Vibration Neutralizer Research Articles

Experimental investigation on a passive self-tuning vibration neutraliser for two distinct frequencies

Experimental investigation on a passive self-tuning vibration neutraliser for two distinct frequencies

Optimal and Quasi-Optimal Automatic Tuning of Vibration Neutralizers

Vibration neutralizers are single-degree-of-freedom devices affixed to vibrating structures in order to reduce the response at a specific troublesome harmonic excitation frequency. As this frequency may vary over time, it becomes imperative to track and adjust the neutralizer to maintain the optimal performance. Recent years have witnessed the emergence of adaptive tunable vibration neutralizers, offering real-time adjustment capabilities through external actions. Thanks to real-time control algorithms, these devices enable the automatic mitigation of vibration levels in mechanical structures. A particularly successful algorithm for the automatic tuning of these devices leverages the phase angle between the base acceleration and the neutralizer’s mass. This study critically examines the justification for employing such an algorithm and scrutinizes its optimal applicability limits, particularly in the context of viscous and structurally damped systems. The findings reveal that this algorithm accurately approximates optimum tuning for systems with low damping. Moreover, from an engineering perspective, the algorithm remains acceptable even for heavily damped structures. Through a focused and comprehensive analysis, this paper provides valuable insights into the efficacy and limitations of the phase-angle-based tuning algorithm, contributing to the advancement of adaptive vibration control strategies in smart structures.

Dynamic coupling of multi-degrees of freedom constrained-layer vibration neutralizers: A new methodology

Dynamic neutralizers, also known as dynamic absorbers, are efficient means of mitigating vibrations in structures. They have been particularly effective in addressing broad-band passive vibration control in structures with high modal density through the use of multi-degrees of freedom (MDoF) and viscoelastic materials (VEMs). Therefore, sandwich-type or constrained-layer beams can offer great potential when used as MDoF control devices. However, there is limited literature exploring these structures as auxiliary systems, with coupling typically assumed to be single-point and limited to only translational degrees of freedom (DoFs). In this context, this article presents a methodology to determine the dynamic behavior of a compound system, coupling the displacement and rotation DoFs between a metal structure–referred to as the primary system–and a MDoF auxiliary system. The coupling is achieved by utilizing an equivalent dynamic stiffness obtained at the base of the auxiliary system through ANSYS finite-element software, providing a robust and comprehensive approach. A Matlab code transfers the auxiliary system's geometry and properties to ANSYS, where the dynamic stiffness at the base is determined and subsequently coupled to the primary system. A MDoF auxiliary system of the constrained-layer type with VEM was studied, and both single-point and distributed coupling were analyzed. The auxiliary system was attached to a cantilever metal beam for numerical and experimental validation. The proposed generalized equivalent dynamic stiffness model accurately estimates the response of the compound system, offering a 25% reduction in response computation time compared to the finite-element model of the complete compound system. This methodology enables the accurate representation of compound system dynamics while minimizing computational time, making it valuable for the optimal design of a set of MDoF viscoelastic dynamic neutralizers.

A Practical Method to Increase the Low Frequency Sound Insulation of Timber Frame Constructions

Timber framed houses have little or no sound insulation at low frequencies. A significant set of noise sources emit loud low frequency noise and for some of these, the noise is single frequency or tonal. Improvement of the low frequency insulation has been shown using two methods: increasing the stiffness and applying vibration neutralizers to the structure of the house. A study was carried out on a wall element to assess the viability of the method in a simplified test facility. Impedance measurements were carried out on a test section consisting of 3 studs and panel construction. An initial field implementation has been carried out on a re-purposed dwelling at the end of the runway at Bergen's airport. Reductions of the order of 5-10dB in the C-weighted indoor noise level have been achieved. The additional attenuation achieved using vibration neutralisers only has effect when the outside noise level exceeds 87dBC.

A passive self-tuning vibration neutraliser using nonlinear coupling between the degrees of freedom

Vibration neutralisers are widely used to suppress vibration of a host structure subject to external excitation at a specific frequency. When attached to a structure, they create a notch filter in the frequency response, reducing the vibration levels considerably. An inherent limitation is related to the narrow frequency range in which they are effective. Over the years, there have been different attempts to make the vibration absorber more robust. These include using active and semi-active control strategies to change the tuning frequency, using piezoelectric elements with shunt circuits, electromagnetic actuators, servo motors, and even exploring nonlinear effects. In many cases, there is a need for an external power source to modify the characteristics of the system. This paper concerns a passive vibration neutraliser that can adapt automatically to one of two frequencies corresponding to the frequency of an external harmonic force. Importantly, it does this without the need for an external power source. The device consists of a beam-like neutraliser that is attached to the host structure at its centre through a roller bearing. The stiffness element is a rectangular beam that can rotate in the bearing, changing the stiffness it presents to the direction of excitation. The paper describes an experimental study into such a device, and an analytical model is proposed that qualitatively captures the time-domain behaviour of the experimental device. A possible mechanism by which the device self-tunes to either of the two frequencies of excitation is discussed. Supplementary material is also provided to show the device in operation.

Response of a multi-degree-of-freedom system with a pounding vibration neutralizer to harmonic and random excitation

Exact steady-state solutions are obtained for the motion of a multi-degree-of-freedom system (MDOF) that is provided, at an arbitrary location within the primary structure, with a highly-nonlinear auxiliary mass damper which resembles a conventional linear dynamic vibration neutralizer (DVN) whose relative motion with respect to the primary system is constrained to remain within a specified gap, thus operating as a “pounding DVN.” This configuration of a conventional DVN with motion-limiting stops could be quite useful when a primary structure with a linear DVN is subjected to transient loads (e.g., earthquakes) that may cause excessive relative motion between the auxiliary and primary systems. Under the assumption that the motion of the composite nonlinear MDOF system under harmonic excitation is undergoing steady-state motion with two symmetric impacts per period of the excitation, an exact, closed-form solution is obtained for the motion of the MDOF as well as the nonlinear damper. This solution is subsequently used to develop an approximate analytical procedure to estimate the stationary response of the pounding DVN when subjected to random excitation with white spectral density and Gaussian probability distribution. Since the vibration control effectiveness of auxiliary mass dampers, whether linear or not, deteriorates considerably when dealing with transient dynamic loads, an extensive investigation is provided for assessing the influence and interaction effects of the major nonlinear system parameters, so as to provide useful guidelines for quantifying the tradeoffs in selecting a suitable strategy to enhance the mitigation capabilities of the subject class of dampers, under stationary as well as nonstationary deterministic and random dynamic environments.

Exact tuning of a vibration neutralizer for the reduction of flexural waves in beams.

In this work, designs of vibration neutralizers for the reduction of flexural waves in beams are proposed. The system considered consists of an Euler-Bernoulli beam experiencing a harmonically travelling wave. The neutralizer, which consists of a mass, spring, and damper (viscous or hysteretic), is attached at a point on the beam. Two designs are considered. In the first, the aim is the minimization of the transmitted energy, and in the second, the aim is the maximization of the energy dissipated in the neutralizer. For minimum energy transmission, the undamped neutralizer can be tuned to reflect all the energy back to its source at the tuning frequency. The tuning stiffness ratio and the neutralizer bandwidth is obtained in an analytical closed form. For maximum energy dissipation, the neutralizer can dissipate up to 50% of the incident energy. The maximum energy dissipated, i.e., 50% of the incident energy, is constant and occurs at the tuning frequency. It is neither affected by the neutralizer mass nor by the tuning frequency. The tuning parameters are obtained analytically. Finally, in all the above cases, the increasing of the neutralizer mass enhances the neutralizer performance. All analytical findings are validated numerically.

Response of Pounding Dynamic Vibration Neutralizer Under Harmonic and Random Excitation

Exact steady-state solutions are obtained for the motion of an single-degree-of-freedom (SDOF) system that is provided with a highly nonlinear auxiliary mass damper (AMD), which resembles a conventional dynamic vibration neutralizer (DVN), whose relative motion with respect to the primary system is constrained to remain within a specified gap, thus operating as a “pounding DVN.” This configuration of a conventional DVN with motion-limiting stops could be quite useful when a primary structure with a linear DVN is subjected to transient loads (e.g., earthquakes) that may cause excessive relative motion between the auxiliary and primary systems. Under the assumption that the motion of the nonlinear system under harmonic excitation is undergoing steady-state motion with two impacts per period of the excitation, an exact, closed-form solution is obtained for the system motion. This solution is subsequently used to develop an approximate analytical solution for the stationary response of the pounding DVN when subjected to random excitation with white spectral density and Gaussian probability distribution. Comparison between the analytically estimated rms response of the primary system and its corresponding response obtained via numerical simulation shows that the analytical estimates are quite accurate when the coupling (tuning parameters) between the primary system and the damper are weak, but only moderately accurate when the linear components of the tuning parameters are optimized. It is also shown that under nonstationary, the pounding DVN provides slightly degraded performance compared to the linear one but simultaneously limits the damper-free motion to specified design constraints.

Some diverse examples of exploiting the beneficial effects of geometric stiffness nonlinearity

Abstract The effects of nonlinearity, particularly stiffness nonlinearity, has been of concern to structural engineers for many years. The main reason for this is because this type of nonlinearity can cause unpredictable dynamics, and considerable effort is necessary to analyse nonlinear structures. However, due to the recent computational advances, and the continuous need to improve the performance and efficiency of structures and mechanical devices, engineers have recently started to investigate whether nonlinearity can be incorporated into structures to provide some benefit. This paper presents four case-studies where this type of nonlinearity can be introduced to good use. The required nonlinear stiffness varies from case to case, but can be realised in each case with a simple geometric arrangement of up to three linear springs. The case-studies involving vibration isolators, vibration neutralizers, vibration energy harvesters and micro-air-vehicles are discussed in this context.

Vibration mitigation of a linear host structure using a passive neutralizer: effect of nonlinearity in the neutralizer suspension

Motivated by some experimental results on a test-rig, this paper presents some observations on the frequency response of a primary linear oscillator when an auxiliary nonlinear oscillator is attached to it, acting as a vibration neutralizer. In the experiments, an electro-dynamic shaker is used as the linear one-degree-of-freedom primary oscillator, and it is excited by an harmonic force. The nonlinear neutralizer is attached to the moving head of the shaker, and it is assembled to achieve a cubic stiffness characteristics, due to geometrical arrangement of linear elastic elements. For very low vibration amplitudes, the whole system behaves predominantly as a two-degree-of-freedom linear oscillator, but when the force excitation to the shaker is increased the shape of the frequency response curve changes, and exhibits resonance peak bending, jump phenomena and instabilities of the harmonic response. A theoretical model of the system is presented, with the aim to capture the qualitative phenomena observed in the experiments.

Theoretical modelling of a beam with attached spring-mass-damper system

Vibrations are always undesirable, wasting energy besides producing noise. In this case, beams which are prominent component in most engineering having no exemption from the vibration effect when imposed by dynamic loading. One of the approach to attenuate vibration of a structure is by having a spring-mass-damper (SMD) system or typically known as vibration neutralizer attached to the vibrating structure. This method is more promising as it does not contribute significant additional energy to the structure. The work presented in this paper describes the frequency response (FRF) of a simply supported beam with an attached SMD system. A mathematical model of a beam was at first developed in the study which was further derived to include the attachment of SMD system. In order to transform the derived equations into a form of graph that can be analysed, Matlab® software was used. The outcome from Matlab® shows that the attachment of SMD onto beam attenuates its vibration significantly. The result also displays a good resemblance FRF when compared with numerical finite element analysis of Ansys®. It is expected that the theoretical derivation demonstrated in this paper provide a helpful reference to future researchers who endeavour to find equations of a simply supported beam with an attached SMD system as well as for a vibration control study.

Hybrid Vibration Control under Broadband Excitation and Variable Temperature Using Viscoelastic Neutralizer and Adaptive Feedforward Approach

Vibratory phenomena have always surrounded human life. The need for more knowledge and domain of such phenomena increases more and more, especially in the modern society where the human-machine integration becomes closer day after day. In that context, this work deals with the development and practical implementation of a hybrid (passive-active/adaptive) vibration control system over a metallic beam excited by a broadband signal and under variable temperature, between 5 and 35°C. Since temperature variations affect directly and considerably the performance of the passive control system, composed of a viscoelastic dynamic vibration neutralizer (also called a viscoelastic dynamic vibration absorber), the associative strategy of using an active-adaptive vibration control system (based on a feedforward approach with the use of the FXLMS algorithm) working together with the passive one has shown to be a good option to compensate the neutralizer loss of performance and generally maintain the extended overall level of vibration control. As an additional gain, the association of both vibration control systems (passive and active-adaptive) has improved the attenuation of vibration levels. Some key steps matured over years of research on this experimental setup are presented in this paper.

Machine Tool Behavior Improvement Using Vibration Neutralizer and Absorber

The article proposes an approach to computation of parameters of dynamic vibration neutralizer and absorber in order to suppress machine tool vibrations during machining process. The approach is based on multi-body model of the machine tool in a state space form and additionally attached passive absorber in a parametric state space form. Such a representation is suitable for fast optimizations of the absorber parameters and other numeric experiments with the model. The article presents comparison of optimized dynamic vibration absorber and neutralizer. There were also compared two approaches to the build of the objective function for the balanced improvement of the behavior in both X and Y axis.

The Application of Multiple Vibration Neutralizers for Vibration Control in Aircraft

A current challenge for researchers is the design and implementation of an effective vibration control method that reduces vibration transmission from vehicle structures such as aircraft. This challenge has arisen due to the modern trend of utilizing lightweight thin panels in aircraft structural design, which have the potential to contribute towards significant vibration in the structures. In order to reduce structural vibration, one of the common approaches is considering vibration neutralizer system attached to the structure. In this study, a vibration neutralizer is developed in a small scale size. The effectiveness of attached vibration neutralizers on a thin plate are investigated through experimental study. Prior to the experiment, a finite element analysis of Solidworks® and analytical modelling of Matlab® are produced in order to determine the structural dynamic response of the thin plate such as the natural frequency and mode shapes. The preliminary results of finite element analysis demonstrate that the first four natural frequency of clamped plate are 48Hz, 121Hz, 194Hz and 242Hz, and these results are in agreement with the plate’s analytical equations. However, there are slight discrepancies in the experiment result due to noise and error occurred during the set up. In the later stage, the experimental works of thin plate are performed with attached vibration neutralizer. Result shows that the attachment of vibration neutralizer produces better outcome, which is about 41% vibration reduction. It is expected that by adding more vibration neutralizer to the structure, the vibration attenuation of thin plate can be significant.

Dynamic analysis and ℋ2 optimisation of a piezo-based tuned vibration absorber

In this article, a piezo-based tuned vibration absorber is proposed and theoretically analysed. The proposed device consists of a proof mass, a piezoelectric actuator and a resilient element (spring). An equivalent mechanical model where the piezoelectric element is connected to a general circuit composed of a resistor, an inductor and a capacitor in series ( RLC) is presented to illustrate the coupling of the electrical components with the mechanical systems. Based on the mechanical replacement model, a C or L circuit can be used to realise a piezo-based tuned vibration neutraliser, while with an RC or RL circuit the piezo-based tuned vibration absorber can be considered as a piezo-based tuned mass damper. For the C and L circuits, tuning strategies are derived to adjust the shunt capacitance and inductance to track the disturbance frequency. In the case of RC and RL shunt circuits, an ℋ2 optimisation criterion is used for tuning the piezo-based tuned mass damper. Closed-form expressions for the optimal tuning parameters are provided in this article.

Vibration reduction at desired locations on a beam by creating nodes using tunable vibration neutralizers

Vibration neutralizers provide an effective method of attenuating tonal vibrations within a structure. In this paper, variable stiffness vibration neutralizers are used to impose zero displacement or nodes to reduce vibration at desired locations on a Euler-Bernoulli beam subjected to forced harmonic excitation. An iterative procedure is developed to find the required resonance frequencies of neutralizers to create nodes at selected locations. Numerical tests are performed to show the viability of the procedure that is developed. Experimental tests are conducted and results are compared with those obtained by numerical tests.

The characteristics of a nonlinear vibration neutralizer

This paper concerns an investigation into the use of cubic nonlinearity in a vibration neutralizer to improve its effectiveness. It is assumed that the frequency of the harmonic excitation is well above the resonance frequency of the machine to which the neutralizer is attached, and that the machine acts as a simple mass. It is also assumed that the response of the system is predominantly at the harmonic excitation frequency of the machine. The harmonic balance method is used to analyze the system. It is shown how the nonlinearity has the effect of shifting the resonant peak to a higher frequency away from the tuned frequency of the neutralizer so that the device is robust to mistune. In a linear neutralizer this can only be achieved by adding mass to the neutralizer, so the nonlinearity has a similar effect to that of adding mass. Some characteristic features are highlighted, and the effects of the system parameters on the performance are discussed. It is shown that, for a particular combination of the system parameters, the effect of the nonlinearity is also to increase the bandwidth of the device compared to the linear neutralizer with similar mass and damping. Some approximate expressions are derived, which facilitate insight into the parameters which influence the dynamics of the system. The results are validated by some experimental work.

A sliding Goertzel algorithm for adaptive passive neutralizers

A common method used in tuning adaptive–passive tuned vibration neutralizers is to adjust its resonance frequency to match the excitation frequency, which has the characteristic that the phase angle between its vibrating mass and its support is −90°. A sliding-Goertzel algorithm is presented and demonstrated for extracting the vibration signals at the frequency of interest. The benefit of using the sliding Goertzel algorithm compared to other methods when used in vibration environments with multiple tones is that additional band-pass notch filtering is not required. This algorithm could also be used for adaptive tuned mass dampers, adaptive Helmholtz resonators, and adaptive quarter-wave tubes.

Modeling and Analysis of Piezoelectric Energy Harvesting Beams Using the Dynamic Stiffness and Analytical Modal Analysis Methods

Abstract The modeling and analysis of base-excited piezoelectric energy harvesting beams have attracted many researchers with the aim of predicting the electrical output for a given base motion input. Despite this, it is only recently that an accurate model based on the analytical modal analysis method (AMAM) has been developed. Moreover, single-degree-of-freedom models are still being used despite the proven potential for significant error. One major disadvantage of the AMAM is that it is restricted to simple cantilevered uniform-section beams. This paper presents two alternative modeling techniques for energy harvesting beams and uses these techniques in a theoretical study of a bimorph. One of the methods is a novel application of the dynamic stiffness method (DSM) to the modeling of energy harvesting beams. This method is based on the exact solution of the wave equation and so obviates the need for modal transformation. The dynamic stiffness matrix of a uniform-section beam could be used in the modeling of beams with arbitrary boundary conditions or assemblies of beams of different cross sections. The other method is a much-needed reformulation of the AMAM that condenses the analysis to encompass all previously analyzed systems. The Euler–Bernoulli model with piezoelectric coupling is used and the external electrical load is represented by generic linear impedance. Simulations verify that, with a sufficient number of modes included, the AMAM result converges to the DSM result. A theoretical study of a bimorph investigates the effect of the impedance and quantifies the tuning range of the resonance frequencies under variable impedance. The neutralizing effect of a tuned harvester on the vibration at its base is investigated using the DSM. The findings suggest the potential of the novel concept of a variable capacitance adaptive vibration neutralizer that doubles as an adaptive energy harvester. The application of the DSM to more complex systems is illustrated. For the case studied, a significant increase in the power generated was achieved for a given working frequency through the application of a tip rotational restraint, the use of segmented electrodes, and a resized tip mass.

The fixed-points theory revisited with new applications

The fixed-points theory has its root dating back to 1932. Hahnkamm suggested that there are two fixed points in the undamped primary structure's frequency response function (FRF) for the two-degree-of-freedom system when a harmonic force is applied to the primary mass. These points are independent of the damping value in the auxiliary system, which is the control system, and their heights are mainly determined by the mass ratio of the device. The desired optimum value of the tuning ratio is obtained when the heights of the fixed points are equal. Fourteen years later, Brock suggested that the optimum value of the damping ratio in the control device can be determined by making the height of the fixed points the maximum. Since then, the fixed-points theory has been used in many applications as one of the design laws in fabricating a vibration neutralizer. In this article, the theory is reformulated by using the conventional definition of the damping ratio. It is proved that the same result can be obtained as in the original derivation. The application of the theory is then extended to the control of global vibration of an undamped continuous structure and is demonstrated on a simply supported beam.