rotating effects, results of this study are applicable in nano-machines such as nano-motors and nano-turbines and other nanostructures.     

Anharmonic vibrations of a nano-sized oscillator with fractional damping

We investigate the nonlinear vibrations of nano-sized cantilever. The elastic force is considered anharmonic, deriving from a Morse potential and the nonlinearity is attributed to the Casimir force. We consider two cases, the first of viscous damping and the second of fractional damping.The solution is also established by using the Adomian decomposition method.     

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.