A semi-active vibration absorber with real-time controlled magnetorheological damper (MR-SVA) for the mitigation of harmonic structural vibrations is presented. The MR damper force targets to realize the frequency and damping adaptations to the actual structural frequency according to the principle of the undamped vibration absorber. The relative motion constraint of the MR-SVA is taken into account by an adaptive nonlinear control of the internal damping of the MR-SVA. The MR-SVA is numerically and experimentally validated for harmonic excitation of the primary structure when the natural frequency of the passive mass spring system of the MR-SVA is correctly tuned to the targeted structural resonance frequency and when de-tuning is present. The results demonstrate that the MR-SVA outperforms the passive TMD at structural resonance frequency by at least 12.4% and up to 60.0%.

The semi-active vibration absorber (SVA) based on controlled semi-active damper is formulated to realize the behaviour of the passive undamped vibration absorber tuned to the actual harmonic disturbing frequency. It is shown that the controlled stiffness force, which is emulated by the semi-active damper to realize the precise real-time frequency tuning of the SVA, is unpreventably combined with the generation of undesirable damping in the semi-active damper whereby the SVA does not behave as targeted. The semi-active stiffness force is therefore optimized for minimum primary structure response. The results point out that the optimal semi-active stiffness force reduces the undesirable energy dissipation in the SVA at the expenses of slight imprecise frequency tuning. Based on these findings, a real-time applicable suboptimal SVA is formulated that also takes the relative motion constraint of real mass dampers into account. The results demonstrate that the performance of the suboptimal SVA is closer to that of the active solution than that of the passive mass damper.

The problem of optimal semi-active damping of cables with bending stiffness is investigated with an evolutionary algorithm. The developed damping strategy is validated on a single strand cable with a linear motor attached close to the anchor position. The motor is operated in force feedback mode during free decay of cable vibrations, during which time the decay ratios of the cable modes are measured. It is shown from these experiments that the damping ratios predicted in simulation are close to those measured. The semi-active damping strategy found by the evolutionary algorithm is very similar in character to that for a cable without bending stiffness, being the superposition of an amplitude-dependent friction and negative stiffness element. However, due to the bending stiffness of the cable, the tuning of the above elements as a function of the relevant cable parameters is greatly altered, especially for damper positions close to a fixed end anchor, where the mode shape depends strongly on bending stiffness. It is furthermore demonstrated that a semi-active damper is able to dissipate significantly more energy for a cable with simply supported ends compared to fixed ends due to larger damper strokes and thereby increased energy dissipation in the device.

This paper investigates numerically and experimentally clipped viscous damping with negative stiffness for semi-active cable damping. From simulations it is concluded that unclipped and clipped viscous damping with negative stiffness is equivalent to unclipped and clipped LQR. It is shown that optimized unclipped viscous damping with negative stiffness generates critical cable damping by an anti-node at the actuator position. The resulting curvature at the actuator position is larger than the curvature close to the anchors due to the disturbance forces which may lead to premature cable fatigue at the actuator position. Optimized clipped viscous damping with negative stiffness does not show this drawback, can be implemented using a semi-active damper and produces twice as much cable damping as optimal viscous damping. Close to the optimal tuning, it leads to approximately the same control force as optimal semi-active friction damping with negative stiffness, which explains the superior cable damping. The superior damping results from the negative stiffness that increases the damper motion. Clipped viscous damping with negative stiffness is validated on a strand cable with a magneto-rheological damper. The measured cable damping is twice that achieved by emulated viscous damping, which confirms the numerical results. A tuning rule for clipped viscous damping with negative stiffness of real cables with flexural rigidity is given.

Disc-type magnetorheological (MR) dampers are controllable semi-active actuators. The MR fluid within these devices is operated in shear mode, instead of the more frequently encountered flow mode. The present paper develops a model for this controllable device based on the measured behavior of an MR fluid sample deformed in a rheometer under operating conditions similar to those found within the damper. It is observed that for these conditions the behavior of the MR fluid is governed by friction. To capture the stick-slip motion of the MR fluid, the damper model is based on the popular LuGre friction model with additional parameters to account for the geometry of the fluid body. The model also includes the response dynamics due to the aggregation and radial migration of particles in the MR fluid body. These dynamics are separated into three first-order elements with time constants in the order of milliseconds, seconds and minutes. The model is validated with measurements on a cable-damper setup subjected to modal excitations.

This investigation optimizes numerically a viscous–friction damper connected to a cable close to one cable anchor for fastest reduction of the total mechanical cable energy during a free vibration decay test. The optimization parameters are the viscous coefficient of the viscous part and the ratio between the friction force and displacement amplitude of the friction part of the transverse damper. Results demonstrate that an almost pure friction damper with negligibly small viscous damping generates fastest cable energy reduction over the entire decay. The ratio between the friction force and displacement amplitude of the optimal friction damper differs from that derived from the energy equivalent optimal viscous damper. The reason for this is that the nonlinearity of the friction damper causes energy spillover from the excited to higher modes of the order of 10%, i.e. cables with attached friction dampers vibrate at several frequencies. This explains why the energy equivalent approach does not yield the optimal friction damper. Analysis of the simulation data demonstrates that the optimally tuned friction damper dissipates the same energy per cycle as if each modal component of the cable were damped by its corresponding optimal linear viscous damper.

This paper investigates numerically the optimal tuning of Coulomb friction dampers on cables, where the optimality criterion is maximum additional damping in the first vibration mode. The expression for the optimal friction force level of Coulomb friction dampers follows from the linear viscous damper via harmonic averaging. It turns out that the friction force level has to be adjusted in proportion to cable amplitude at damper position which is realized by amplitude feedback in real time. The performance of this adaptive damper is assessed by simulated free decay curves from which the damping is estimated. It is found that the damping efficiency agrees well with the expected value at the theoretical optimum. However, maximum damping is larger and achieved at a force to amplitude ratio of 1.4 times the analytical value. Investigations show that the increased damping results from energy spillover to higher modes evoked by the amplitude proportional Coulomb friction damper which clamps the cable at its upper and lower positions. The resulting nonsinusoidal cable motion clearly violates the assumption of pure harmonic motion and explains why such dampers have to be tuned differently from optimal linear viscous dampers.

This paper presents a solution to the problem of cable vibration mitigation using a semi-active damping device. The optimal control of such a device is investigated with an evolutionary algorithm. A fitness function for the algorithm is defined, as the total energy removed from the cable by the damper in a numerical simulation. The initial and end conditions of the optimization are defined such that the solution is optimal for a single mode of vibration. The solution produced by the evolutionary algorithm is shown to outperform other popular semi-active control strategies for the given conditions, removing as much as 2.0 and 1.2 times more energy than the optimal linear viscous damper and clipped linear quadratic regulator controller, respectively. It is furthermore shown that the solution can be given as a simple control law parametrized with a single parameter. The performance of the control law derived is assessed by means of numerical simulation with a free vibration decay test. Due to the multiple modes of vibrations induced by the nonlinear damper in this test, the control law performance is slightly decreased compared to the aforementioned efficiency.

Rain–wind induced stay cable vibrations may occur at different cable eigenfrequencies. Therefore, external transverse dampers have to be designed for several target cable modes. The resulting modal damping ratios have to fulfil Irwin’s criterion for minimum Scruton number such that rain–wind induced vibrations can be excluded. For this situation, this paper presents a systematic and easy applicable design procedure for linear viscous dampers that respects Irwin’s criterion, minimizes the damper position and leads to almost minimum variance of the target modal damping ratios. Minimum damper position is preferable from the aesthetic point of view, and it minimizes the installation costs, reduces the damper support flexibility and thereby increases the damper efficiency. Minimum variance of the target modal damping ratios maximizes the safety against large amplitude vibrations due to the unpredictability of the predominant mode.

The dissipated cycle energy of magnetorheological (MR) dampers operated at constant current results from controllable hysteretic damping and from almost current independent, small viscous damping. Thus, the emulation of Coulomb friction and linear viscous damping necessitates current modulation during one vibration cycle and therefore current drivers. To avoid this drawback, a cycle energy control (CEC) approach is presented which controls the hysteretic MR damper part such that the total MR damper energy equals the energy of optimal linear viscous damping by constant current during one cycle. The excited higher modes due to the hysteretic damping part are partially damped by the MR damper viscous part. Simulations show that CEC copes better with damper force dynamics and constraints than emulated linear viscous damping due to the slow control force dynamics of CEC which are given by cable amplitude dynamics. It is demonstrated that CEC of MR dampers with viscosity of approximately 4.65% of the optimal modal viscosity performs better than optimal linear viscous damping. The reason is that this damper viscosity represents an optimal compromise between maximum energy spillover to higher modes due to the controllable hysteretic part which produces more cable damping and maximum viscous damping of these higher modes. Damping tests on a cable with an MR damper validate the CEC approach.

This paper validates an approach to damage detection and localization based on finite-element model updating (FEMU). The approach has the advantage over other existing methods to FEMU that it simultaneously updates all three finite-element model matrices at the same time preserving their structure (connectivity), symmetry and positive-definiteness. The approach is tested in this paper on an experimental setup consisting of a steel cable, where local mass changes and global change in the tension of the cable are introduced. The new algorithm is applied to identify the size and location of different changes in the structural parameters (mass, stiffness and damping). The obtained results clearly indicate that even small structural changes can be detected and localized with the new method. Additionally, a comparison with many other FEMU-based methods has been performed to show the superiority of the considered method.

This paper describes the measured damping characteristics of a cable with perpendicularly attached magnetorheological fluid damper. First, the damping of the free cable is measured for reference. Then, the magnetorheological fluid damper is connected to the cable in order to measure the resulting damping at different constant damper current levels. The experimental data shows clearly that the optimal current level providing maximum additional damping to one targeted mode is in inverse ratio to the mode number. Since the force trajectory at constant current of the MR damper under consideration describes nearly a Coulomb friction, the viscosity of an ideal viscous damper dissipating the same amount of energy is estimated. Also this equivalent viscosity depends in inverse ratio on the mode number. If the control target is maximum damping of several modes, the damper current hardly depends on the control target. Furthermore, the measurements demonstrate that external dampers lead to an increase of the structural resonance frequencies since MR dampers producing large forces at high current levels represent additional, fairly stiff supports. This is in contradiction to enhanced structural damping which evokes decreasing resonance frequencies.

The vibration mitigation performance of different feedback controlled damping devices for cable vibration mitigation is investigated. A model-based designed LQG controller estimates the vibration state based on a validated linear cable model. The main nonlinearity of the connected system damping device - cable is compensated by its inverse function. The simulated damping devices are actuator and controllable damper without any actuator/damper dynamics. It is assumed that further constraints such as minimum or maximum force limitations do not exist. The theoretical study compares the potential of vibration mitigation using a feedback controlled actuator and a feedback controlled damper. The comparative study is simulated for two positions of the damping device. One is near the anchorage, which is the only possible position on a real cable-stayed bridge. The other position is characterized by the largest cable displacement within the frequency range of the first four modes. In order to guarantee a fair comparison, the optimal controller parameters are determined for the active controlled actuator and semi-active controlled damper for both positions. The simulation results demonstrate, first, that active controlled actuators can hardly mitigate vibrations more effectively than semi-active controlled dampers because vibration energy must be dissipated. Second, the position of the damping device shows a negligible influence on the mitigation performance because smaller displacements and therefore smaller velocities near the anchorage are compensated by larger actuator/damper forces.

This paper presents a mean value model of a pressure wave supercharger together with a spark ignition engine including external exhaust gas recirculation. The model of the pressure wave supercharger is based on linear one-dimensional gas dynamics. It includes an approach for the mixing zone between exhaust gases and fresh air which permits the calculation of the exhaust gas recirculation rate within the charger. The mass flow of the recirculated exhaust gas is the combined effect of too large an exhaust gas penetration into the cell wheel of the charger and of incomplete scavenging of the cell wheel. The model of the pressure wave supercharger is validated by the identification of four physically based model parameters and shows an error smaller than 5 per cent over the operating range investigated. The model can be integrated into an overall engine system model which predicts transient exhaust gas recirculation effects during load steps with good accuracy. The system model demonstrates that exhaust gas recirculation during transients is mainly caused by incomplete scavenging of the cell wheel and not by the exhaust gas penetration into the cell wheel being too large. Both the model of the pressure wave supercharger and the overall engine system model are validated by steady state and transient measurements on a dynamic test bench.