Search Results (17)

The dynamic vibration absorber (DVA) based on delayed fractional PID (DFOPID) can achieve a more superior vibration suppression effect. However, the strong nonlinear characteristics of the system and the computational burden resulting from its high dimensionality make solving and optimizing more challenging. This paper presents a coupled model of DFOPID and DVA, exploring its parameter tuning mechanism and optimization problem. First, using the averaging method and Lyapunov stability theory, the amplitude-frequency equation and the stability condition of the steady-state solution of the primary system are derived. Numerical simulations validate the accuracy of the analytical result. Next, based on the mechanics of vibration, the approximate expressions of the controller under different differential conditions are calculated, and their equivalent action mechanisms are analyzed. Finally, by minimizing the maximum amplitude of the primary system as the objective function, the Particle Swarm Optimization (PSO) algorithm is applied to optimize the parameters of the passive DVA and the DVA models controlled by PID, FOPID, and DFOPID, successfully addressing the parameter optimization challenges posed by traditional fixed-point theory. The vibration reduction performance is compared across different loading environments. The results demonstrate that the model presented in this paper performs the best, exhibiting excellent vibration suppression and robustness. Full article

This study explores the use of a passive control technique to mitigate aeroelastic effects on a wing operating near the ground. An aeroelastic model, based on a typical airfoil section, equipped with a nonlinear tuned vibration absorber (NLTVA), is established to study the interactions between the airfoil’s dynamics, aerodynamics, and the nonlinear energy dissipation mechanisms. Geometric nonlinearity is incorporated into the airfoil’s dynamics to account for possible large wing deflection and rotation. The flow is modeled based on the nonlinear unsteady discrete vortex method with the ground effect simulated using the mirror image method. Stability analyses are conducted to study the influence of NLTVA parameters on flutter mitigation and the bifurcation behavior of the airfoil near the ground. The numerical results demonstrate that the NLTVA effectively delays the onset of flutter and promotes a supercritical bifurcation in the presence of ground effect. Optimally tuning the NLTVA’s linear parameters significantly increases flutter speed, while selecting the optimal nonlinear parameter is key to preventing subcritical behavior near the ground and reducing the amplitude of post-flutter limit cycle oscillations. Overall, this study highlights the potential of the NLTVA in enhancing the aeroelastic stability of flying vehicles with highly flexible wings, especially under the influence of ground effects during takeoff and landing. Full article

Tuned liquid column damper (TLCD) is a well-known liquid damper designed to absorb the vibration of structures used in many applications, such as high-story buildings, wind turbines, and offshore platforms, requiring an accurate mathematical determination of the liquid level to model the TLCD structure system motion. The mathematical model of a TLCD is a nonlinear ordinary differential equation, unlike the structure, due to the term containing a viscous damping coefficient, and cannot be solved analytically. In this study, the fluid behavior of a TLCD without an orifice, directly connected to a shaking table under harmonic excitation, was investigated experimentally and a new linearization coefficient was proposed to be used in the mathematical model. First, the nonlinear mathematical model was transformed to a nondimensional form to better analyze the parameter relations, focusing on the steady-state amplitude of the liquid level during the harmonic excitation. The experimental data were then processed using the fourth-order Runge–Kutta method, and a correlation to calculate the viscous damping coefficient was proposed in the dimensionless form. Accordingly, a novel empirical model was proposed for the dimensionless steady-state amplitude of the liquid level using this correlation. Finally, with the help of the proposed correlation and the empirical model, an original linearization coefficient was introduced which does not need experimental data. The nonlinear mathematical model was linearized by using the developed linearization coefficient and solved analytically using the Laplace transform method. The study presents a generalized method for the analytical determination of the liquid level in a non-orifice TLCD under harmonic excitation, using a correlation and an empirical model proposed for the first time in this study, providing a novel and simple solution to be used in the examination of various TLCD structure systems. Full article

Tower fatigue and strength are crucial operational concerns of floating offshore wind turbines (FOWTs) due to the escalation of the vibration phenomena observed on these structures as compared to land-based ones. FOWT towers are excited by wave and wind polyperiodic disturbances yielding continual transient states of structural vibration that are challenging for vibration mitigation systems. Thus, the paper investigates a novel implementation of nonlinear optimal-based vibration control solutions for the full-scale, tension leg platform (TLP)-based, NREL 5MW wind turbine tower-nacelle model with a 10-ton tuned vibration absorber (TVA), equipped with a magnetorheological (MR) damper, located at the nacelle. The structure is subjected to excessive wave and wind excitations, considering floating platform motions derived from model experiments in a wave tank. The MR damper operates simultaneously with an electromagnetic force actuator (forming a hybrid TVA) or independently (a semiactive TVA). The study includes both actuators’ nonlinearities and dynamics, whereby the former are embedded in the Hamilton-principle-based nonlinear control solutions. The TVA is tuned either to the NREL 5MW tower-nacelle 1st bending mode frequency (TVA-TN) or to the TLP surge frequency (TVA-TLP). The optimal control task was redeveloped concerning the TVA stroke and transient vibration minimisation, including the implementation of the protected structure’s acceleration and relative displacement terms, as well as the nonzero velocity term in the quality index. The regarded model is embedded in a MATLAB/Simulink environment. On the basis of the obtained results, the TVA-TN solution is by far superior to the TVA-TLP one. All the regarded TVA-TN solutions provide a tower deflection safety factor of ca. 2, while reference systems without any vibration reduction solutions or with a passive TVA-TLP are at risk of tower structural failure as well as the hybrid TVA-TLP system. The obtained TVA stroke reductions of 25.7%/22.0% coincide with 3.6%/10.3% maximum tower deflection reductions for the semiactive/hybrid TVA-TN case (respectively) with regard to the previously developed approaches. Moreover, these reductions are obtained due to the sole control algorithm enhancement; thus, no additional resources are necessary, while this attainment is accompanied by a reduction in the required MR damper force. The lowest obtained TVA stroke amplitude of 1.66 m is guaranteed by the newly introduced semiactive control. Its hybrid equivalent ensures 8% lower primary structure deflection amplitude and reduced nacelle acceleration levels thanks to the utilisation of the force actuator of the relatively low power (ca. 6 kW); the trade-off is an increased TVA stroke amplitude of 2.19 m, which, however, is the lowest among all the tested hybrid solutions. The analysed reference passive TVA systems, along with a modified ground-hook hybrid solution, can hardly be implemented in the nacelle (especially along the demanding side–side direction). The latter, being the well-proven hybrid solution for steady-state tower deflection minimisation, yielded unsatisfactory results. The achievements of the study may be used for an effective design of a full-scale vibration reduction system for the TLP-based floating wind turbine structure. Full article

Theoretical and non-dimensional investigations have been performed to study the vibration control potential of approaches that are not only based on viscoelastic but also on endochronic elements. The latter are known from the endochronic theory of plasticity and provide the possibility of establishing rate-independent schemes for vibration control. The main question that has to be answered is: Can rate-independent damping be efficiently used to reduce mechanical vibrations? To answer this question, non-dimensional models for dynamical systems are derived and analyzed numerically in the time domain as well as in the frequency domain. The results are used to compare the performance of an optimally tuned endochronic absorber to the performance of an optimally tuned dynamic absorber with viscoelastic damping. Based on a novel closed-form representation for non-linear systems with endochronic elements, it has been possible to prove that the rate-independent control of vibration results in an overall control profit that is close to the control profit obtained by the application of well-established approaches. It has also been found that the new concept is advantageous if anti-resonances have to be considered in broadband vibration control. Based on these novel findings, a practical realization in the context of active vibration control is proposed in which the rate-independent control law is implemented with an appropriate signal processing hardware. Full article

The paper presents an experimental implementation of an optimal-based vibration control for a scaled wind turbine tower-nacelle structure. A laboratory model of the approximate power scale of 340 W, equipped with a nonlinear tuned vibration absorber (TVA), is analysed. For control purposes, a combined operation of a small-scale electric servo drive and a magnetorheological (MR) damper is used in the TVA system. Nonlinearities of both the electric drive and the MR damper are intrinsic parts of the adopted nonlinear control concept. The aim of the research is the simple-hardware real-time implementation and the experimental investigation of the simultaneous actuator and damper control, including the analysis of the influence of optimal control law parameters and quality function weights on the vibration attenuation efficiency and actuator energy demand. As a reference, an optimal-based, modified ground-hook control with the single goal of the primary structure deflection minimisation is used along with the passive system with zero MR damper current and idling electric actuator, proving the advantages of the proposed method. The regarded solutions guarantee 57% maximum structure deflection reduction concerning the passive TVA configuration, using an MR damper of 32 N maximum force and an electric drive of 12.5 N nominal force and 0.76 W nominal power. An interesting alternative is the optimal control concept tuned with regard to the actuator power minimisation—it provides 30% maximum structure deflection attenuation (concerning the passive TVA configuration) while using a passive damper of 3.3 N maximum force and an actuator of 0.17 W nominal power only. It makes evident the advantage of the properly tuned optimal control algorithm over the modified ground-hook law—it requires 51% less actuator energy than the latter parametrised to exhibit the same vibration attenuation properties. Full article

The NES (nonlinear energy sink) is a new type of nonlinear tuned mass damper that is connected to the shock-absorbing main structure through strong nonlinear stiffness and viscous damping. The vibrational energy in the main structure is transferred to the NES oscillator by means of target energy transfer. A shaking table test of a 1:4 scaled RC (Reinforced Concrete) frame structure model with a new type of NES shock absorber was conducted to study the damping effect of the NES shock absorber, especially for the influence of joint strength and deformation. The NES used in this experiment has a relatively large nonlinear stiffness and a wide vibration absorption frequency band. The variation of reinforcement strains, node failure mode, and structural natural frequency of 1 story and two-layer joints of the model frame structure with NES were studied. The test results showed that NES could effectively reduce the strains of longitudinal reinforcement and stirrup in beams and columns and delay the plastic hinge development at the bottom and the top of the column. The frame model with NES installed has failures at the beam ends and shear failures at the nodes, realizing the seismic mechanism of solid columns and weak beams. Compared with ordinary seismic structures, the NES can effectively reduce the shear stress of concrete at the joints and alleviate the shear failure of joints. The final failure of the NES shock absorbing structure was the yielding of the steel bars at the bottom of the column and the crushing of the concrete at the foot of the column, and the connection between the column foot and the backplane became loose simultaneously. The decreasing rate of the vibration frequency declined due to the NES with varied broadband absorbing capability. It can be seen that the NES shock absorber not only has a good effect on reducing the seismic response of the structure, but more importantly, the damage of the structural nodes is greatly reduced, and therefore, the seismic capacity of the structure improved. Full article

Nonlinear energy sinks (NES) have recently attracted significant interest for the suppression of unwanted vibrations in a variety of mechanical systems. The key advantage in employing this (vibration absorber) approach is the broadband nature of the interactions with a primary system for which vibration energy dissipation is required. Thus, the effectiveness of the NES is decoupled from the need of tuning to specific frequencies. Nevertheless, NES for rotational fluctuations of powertrains have received limited attention in the literature. In this work, a design for a rotational NES to mitigate speed fluctuations in gear trains is presented and tested experimentally. The development of the proposed system is underpinned by previous optimisation studies conducted by the authors, where a disk was utilised as an inerter NES. A set of beams couple the inerter with the wheel gear of a spur gear pair with a nonlinear restoring torque, which is designed to approach the desired essential nonlinearity within realistic practical tolerances. Static and dynamic identification is conducted to confirm the desired characteristics. Despite uncertainties in the prototype testing, the approach is found to reduce the speed fluctuations on the gear pair output shaft, with appropriate predictability established for the model and the design procedure. Full article

A wide variety of hyperelastic rubber-like materials, exhibiting strong nonlinear stress–strain relations under large deformations, is applied in various industrial mechanical systems and engineering applications involving shock and vibration absorbers. An optimal design procedure of an elevator chassis crashing on a hyperelastic shock absorber in a fail scenario, applicable in large-scale mechanical systems or industrial structures of high importance under strong nonlinear dynamic excitation, is presented in this work. For the characterization of the hyperelastic absorber, a Mooney–Rivlin material model was adopted, and a series of in-lab compression quasi-static tests were conducted. Applying a fully parallelizable state-of-the-art stochastic model updating methodology, coupled with robust, accurate and efficient Finite Element Analysis (FEA) software, the hyperelastic behavior of the shock absorber was validated under uniaxial large deformation, in order to tune all material parameters and develop a high-fidelity FE model of the shock absorber system. Next, a series of in situ full-scale experimental trials were carried out using a test-case elevator chassis, representing the crash scenario on the buffer absorber system, after a controlled free fall. A limited number of sensors, i.e., triaxial accelerometers and strain gauges, were placed at characteristic points of the real structure of the elevator chassis recording experimental data. A discrete Finite Element (FE) model of the experimentally tested arrangement involving the elevator chassis and updated buffer absorber system along with all boundary conditions was developed and used in explicit nonlinear analysis of the crash scenario. Steel material properties and the characterized updated Mooney–Rivlin material model were assigned to the elevator chassis and buffer, respectively. A direct comparison of the numerical and experimental data validated the reliability and accuracy of the methodology applied, whereas results of the analysis were used in order to redesign and optimize a new-design elevator chassis, achieving minimum design stresses and satisfying serviceability limit states. Full article

The online frequency estimation of forced harmonic vibrations on a building-like structure, using a nonlinear flexible vibration absorber in a cantilever beam configuration, is addressed in this article. Algebraic formulae to compute online the harmonic excitation frequency on the nonlinear vibrating mechanical system using solely available measurement signals of position, velocity, or acceleration are presented. Fast algebraic frequency estimation can, thus, be implemented to tune online a semi-active dynamic vibration absorber to obtain a high attenuation level of undesirable vibrations affecting the main mechanical system. A semi-active vibration absorber can be tuned for application where variations of the excitation frequency can be expected. Adaptive vibration absorption for forced harmonic vibration suppression for operational scenarios with variable excitation frequency can be then performed. Analytical, numerical, and experimental results to demonstrate the effectiveness and efficiency of the operating frequency estimation, as well as the acceptable attenuation level achieved by the tunable flexible vibration absorber, are presented. The algebraic parametric estimation approach can be extended to add capabilities of variable frequency vibration suppression for several configurations of dynamic vibration absorbers. Full article

This is a theoretical, numerical, and experimental study on the vibration attenuation capability of the dynamic response of a building-like structure using a dynamic vibration absorber in cantilever flexible beam configuration, taking into account gravitational effects associated with its mass. The dynamic model of the primary vibrating structure with the passive vibration control device is obtained using the Euler–Lagrange formulation considering the flexible vibration absorber as a generalized system of one degree of freedom. The application of the Hilbert transform to the frequency response function to determine the tuning conditions between this nonlinear flexible beam vibration absorber and the primary system is also proposed. In this fashion, Hilbert transform analysis is then carried out to show that nonlinearities present in the dynamic model do not significantly contribute to the performance of the implemented absorber. Therefore, it is valid to linearize the equations of motion to obtain the tuning condition in which the flexible vibration absorber can attenuate undesirable harmonic vibrations that are disturbing to the building-like flexible structure. Thus, the present study shows that the Hilbert transform can be applied to obtain tuning conditions for other configurations of dynamic vibration absorbers in nonlinear vibrating systems. Simulation and experimental results are included to demonstrate the efficient performance of the presented vibration absorption scheme. Full article

Conventional dynamic vibration absorbers are physical control devices designed to be coupled to flexible mechanical structures to be protected against undesirable forced vibrations. In this article, an approach to extend the capabilities of forced vibration suppression of the dynamic vibration absorbers into desired motion trajectory tracking control algorithms for a four-rotor unmanned aerial vehicle (UAV) is introduced. Nevertheless, additional physical control devices for mechanical vibration absorption are unnecessary in the proposed motion profile reference tracking control design perspective. A new dynamic control design approach for efficient tracking of desired motion profiles as well as for simultaneous active harmonic vibration absorption for a quadrotor helicopter is then proposed. In contrast to other control design methods, the presented motion tracking control scheme is based on the synthesis of multiple virtual (nonphysical) dynamic vibration absorbers. The mathematical structure of these physical mechanical devices, known as dynamic vibration absorbers, is properly exploited and extended for control synthesis for underactuated multiple-input multiple-output four-rotor nonlinear aerial dynamic systems. In this fashion, additional capabilities of active suppression of vibrating forces and torques can be achieved in specified motion directions on four-rotor helicopters. Moreover, since the dynamic vibration absorbers are designed to be virtual, these can be directly tuned for diverse operating conditions. In the present study, it is thus demonstrated that the mathematical structure of physical mechanical vibration absorbers can be extended for the design of active vibration control schemes for desired motion trajectory tracking tasks on four-rotor aerial vehicles subjected to adverse harmonic disturbances. The effectiveness of the presented novel design perspective of virtual dynamic vibration absorption schemes is proved by analytical and numerical results. Several operating case studies to stress the advantages to extend the undesirable vibration attenuation capabilities of the dynamic vibration absorbers into trajectory tracking control algorithms for nonlinear four-rotor helicopter systems are presented. Full article

This paper presents an implementation of a nonlinear optimal-based wind turbine tower vibration control method. An NREL 5.0 MW tower-nacelle model equipped with a hybrid tuned vibration absorber (HTVA) is analysed against the model equipped with a magnetorheological TVA (MRTVA). For control purposes, a 3 kN active actuator in parallel with a passive TVA is used in the HTVA system, while an MR damper is built in the MRTVA instead of a viscous damper, as in a standard TVA. All actuator force constraints are embedded in the implemented nonlinear control techniques. By employing the Pontryagin maximum principle, the nonlinear optimal HTVA control proposition was derived along with its simplified revisions to avoid a high computational load during real-time control. The advantage of HTVA over MRTVA in vibration attenuation is evident within the first tower bending frequency neighbourhood, with HTVA also requiring less working space. Using the appropriate optimisation fields enabled an 8-fold reduction of HTVA energy demand along with a (further) 29% reduction of its working space while maintaining a significant advantage of HTVA over the passive TVA. The obtained results are encouraging for the assumed mass ratio and actuator force limitations, proving the effectiveness and validity of the proposed approaches. Full article

A solution of the vibration attention problem on a flexible structure from a dynamic vibration absorption perspective is experimentally and numerically studied in this article. Linear and nonlinear dynamic vibration absorbers are properly implemented on a primary structure of n degrees of freedom through a modal decomposition analysis and using the tuning condition when the primary system has one single degree of freedom. A time-domain algebraic identification scheme for on-line modal parameter estimation of flexible structures is presented. A fast frequency estimation of harmonic excitation force is also obtained. A Hilbert transform analysis of the frequency response function for the case of nonlinear dynamic vibration absorption is introduced. In this way, influence of this particular passive nonlinear control device on system dynamic response can be determined. The proposed approach is validated on an harmonically perturbed building-like structure, which is discretized in a finite number of degrees of freedom. The flexible structure is subjected to resonant operational conditions, and coupled to a pendulum vibration absorber configured as a tuned mass damper as well as an autoparametric system. Full article

Friction-induced vibrations are a significant problem in various engineering applications, while dynamic vibration absorbers are an economical and effective tool for suppressing various kinds of vibrations. In this study, the archetypal mass-on-moving-belt model with an attached dynamic vibration absorber was considered. By adopting an analytical procedure, the optimal tuning of the absorber’s parameters was defined. Furthermore, the bifurcations occurring at the loss of stability were analytically investigated; this analysis illustrated that a properly chosen nonlinearity in the absorber’s stiffness permits controlling the supercritical or subcritical character of the bifurcation. However, a numerical analysis of the system’s dynamics, despite confirming the analytical results, also illustrated that the system’s global behavior is only slightly affected by the bifurcation character. Indeed, a dynamic vibration absorber possessing a perfectly linear restoring force function seems to provide the optimal performance; namely, it minimizes the velocity range for which stick–slip oscillations exists. Full article