Wide Range Of Excitation Frequencies Research Articles

Damping efficiency of the fractional Duffing system and an assessment of its solution accuracy

Dynamical systems with high damping efficiency in a wide frequency band can be useful on a small scale – for harvesting energy from ambient vibrations, and on a large scale – for damping harmful vibrations of mechanical structures. In this paper we present an assessment of the quality of solutions and damping efficiency of systems with fractional order derivatives. To simulate the fractional system the fourth-order Runge–Kutta method and Grünwald–Letnikov methods are used. We propose a coefficient for assessing the quality of solutions to fractional systems by reference to the quality of the calculated energy balance. As an exemplary system we study the Duffing model with embedded additional fractional-order derivative terms. Based on this coefficient, intervals of key numerical simulation parameters are determined to ensure the appropriate quality for the calculations of energy flows and energy balance. The determined values of these parameters are then used in tests of the damping efficiency of the studied system. Our results show that by modifying the fractional terms it is possible to configure a system that exhibits a “broadband effect”, i.e. a system that is characterized by high-amplitude vibrations and, consequently, high energy efficiency in a wide range of excitation frequencies.

Visualization of Chladni Patterns at Low-Frequency Resonant and Non-Resonant Flexural Modes of Vibration

In this study, Chladni patterns corresponding to resonant and non-resonant vibration modes are visualized on square plates made in steel and aluminum alloys in the low frequency domain of 10–210 Hz. Using a laser sensor, the plate displacement at its central excitation point is measured, and from the obtained frequency response, the resonant and anti-resonant vibration modes are identified. Using the quality-factor method, the damping ratio corresponding to the 1st resonant peak is evaluated. Over a wide range of excitation frequencies, transitions of Chladni figures between resonant patterns via non-resonant patterns could be observed. Such Chladni figures, of the simplest geometrical configuration, can be used to achieve a certain desired movement path of the particles on the vibrating plate by controlling the excitation frequency.

A Hybrid Actuator Model for Efficient Guided Wave based Structural Health Monitoring Simulations

Abstract Simulation has been recognized as a promising option to reduce the time and costs associated with determining Probability of Detection (POD) curves to demonstrate the performance of Guided Wave based Structural Health Monitoring (GW-SHM) systems. Time domain transient spectral finite element schemes have been used for large GW-SHM simulation campaigns, but the most common piezoelectric transducer model used for actuation, the pin force model, has limitations in terms of its range of validity. This is because the excitation frequency for the pin force model has only been validated far below the first electromechanical resonance frequency of the piezoelectric transducer mainly due to not considering the normal stress and dynamics of the transducer. As a result, the value of simulation tools for performance demonstrations may be limited. To address this limitation, this paper introduces a Hybrid Actuator Model that integrates frequency-dependent complex interfacial stresses in both the shear and normal directions, computed using finite elements. These surface stresses are compatible with time domain transient spectral finite element schemes, enabling their seamless integration without compromising the required performance for conducting intensive simulation campaigns. The proposed hybrid actuator model undergoes validation through a combination of simulation and experimental studies. Additionally, a comprehensive parametric study is conducted to assess the model's validity across a wide range of excitation frequencies. The results demonstrate the accurate representation of the transduction signal above the piezoelectric transducer's first free electromechanical resonance frequency.

Nonlinear Dynamic Response of Galfenol Cantilever Energy Harvester Considering Geometric Nonlinear with a Nonlinear Energy Sink

The nonlinear energy sink (NES) and Galfenol material can achieve vibration suppression and energy harvesting of the structure, respectively. Compared with a linear structure, the geometric nonlinearity can affect the output performances of the cantilever beam structure. This investigation aims to present a coupled system consisting of a nonlinear energy sink (NES) and a cantilever Galfenol energy harvesting beam with geometric nonlinearity. Based on Hamilton’s principle, linear constitutive equations of magnetostrictive material, and Faraday’s law of electromagnetic induction, the theoretical dynamic model of the coupled system is proposed. Utilizing the Galliakin decomposition method and Runge–Kutta method, the harvested power of the external load resistance, and tip vibration displacements of the Galfenol energy harvesting model are analyzed. The influences of the external excitation, external resistance, and NES parameters on the output characteristic of the proposed coupling system have been investigated. Results reveal that introducing NES can reduce the cantilever beam’s vibration while considering the geometric nonlinearity of the cantilever beam can induce a nonlinear softening phenomenon for the output behaviors. Compared to the linear system without NES, the coupling model proposed in this work can achieve dual efficacy goals over a wide range of excitation frequencies when selecting appropriate parameters. In general, large excitation amplitude and NES stiffness, small external resistance, and small or large NES damping values can achieve the effect of broadband energy harvesting.

Period-doubling cascade route to chaos in an initially curved microbeam resonator exposed to fringing-field electrostatic actuation

This paper explores the chaotic dynamics of a piezoelectrically laminated initially curved microbeam resonator subjected to fringing-field electrostatic actuation, for the first time. The resonator is fully clamped at both ends and is coated with two piezoelectric layers, encompassing both the top and bottom surfaces. The nonlinear motion equation which is obtained by considering the nonlinear fringing-field electrostatic force, includes geometric nonlinearities due to the mid-plane stretching and initial curvature. The motion equation is discretized using Galerkin method and the reduced order system is numerically integrated over the time for the time response. The variation of the first three natural frequencies with respect to the applied electrostatic voltage is determined and the frequency response curve is obtained using the combination of shooting and continuation methods. The bifurcation points have been examined and their types have been clarified based on the loci of the Floquet exponents on the complex plane. The period-doubled branches of the frequency response curves originating from the period doubling (PD) bifurcation points are stablished. It's demonstrated that the succession PD cascades leads to chaotic behavior. The chaotic behavior is identified qualitatively by constructing the corresponding Poincaré section and analyzing the response's associated frequency components. The bifurcation diagram is obtained for a wide range of excitation frequency and thus the exact range in which chaotic behavior occurs for the system is determined. The chaotic response of the system is regularized and controlled by applying an appropriate piezoelectric voltage which shifts the frequency response curve along the frequency axis.

Hypercompression in a tapered, viscous, nonlinear cochlear model

In our current research, we focus on predicting the stationary nonlinear response of a cochlear model that extends from the base to the apex when subjected to harmonic input, taking into account the tapering of the cochlear scalae along with electromechanical coupling of outer hair cells and the microstructures of the organ of Corti. We are interested in explaining the paradoxical phenomenon of hypercompression in the motion of the reticular lamina (RL), whereby the response decreases with an increase in the acoustic excitation at the stapes. We derive frequency–response curves for both the basilar membrane and RL at various locations, exploring a wide range of excitation frequencies and amplitudes. In accordance with experimental data, we find that the RL exhibits hypercompression at the base of the cochlea. This behavior is found to arise from the interaction of saturating nonlinearity arising from the active process and the linear response identified as the passive response to acoustic stimulus. These two responses are not synchronized in phase. As the excitation level increases, the two effects tend to partially cancel, giving rise to lower responses with increasing sound pressure levels. [Work supported by NIH-NIDCD R01 04084.]

Experimental study of sloshing characteristics in a rectangular tank with elastic baffles

A series of laboratory experiments are conducted to investigate liquid sloshing in a rectangular tank with a vertical baffle of varying elasticity under horizontal excitations. Image processing techniques are introduced to track baffle displacement, as well as to identify the free surface and the bubble. Dye visualization is employed to reveal the vortex behavior around the baffle. The air entrainment mechanism, including jet impinging, air cavity formation and deformation, and turbulent mixing, is analyzed. Moreover, the study investigates the effect of baffles with different stiffness on suppressing liquid sloshing across a wide range of excitation frequencies. The results show that the peak frequencies of the maximum free surface elevation-frequency curves correspond to the first natural frequency of fluid, the sub-resonance frequency, and the wet natural frequency of the elastic baffle. It is also found that the elastic baffle can effectively reduce liquid sloshing within a certain frequency range and balance the slamming impact both on the wall and the baffle, providing promising prospects for its practical applications.

A Two-Degree-of-Freedom Vibro-impact Triboelectric Energy Harvester for larger bandwidth

The efficiency of the energy harvesters can be improved by increasing the harvester bandwidth. Toward this, we presented a Two-Degree of Freedom (2-DOF) Vibro-impact Triboelectric Energy Harvester by combining multi-modality and piecewise linearity of two close resonant frequencies. The harvester structure consists of a primary cantilever beam attached to a secondary cantilever beam through a tip mass. The secondary beam is attached in the opposite direction to the primary beam. The secondary beam’s bottom surface acts as a triboelectric generator’s upper electrode. A lower electrode with bonded Polydimethylsiloxane (PDMS) insulator is attached at some gap separation distance underneath the upper electrode to create an impact structure. When the system vibrates, an impact between the triboelectric layers generates an alternating electrical signal. A 2-DOF system with lumped parameter theoretical model was developed to extract the governing equations. In addition, the experimental results were extracted to validate the theoretical model. Afterward, parametric analysis based on the variation of gaps, resistance, and surface charge density was theoretically investigated. Finally, the proposed harvester demonstrated an increase in the maximum output voltage by more than 300%, and a 250% increase in the bandwidth, by changing the excitation level from 0.1 g to 0.7 g. The result of this study can pave the way for an efficient energy harvester that can scavenge ambient vibrations over a wide range of excitation frequencies.

Broadband omnidirectional piezoelectric–electromagnetic hybrid energy harvester for self-charged environmental and biometric sensing from human motion

Vibration induced by human motions features a wide frequency spectrum and spatiotemporal-variable directions. Yet, it is challenging to concurrently expand frequency bandwidth and achieve multidirectional capability for effectively human-induced biomechanical energy harvesting and biometrics sensing. In this paper, we report a piezoelectric–electromagnetic hybrid energy harvester with coupled vibrational stabilization and induced frequency-up rotational mechanisms for omnidirectional and broadband vibration energy harvesting. Experimental studies demonstrate the proposed hybrid energy harvester operates effectively over a wide excitation frequency range from 6.0 to 16.0 Hz with omnidirectional responses. The piezoelectric conversion unit can provide a maximum output power of 0.9 mW and the electromagnetic conversion unit’s maximum output power is 22.7 mW. The hybrid energy harvester satisfies the power requirements of different types of portable electronics and realizes various self-charged sensing electronics that are stimulated by human movement. Various types of human motion signals are detected by piezoelectric and electromagnetic units via machine learning techniques to realize self-powered motion monitoring. Compared with a single type of signal, the identification accuracy of the hybrid device is improved from 85.6% to 100%. The proposed energy harvester for self-powered sensing paves the way to green intelligent life such as health management, environmental monitoring and human-machine interaction.

A Hybrid Damper with Tunable Particle Impact Damping and Coulomb Friction

A particle impact damper (PID) dissipates the vibration energy of a structure through impacts within the damper. The PID is not commonly used in practice mainly because of its low damping-to-mass ratio and the difficulty in achieving its optimal design due to its nonlinear characteristics. In contrast, a Coulomb friction damper (FD) can offer a higher damping force-to-mass ratio than other dampers, but it is also difficult to be controlled precisely due to its nonlinear characteristics and excessive frequency sensitivity regarding the resonant frequency. This paper examines a hybrid damper by combining a particle impact damper and a Coulomb friction damper (PID + FD) theoretically and experimentally. A theoretical model of the proposed damper is developed and tested numerically on a single-degree-of-freedom (SDOF) structure. The predicted results are validated by experimental tests on a prototype of the proposed damper. The damping force provided by the FD in the prototype can be varied by adjusting the normal force applied through a compression spring, while the vibration energy dissipation by the PID can be varied by changing the cavity size of the PID. A parametric analysis of the proposed hybrid damper has been performed. The proposed hybrid damper can reduce the maximum vibration amplitude of the SDOF primary structure by 66% and 43% compared with using the FD and PID only. The proposed damper is found to be effective over a wide range of excitation frequencies. Furthermore, the proposed hybrid damper achieves a similar vibration suppression performance to the traditional tuned mass damper (TMD) of a similar mass ratio. The proposed damper does not require an optimally tuned natural frequency and damping, unlike the TMD, and therefore it does not have the detuning problem associated with the TMD. In addition, the performance of the proposed damper is tested and compared with the TMD for random earthquake excitation data. Consequently, the proposed hybrid damper may be a simpler and better alternative to the TMD in passive vibration control applications.

Comparative assessment of liquid sloshing in dry and wet storage tank of floating offshore platform

In order to explore the characteristics of the single-layer liquid sloshing in offshore dry oil storage tank and the two-layer liquid sloshing in offshore wet oil storage tank, two series of experiments were carried out: one was free surface sloshing in a closed rectangular tank partially filled with colored water, and the other was interfacial sloshing in the identical tank but completely filled with white oil and colored water. The tank was mounted on a shake table and was subjected to harmonic horizontal excitation with different excitation amplitudes and a wide range of excitation frequencies, including the first seven natural modes of single-layer or two-layer liquid system. The present study find that the frequency responses of interfacial sloshing wave are analogous to those of the free surface sloshing wave, but smaller in amplitudes. The experiments also produce results that are unique to the two-layer liquid sloshing. For example, when the external excitation frequency is equal to or close to the odd mode natural frequency of two-layer liquid system, a complicated three-dimensional (3D) gravity-capillary wave might be generated at the oil-water interface. Finally, the comparisons of free surface and interfacial sloshing in the viscous damping ratio, higher sloshing modes, impact pressure amplitude and mass center displacement were conducted, which revealed the superiority of wet storage technology in structural safety and dynamic stability.

Multi-objective optimal design of double tuned mass dampers for structural vibration control

A double tuned mass damper (DTMD) for suppressing oscillations of civil structures is proposed in this study. DTMD is a combination of an undamped TMD and a smaller TMD. The impact of parameters on the essential characteristics, as well as the vibration absorption capacity of DTMD, is investigated. Using genetic algorithms (GA), the optimum parameters of DTMD are determined by minimizing the peak dynamic magnification factor of structural responses for a wide range of excitation frequencies. The effectiveness and robustness of DTMD are also compared with those of the optimized TMD having a similar weight as the DTMD. Furthermore, multi-objective optimization designs of DTMD (for both two-objective and three-objective) are also developed here. This study indicates that the DTMD is more effective than a single TMD. If keeping a similar efficiency to that of an optimized TMD, the optimum DTMD has a broader domain for choosing the frequency and damping ratio. In this sense, a DTMD is much more robust than a single TMD.

Sharp-edge-based acoustofluidic chip capable of programmable pumping, mixing, cell focusing, and trapping

Precise manipulation of fluids and objects on the microscale is seldom a simple task, but, nevertheless, crucial for many applications in life sciences and chemical engineering. We present a microfluidic chip fabricated in silicon–glass, featuring one or several pairs of acoustically excited sharp edges at side channels that drive a pumping flow throughout the chip and produce a strong mixing flow in their vicinity. The chip is simultaneously capable of focusing cells and microparticles that are suspended in the flow. The multifunctional micropump provides a continuous flow across a wide range of excitation frequencies (80 kHz–2 MHz), with flow rates ranging from nl min−1 to μl min−1, depending on the excitation parameters. In the low-voltage regime, the flow rate depends quadratically on the voltage applied to the piezoelectric transducer, making the pump programmable. The behavior in the system is elucidated with finite element method simulations, which are in good agreement with experimentally observed behavior. The acoustic radiation force arising due to a fluidic channel resonance is responsible for the focusing of cells and microparticles, while the streaming produced by the pair of sharp edges generates the pumping and the mixing flow. If cell focusing is detrimental for a certain application, it can also be avoided by exciting the system away from the resonance frequency of the fluidic channel. The device, with its unique bundle of functionalities, displays great potential for various biochemical applications.

Extended bandwidth of 2DOF double impact triboelectric energy harvesting: Theoretical and experimental verification

Increasing the bandwidth of the vibrational energy harvesters is one of the research emphases to maximize the energy harvested from the ambient. Here we design a Two-Degree of Freedom (2DOF) Vibro-impact Triboelectric Energy Harvester with a double impact configuration, which combines multi-modality and piecewise linearity to improve the harvesting bandwidth of triboelectric energy harvesters. The harvester structure consists of a primary cantilever beam attached to a secondary cantilever beam through a tip mass opposite the primary beam. The tip of each beam was designed to act as a multi-layers triboelectric energy harvester. When the system is subjected to a base excitation, the beams will vibrate, resulting in an impact between the triboelectric layers, and an alternating electrical signal is generated. The two beams are designed to have close natural frequencies, and under the effect of the impact, the bandwidths of the resonators are combined to create a wide bandwidth, hence increasing the efficiency of the energy harvester. A theoretical 2DOF lumped parameter model was developed to extract the governing equations of the double impact system. A simulation analysis was conducted to examine the structure’s dynamic behavior at different excitation levels, separation distance, and surface charge density to extract an optimal parameter for combining beams’ bandwidths. A wide bandwidth of 23 Hz was achieved at an excitation frequency of 0.7 g. Finally, experimental results were extracted to validate the simulation results. The system demonstrates the capability of connecting multi-modality and piecewise linearity to significantly broaden the bandwidth of the triboelectric energy harvester for scavenging ambient vibrations over a wide range of excitation frequencies.

Topology Optimization for Harmonic Excitation Structures with Minimum Length Scale Control Using the Discrete Variable Method

Continuum topology optimization considering the vibration response is of great value in the engineering structure design. The aim of this study is to address the topological design optimization of harmonic excitation structures with minimum length scale control to facilitate structural manufacturing. A structural topology design based on discrete variables is proposed to avoid localized vibration modes, gray regions and fuzzy boundaries in harmonic excitation topology optimization. The topological design model and sensitivity formulation are derived. The requirement of minimum size control is transformed into a geometric constraint using the discrete variables. Consequently, thin bars, small holes, and sharp corners, which are not conducive to the manufacturing process, can be eliminated from the design results. The present optimization design can efficiently achieve a 0–1 topology configuration with a significantly improved resonance frequency in a wide range of excitation frequencies. Additionally, the optimal solution for harmonic excitation topology optimization is not necessarily symmetric when the load and support are symmetric, which is a distinct difference from the static optimization design. Hence, one-half of the design domain cannot be selected according to the load and support symmetry. Numerical examples are presented to demonstrate the effectiveness of the discrete variable design for excitation frequency topology optimization, and to improve the design manufacturability

On the Application of Support Vector Method for Predicting the Current Response of MR Dampers Control Circuit

Magnetorheological (MR) dampers are controlled energy-dissipating devices utilizing smart fluids. They operate in a fast and valveless manner by taking advantage of the rheological properties of MR fluids. The magnitude of the response of MR fluids, when subjected to magnetic fields, is of sufficient magnitude to employ them in various applications, namely, vibration damping, energy absorption, exoskeletons, etc. At the same time, predicting their response to arbitrary mechanical and electrical inputs is still a research challenge. Due to the non-linearities involved in material properties or the design of the solenoid used for activating the fluid modeling the relationships between the control circuit and the material’s response is complex. Modeling studies can be classified into two categories. The parametric approach requires the knowledge of the internal material’s properties and takes advantage of physics formulas to infer the I/O relationships present in the damper. For comparison, the non-parametric approach harnesses various data mapping techniques to describe the device’s behavior. While the latter is more suited for design studies, the former seems ideal for control algorithm prototyping and the like. In this study, based on the so-called Support Vector Method (SVM), the authors develop a non-parametric model of the control circuit of an exemplary rotary MR damper. To the best of the author’s knowledge, it is the first attempt at an SVM application for MR dampers’ control circuit modeling. Using the acquired experimental data, the I/O relationships are inferred using the SVM algorithm, and its performance is verified across a wide range of excitation frequencies. The obtained results are satisfactory, and the current response of the MR damper is well-predicted. The model performance shows the potential for incorporating it into model-based prototyping and designing of MR control systems.

Field testing of gravel-rubber mixtures as geotechnical seismic isolation

We present the results of the forced-vibration experiments performed at the large-scale prototype structure of EuroProteas founded on gravel-rubber mixture (GRM) layers acting as a means of Geotechnical Seismic Isolation (GSI). Three GRM with different rubber content per mixture weight (0%, 10%, and 30%) but the same mean grain size ratio were used as foundation soil. Each GRM-structure system was subjected to harmonic forces in a wide range of excitation frequencies and force amplitude. It was found that a 0.5 m thick GRM foundation soil layer with 30% rubber content can effectively isolate the structure. The strong effect of the rubber fraction was expressed in the detected period elongation and the dominating rocking component which leads to a more “rigid-body” response of the structure. Moreover, the developed base shear and base moment are significantly reduced regardless of the excitation frequency, while the increased damping of the system and the important energy dissipation demonstrate the effectiveness of the GRM foundation soil layer. Overall, the experimental results demonstrated that the use of GRM as a GSI system can be considered as a low-cost alternative seismic isolation technique.

Modeling dynamics of a planetary variator applied in the adaptive TMDVI

A planetary variator, which is a type of the continuously variable transmission (CVT), is described in terms of dynamical modeling and assessment of its efficacy in the tuned mass damper with a variable inerter (TMDVI). An off-the-shelf planetary variator is used and modified for this application. Then, kinematic and dynamic models of the device are developed and its parameter values are determined. In the next step, the model is validated experimentally. In the second, theoretical part of the paper, an implementation of the modified device as a part of the TMDVI is considered. The variator enables tuning of the natural frequency of the TMDVI to the current frequency of excitation and allows the resonance frequency to be crossed via an optimal path with a low oscillation amplitude of the main body. Additionally, the previously proposed method to control the TMDVI to obtain efficient mitigation of vibrations in a wide range of excitation frequencies is extended. • The paper presents experimental examination of a planetary variator. • We derive validated mathematical model of a planetary variator. • We show possible application of a variator as a part of a tuned mass damper with variable inertance. • We propose an optimization method that allows efficient mitigation of vibrations. • We show response of a damped system with optimized damper.

Oscillation Control of Two-Wheeled Robot using a Gyrostabilizer

Two-wheeled robots are popular in transportation applications because of their high maneuverability. In this research, the oscillation attenuation performance of the control moment gyroscope (CMG) for the two-wheeled robot was studied. The stored kinetic energy of a CMG can offer a weight and volume saving compared to conventional vibration absorbers. This CMG is also more reactionless than other conventional absorbers by transforming the impact of angular momentum to unidirectional thrust along the center of gravity. The gimbals can precess while providing the angular momentum under the gravitational force. This study indicated that the CMG can operate in a wide range of excitation frequencies to balance the robot in a stable period. Because the flywheel speed is much easier changed to thrust against the unwanted oscillations disturbing the robot stability. There is a relation between the gimbal amplitude and the flywheel speed of CMG, in which the required flywheel speed can be reduced if the higher gimbal amplitude is chosen. It can be also concluded from the study that the oscillation amplitudes at the target frequency can decrease as much as flywheel speed increases. There was also a mathematical model using ANSYS software. The simulation results using ANSYS matched well with the theoretical results of the Lagrangian model.

Resonance in the flow past a highly confined circular cylinder

A three-dimensional direct numerical simulation is carried out to investigate the response of the flow past a highly confined circular cylinder to single-mode sinusoidal perturbations. The Reynolds number is fixed at 1000, and the blockage ratio (the ratio of the cylinder diameter to the distance between two lateral walls) is fixed at 0.6. Local perturbations are introduced upstream of the cylinder at normalized excitation frequencies (fe/f0) from 0.2 to 3.4, where f0 is the vortex shedding frequency in an unperturbed flow. It is observed that the vortex shedding frequency of the perturbed flows (fs) and the excitation frequency (fe) are locked-on in four distinct modes including fs = 2.0fe, fs = 1.5fe, fs = 1.0fe, and fs = 0.5fe, respectively. Among them, the fundamental lock-on with fs = 0.5fe appears over a wide range of excitation frequencies (fe/f0 = 1.4–2.8). By contrast, only the fundamental lock-on regime of fs = 0.5fe is observed when perturbing an unconfined flow at the same Reynolds number, highlighting the significant impact of confinement on the lock-on behavior. It is further revealed that the lock-on behavior is controlled by the responses of separated shear layers in the near wake, which switch from higher modes to lower modes with increasing excitation frequency in the confined flow.