Multi-mode Vibration Research Articles

Multi-mode reduction of structure by viscoelastic material containing embedded ball-like mass

The authors have been studying a multimodal and multiaxial vibration reduction device called eMDVA (embedded Mass Dynamic Vibration Absorber) which consists of a spherical shaped mass embedded in viscoelastic material. In a recent paper, we developed an FEM model based on experimental results of the eMDVA with spherical viscoelastic material and used it to design ellipsoid-shaped viscoelastic material. This paper presents an experimental investigation of the multiaxial vibration reduction ability of the eMDVA and compare the experimental result with the numerical ones by the FEM model. An eMDVA with ellipsoid-shaped viscoelastic material designed by the FEM model was constructed and its vibration characteristics were measured. Then, a series of vibration measurement tests for a 1:10 scale model of the underframe of a railway vehicle by applying the eMDVA has been conducted and the multi-mode vibration reduction effect has been confirmed.

Vibration characteristic design of a multi-modal and multi-axis dynamic vibration absorber consists of viscoelastic material containing embedded ball-like mass

Vibration characteristic design of a multi-modal and multi-axis dynamic vibration absorber consists of viscoelastic material containing embedded ball-like mass

Two-color resonance enhanced multiphoton ionization spectroscopy of o-hydroxybenzonitrile and Franck-Condon simulation

The cyano group is a typical electron-withdrawing group, which has aroused the interest of relevant researchers. Many papers reported the dispersed fluorescence spectra of o-hydroxybenzonitrile, its dimers, and complexes with small molecules, aiming to study the intermolecule hydrogen bond and the vibration features of the electronic ground state. There are also reports on using fluorescence excitation spectra to study excited state vibrations, but no report on the systematical analyzing of the vibration features of excited state spectra. Compared with fluorescence spectroscopy, resonance enhanced multiphoton ionization (REMPI) spectroscopy detects ions to obtain excited state energy level data, which has mass-resolution capability, and eliminates the interference of impurities with different charge-to-mass ratios. The strong electron-withdrawing ability of cyano group results in higher ionization energy for molecules containing cyano groups. Many REMPI experiments on benzonitrile derivatives require two-color lasers. In this paper, two-color resonance enhanced two-photon ionization experiment is performed by using a home-made linear time-of-flight mass spectrometer, and the vibration-resolved REMPI spectrum of o-hydroxybenzonitrile is obtained for the first time. Combining the high-precision density functional theory calculations with the Franck-Condon spectral simulations, the spectral characteristics are analyzed in detail, and a large number of fundamental, overtone and combined vibrations are found. The spectral assignment is carried out as accurately as possible. Most of the fundamental vibrations located at ring are assigned to the in-plane distortion or swing of the ring, which is related to the expansion of the ring during the molecular excitation. Theoretical and experimental results show that the low-frequency signal of REMPI spectrum is strong, the background is low, the band is less, and the resolution is good. As the vibration frequency increases, the signal changes in the worse direction. This is because the low-frequency spectrum mainly comes from the low-frequency fundamental vibrations and a little contribution from overtones. As the vibration frequency increases, the contributions from overtone and combined vibrations gradually increase, resulting in dense bands and low resolution. Theoretical calculations show that the high-order vibration and combination of multi-mode vibrations usually have a lower Franck-Condon factor, so the signal gradually becomes weak as the frequency increases, and the signal-to-noise ratio becomes worse.

Effectiveness of In-Service Dampers over Long-Term Operation for Cable Vibration Suppression: A Study Based on Field Testing

In order to explore the operation mechanism of dampers used on super long-span bridges, the characteristics of dampers in long-term operation are studied through field tests. Firstly, viscous damper and liquid leakage MR damper are selected to test the influence of fluid connecting rod on its damping force; Then, wireless and wired sensors are used to collect the acceleration response of cables with viscous dampers and MR dampers. Finally, the vibration characteristics of the cable are analyzed, and the control performance of the selected damper is evaluated. The results show that the high-order multi-modal vibration of the cable will occur in the range of 2-6hz whether the damper is installed or not. In addition, fluid leakage may reduce the additional modal damping ratio achieved by MR damper.

Mode coupling and locking of a Π-shaped cantilever resonator using laser-induced asymmetric modulation

Mechanical resonators, such as microcantilevers, demonstrate significant potential for use in information technology. Cantilevered beams of various geometries clamped at one end form the most ubiquitous structures in microelectromechanical systems that support multimode vibration for the detection, conversion, and processing of small signals. In this study, we demonstrate that the potential of these devices can be further extended by utilizing a strategy based on mode coupling and locking induced by asymmetric photothermal modulation. A cantilever was designed to have a Π-shape with a specific geometry such that the resonant frequencies of the two orthogonal modes are close to one another. Additionally, we show that mode coupling between the two modes, which are originally orthogonal to one another, can be achieved through laser-induced photothermal modulation. In particular, the two modes can be parametrically tuned to become degenerate through mode coupling with a significant increase in the quality factor from 112 to 839. This approach is universal and can be extended to improve the detection limits of microresonators in high-dissipation environments with enhanced signal-to-noise ratios.

Novel spacer-tuned-mass-damper system for controlling vibrations of hangers

This work proposes a novel spacer-tuned-mass-damper system to control the vibration of a hanger, which is composed of a spacer and a tuned mass damper. The spacer is mainly used to restrict the relative displacement of each hanger and to provide a guided bar for the moving mass. Firstly, the mechanics of vibration suppression of the spacer-tuned-mass-damper is explained in detail. Then, a feedback-based optimizing methodology for the spacer-tuned-mass-damper system’s parameters is proposed and implemented. Finally, a design example is carried out on a pin-joint hanger model to demonstrate the viability of the developed design strategy. It can be seen from the numerical results that the spacer-tuned-mass-damper system designed by the proposed optimization method is effective in mitigating multi-mode vibrations.

Experimental modal identification of smart composite structure applied to active vibration control

This paper proposes an experimental modal identification method for vibration control of multi-actuators and multi-sensors complex smart structures. The general formulation avoids the difficulty of the coupling coefficients identification in electromechanical systems through a modal reduced-order model and uses first-order polynomials as phase correctors for the numerators of the identified transfer functions. Then, a frequency-shaped linear quadratic controller is designed to control multiple modes on a smart composite structure with integrated transducers. The experimental results obtained in terms of multi-modal vibration control were promising with attenuations up to 20 dB on the target modes, confirming the efficiency of the proposed identification and control method for future applications with more extended and complex composite smart structures.

Inerter dampers with linear hysteretic damping for cable vibration control

Long stay cables in cable-stayed bridges have low and close-spaced modal frequencies and are subjected to multimode vibrations, e.g., rain–wind vibrations and vortex-induced vibrations. Many types of dampers used in practice for cable vibration control can be described using a linear hysteretic damping model, e.g., high-damping rubber dampers and viscous-shear dampers. Such dampers are able to provide frequency-independent damping effects while the maximal achievable damping is limited due to their intrinsic stiffness effect. Therefore, this study investigates dampers with linear hysteretic damping enhanced by inerters for cable vibration control. A general inerter damper, consisting of a spring with complex stiffness and an inerter in parallel which is then connected to another inerter in series, is attached to a cable for dynamic analyses. Complex modal analysis is performed to appreciate cable damping. The optimal damping effect is discussed with reference to dynamic properties of the damper with respect to frequency, with comparison to the system of a cable with an inerter damper with viscous damping. It is found that two inerters, respectively in parallel and in series with a damper of linear hysteretic damping, can achieve a large improvement on multimode damping of a cable. The inertance of the inerter in series with the damper needs to be large for optimal performance while a small inertance of the other inerter is preferable. Furthermore, a case study based on a cable attached with a viscous-shear damper on the Sutong Bridge is conducted to show the feasibility of the inerter dampers.

Improved Adaptive Augmentation Control for a Flexible Launch Vehicle with Elastic Vibration.

The continuous development of spacecraft with large flexible structures has resulted in an increase in the mass and aspect ratio of launch vehicles, while the wide application of lightweight materials in the aerospace field has increased the flexible modes of launch vehicles. In order to solve the problem of deviation from the nominal control or even destabilization of the system caused by uncertainties such as unknown or unmodelled dynamics, frequency perturbation of the flexible mode, changes in its own parameters, and external environmental disturbances during the flight of such large-scale flexible launch vehicles with simultaneous structural deformation, rigid-elastic coupling and multimodal vibrations, an improved adaptive augmentation control method based on model reference adaption, and spectral damping is proposed in this paper, including a basic PD controller, a reference model, and an adaptive gain adjustment based on spectral damping. The baseline PD controller was used for flight attitude control in the nominal state. In the non-nominal state, the spectral dampers in the adaptive gain adjustment law extracted and processed the high-frequency signal from the tracking error and control-command error between the reference model and the actual system to generate the adaptive gain. The adjustment gain was multiplied by the baseline controller gain to increase/decrease the overall gain of the system to improve the system’s performance and robust stability, so that the system had the ability to return to the nominal state when it was affected by various uncertainties and deviated from the nominal state, or even destabilized.

Design of a Bézier-Profile Plate for Closely Spaced Multimodal Vibration Energy Harvesting

A cubic Bézier-profile plate for multimodal vibration energy harvesting was developed. The design of the plate was based on an optimization procedure in which the profile of the plate was optimized via the parameters of a cubic Bézier curve to meet the requirements. The multimodal energy harvesting of the plate exploited its first bending mode and its first twisting mode. The conversion of vibration energy into electrical energy was by electromagnetic induction with a magnet attached to a corner of the plate. These two closely spaced vibration modes achieved the multi-modal energy harvesting of the device. Prototypes of the device were manufactured using a numerical-control machining process. The experimental results were in good agreement with the design specifications. With the same base lengths, height, and thickness, the maximum von Mises stress of the proposed plate was much lower due to its bell-shaped profile. The cubic Bézier curve chosen for the plate profile was effective for design of the closely-spaced multimodal vibration energy harvester. With the flexibility of its controllable parametric curve, a high design freedom of the energy harvester with specified frequency ratios could be achieved.

Artificial Intelligence-Based Optimization of a Bimorph-Segmented Tapered Piezoelectric MEMS Energy Harvester for Multimode Operation

This paper presents a study on the design and multiobjective optimization of a bimorph-segmented linearly tapered piezoelectric harvester for low-frequency and multimode vibration energy harvesting. The procedure starts with a significant number of FEM simulations of the structure with different geometric dimensions—length, width, and tapering ratio. The datasets train the artificial neural network (ANN) that provides the fitting function to be modified and used in algorithms for optimization, aiming to achieve minimal resonant frequency and maximal generated power. Levenberg–Marquardt (LM) and scaled conjugate gradient (SCG) methods were used to train the ANN, then the goal attainment method (GAM) and genetic algorithm (GA) were used for optimization. The dominant solution resulted from optimization by the genetic algorithm integrated with the ANN fitting function obtained by the SCG training method. The optimal piezoelectric harvester is 121.3 mm long and 71.56 mm wide and has a taper ratio of 0.7682. It ensures over five times greater output power at frequencies below 200 Hz, which benefits the low frequency of the vibration spectrum. The optimized design can harness the power of higher-resonance modes for multimode applications.

A study of a new hybrid vibration energy harvester based on broadband-multimode

To improve the energy conversion efficiency and working frequency bandwidth of a single frequency piezoelectric vibration energy harvester, a new type of hybrid vibration energy harvester is developed which is combined with the mechanism of piezoelectric and electromagnetic energy conversion. The system comprises of a PZT cantilever beam, an elastic suspended magnetic mass, a magnet block attached to the end of the cantilever beam and a resonator. The addition of resonator can not only increase the mode, but also adjust the frequency of harvester flexibly. Nonlinear magnetic force of magnet block not only broadens the frequency band and improves the output performance of the system, but also changes the resonant frequency to make the harvester have better adjustable performance. On this basis, an improved electromechanical coupled analytical model of continuum is proposed which can be solved by the Runge-Kutta algorithm and the influence of different factors (the mass and spring stiffness of the resonator, as well as the electromechanical coupling coefficient, electromagnetic coupling coefficient, magnet mass and magnetic flux) on the output are analyzed. According to the prototype of the vibration energy harvester developed, an experimental system was built. The performance of the independent and hybrid energy harvesters is evaluated by experimental and analytical methods. The peak output voltage of the piezoelectric part was about 4 times that of the electromagnetic part. The peak output current of the electromagnetic part is about 30 times that of the piezoelectric part. The study results show that the proposed new hybrid vibration energy harvester can achieve a wider frequency range and multimodal vibration energy harvesting. In addition, the bandwidth and power of the harvester can be dynamically adjusted by changing the resonator or electromechanical coupling coefficient, and the bandwidth of the harvester can also be adjusted by changing the quality and characteristics of the magnet.

Multimodal vibration suppression of nonlinear Euler–Bernoulli beam by multiple time-delayed vibration absorbers

Multimodal vibration suppression of nonlinear Euler–Bernoulli beam by multiple time-delayed vibration absorbers

Noncontact operational modal analysis of light poles by vision-based motion-magnification method

Light and sign poles on elevated highway bridge are secondary structural elements that support functionality of a highway system. Over the time, they may suffer from fatigue damage due to traffic, wind, and earthquake-induced vibration in a direct or indirect manner. As a secondary structural component, vibrations of light and sign poles are influenced by the bridge vibration, the primary structure. Structural condition assessment of the light and sign poles are normally conducted by visual inspection and/or vibration measurement using contact or noncontact method. In this paper, a vision-based vibration measurement of the light poles on elevated highway bridges using motion magnification and dynamic mode decomposition methods is proposed. Using the method, vibrations of the light poles are captured by video camera and the phase-based motion magnification method is implemented to magnify micro-vibration of the structure. By employing discretized centroid searching method, spatial displacements of the light poles are extracted. Modal parameters of the structure are then identified from the displacement responses by dynamic mode decomposition method. The study includes laboratory experiments for verification, and the full-scale implementation on existing light poles on elevated highway bridges. The vision-based results are compared with the noncontact vibration measurement using Laser-Doppler vibrometers. Results of experiments and full-scale tests demonstrate the capability of the proposed method in extracting multi-mode vibration characteristics of the light poles accurately in a noncontact long-distance measurement.

LQR control on multimode vortex-induced vibration of flexible riser undergoing shear flow

Under the actions of ocean currents and/or waves, deep-sea flexible risers are often subject to vortex-induced vibration (VIV). The VIV can lead to severe fatigue and structural safety issues caused by oscillatory periodic stress and large-amplitude displacement. As flexible risers have natural modes with lower frequency and higher density, a multimode VIV is likely to occur in risers under the action of ocean currents, which is considered as shear flow. To decrease the response level of the VIV of the riser actively, a multimode control approach that uses a bending moment at the top end of the riser via an LQR optimal controller is developed in this study. The dynamic equations of a flexible riser including the control bending moment in shear flow are established both in the time and state-space domains. The LQR controllers are then designed to optimize the objective function, which indicates the minimum cost of the riser's VIV response and control input energy based on the Riccati equation of the closed-loop system under the assumption that the lift coefficient distribution is constant. Finally, the VIV responses of both the original and closed-loop systems under different flow velocities are examined through numerical simulations. The results demonstrate that the designed active control approaches can effectively reduce the riser displacement/angle by approximately 71%–89% compared with that of the original system. Further, for multimode control, the presented mode-weighted control is more effective than the mode-averaged control; the decrease in displacement is approximately 1.13 times than that of the mode-averaged control. Owing to the increase in flow velocity as more and higher-order modes are excited, the VIV response of the original system decreases slightly while the frequency response gradually increases. For the closed-loop system, the response becomes smaller and more complicated, and the efficiency of the controller becomes lower at a certain flow velocity.

Multilayer toroidal tuned liquid column dampers for seismic vibration control of structures

The toroidal tuned liquid column damper (TTLCD) is a recently developed device, which extends the application scenarios of liquid column dampers to multidirectional vibration control. Based on the single-TTLCD, this article creatively designs a multilayer-TTLCD, composed of several cylinder shells and baffles, to improve the damping performance in multidirection. The real-time hybrid simulation (RTHS) technique is employed to experimentally investigate the control efficiency of the multilayer-TTLCD. It is confirmed that the multilayer configuration makes it possible to incorporate more oscillating liquid into the columns of the container without extra occupied floor area, and thus the liquid mass can be raised. Due to the increase of the liquid mass, the multilayer-TTLCD shows certain improvements on peak and root-mean-square (RMS) displacement mitigation over the single-TTLCD when suppressing one specific structural vibration mode. More importantly, it is found that the multilayer-TTLCD is beneficial in multimodal vibration damping and has potential to control multi-order modal responses of structures simultaneously with a wide frequency range.

Damping characteristics of single-layer aluminum alloy reticulated spatial structures based on improved modal parameter identification method

An improved identification method is proposed for the modal parameter identification of multi-modal vibration attenuation signals based on the analytical mode decomposition and the particle swarm optimization. Through examples of analog signals, it is proved that the proposed method can identify modal parameters under a strong colored noise environment. Field tests were carried out on four in-service aluminum alloy reticulated structures to obtain the acceleration response of the structures. The improved identification method proposed in this paper is used to identify the modal parameters of each acceleration response curve, based on which the damping characteristics of the aluminum alloy reticulated structures are analyzed. The results show that the damping characteristics of such structures obey a three-stage change rule, with the increase of the acceleration amplitude. In addition, a practical calculation method of the damping ratios of aluminum alloy reticulated structures is proposed on the basis of the experimental results.

“Multimode vibration cutting” – A new vibration cutting for highly-efficient and highly-flexible surface texturing

This paper proposes a new vibration cutting method named “multimode vibration cutting” for precision surface texturing. The proposed cutting method utilizes multiple unidirectional vibration modes mainly in the depth-of-cut direction. The vibrations at multiple frequencies induced to the tool tip can generate not only sinusoidal but also highly-flexible trajectories such as trapezoidal, triangular, and distorted triangular waves. Notably, only a sinusoidal vibration can be induced when a single resonant vibration is applied to the tool tip. Compared to conventional highly-flexible cutting methods for surface texturing, such as the utilization of fast tool servo and amplitude control of ultrasonic elliptical vibration cutting, the proposed method is highly-efficient because of its direct usage of high resonant frequencies. Compared to conventional highly-efficient cutting methods for surface texturing, such as linear and elliptical vibration cutting which mainly utilizes the vibration component in the depth-of-cut direction, the proposed method can generate highly-flexible trajectories for various micro texture profiles. In this study, an ultrasonic multimode vibration device is developed, and the mechanics of generating multimode vibrations are demonstrated. Turning experiments with several texture profiles are performed to confirm the validity of the proposed method for highly-efficient and highly-flexible micro/nano surface texturing.

Nonlinear vibration mitigation of a flexible rotor shaft carrying a longitudinally dispositioned unbalanced rigid disc

This study is dedicated to investigate the nonlinear dynamics of a system composed of a flexible rotor shaft carrying a longitudinally dispositioned unbalanced rigid disc. The less-attended multi-modal nonlinear vibration analysis of rotor structures, considering the effect of geometric and inertial nonlinearities due to the large deflection of the flexible structure, is investigated in this study. To this end, the flexible shaft is modelled using the Euler–Bernoulli beam theory. In order to model the unbalanced rigid disc, it is considered as combination of a symmetric disc with an additional eccentric lump mass. The equations of motion of the system are derived using the extended Hamilton principle. Assuming the inextensional shaft and considering high twisting rigidity of the shaft, the flexural-flexural vibrations of the system of rotor shaft-disc are studied in this paper. The equations of motion are discretized using the Galerkin method exploiting various reduced order models including single-mode, two-mode, and three-mode approximations. In order to obtain the steady-state response of the system, two methods are used in this study. The first method is to use the semi-analytical modified complex averaging technique along with the numerical arc-length continuation method. The second method is using the direct integration in MATLAB. The nonlinear dynamics of different systems such as a system consisting only a flexible shaft and a system of flexible shaft carrying an unbalanced rigid disc at different positions along the shaft are investigated. The results show that geometric nonlinearity of the flexible shaft is dominating the inertial nonlinearity and hence, the system demonstrates a hardening nonlinear behaviour at the vicinity of the first two resonances. Besides, it is shown that dispositioning the unbalanced disc along the flexible shaft results in change in the nonlinear dynamics of the system at various modes. It is illustrated that if the unbalanced disc is located at the node of one of the modes of the vibration of the system, that mode is not excited, as expected. The results of the paper reveal that the longitudinal disposition plays a key role in the instability analysis of the system of rotor shaft-disc, as well as the radial unbalance. In the second part of the paper, nonlinear vibration of the system of a flexible rotor shaft with a longitudinally dispositioned unbalanced rigid disc is mitigated using nonlinear energy sink (NES). Two different conditions of the unbalanced disc are considered for the system. For each case, the NES is designed to control the undesired nonlinear vibration of the system close to the first two natural frequencies. The results show that the designed NESs are capable of controlling the system with different dynamic responses including periodic, quasi-periodic, chaotic, and also the system with unstable dynamic response that may lead to collapse of the system.

A strip speaker using the traveling bending wave on a beam controlled by three actuators

The inherent weakness of conventional panel speakers is the inevitable multi-modal vibration behavior, resulting in severe fluctuation in the radiated sound spectrum, which is detrimental to the sound quality. A panel speaker that is actively controlled by array actuators at the panel edges has been proposed as a solution to the problem, but the increased cost and complexity due to a large number of actuators remain a challenge. In this study, a panel speaker using a thin beam, called a strip speaker, that adopts only three actuators is proposed to alleviate the modal fluctuation problem. When the middle position of the beam is excited by the primary actuator, the propagated bending wave field there from is controlled by two actuators at either end of the beam that prevents reflection of the wave. To achieve this, the inverse problem is derived by using the transfer function between the actuators and the coefficients of the reflected waves, from which an appropriate gain of the two control actuators is obtained as the inverse solution. For validation, a thin beam with a size of 315 × 40 × 2 mm3 is tested by simulation and experiment. Peaky resonant responses are made to disappear by controlling the vibration field, and the input mobility of the primary actuator becomes like that of an infinite beam. The boundary of the beam, which is newly defined at the location of the control actuators, is converted into an anechoic termination. The effect of the beam material is also tested by comparing aluminum and acrylic beams. It is shown that the damping of the acrylic beam is favorable in resulting a flat response, but its effective frequency range is lowered from that of the aluminum beam. In the experiment, the control actuators near the ends of unknown boundary conditions are located at the position to minimize the total input power for control. The experimental results of the controlled vibration field and radiated sound spectrum agree well with the predicted characteristics. It is shown that the proposed strip speaker with the traveling wave control method can be used to produce excellent acoustic performance.