Amplitude Free Vibration Research Articles

Experimental evaluation of damping models for a nonlinear pendulum system

Popular damping models for a single pendulum system were experimentally evaluated in this study. The comparison between the numerical and experimental responses showed that neither linear viscous damping model nor squared velocity proportional viscous damping model was able to well capture the free vibration amplitudes of the pendulum in both large and small amplitude ranges. Specifically, the amplitudes of the numerical model with linear viscous damping decreased slower at the large amplitude vibration but faster at the small amplitude vibration than the experimental amplitudes did. The trend was reverse in the numerical model with the squared velocity proportional viscous damping model. Based on the experimental data and a numerical method combined with a fitting approach, a complete quadratic viscous damping model for the pendulum was derived. The model was able to confidently predict the free vibration amplitudes of the pendulum in both large and small amplitude ranges. This study provides analysts with the sense of the accuracy of some popular damping models for a nonlinear pendulum system. It also demonstrates the use of a fitting approach to retrieve physical properties of a system from experimental data. The contents of this paper are suitable for gifted high school students and undergraduate students.

Torsional vibration test and analysis of an internal combustion engine power assembly by RLV-5500

The vibration characteristics of marine power plant and propulsion system shafting directly affect the navigation safety of the ship. Shafting torsional vibration is an important parameter to evaluate the stability and reliability of shafting. The demand of ship shafting torsional vibration measurement is gradually developing towards high resolution and high accuracy. According to the characteristics of ship shafting installation and operation, this paper selects an internal combustion engine powertrain as the test object, and uses rlv-5500 rotary laser vibration measurement system to test the shafting torsional vibration. The time-frequency analysis of the test results is carried out to calculate the comprehensive angular displacement and the angular displacement amplitude of each harmonic order. The maximum comprehensive amplitude of crankshaft free end torsional vibration is 0.33 °. The crankshaft will not be damaged by torsional vibration.

Free vibration of viscoelastically supported beam bridges under moving loads: Closed-form formula for maximum resonant response

In this paper, a closed-form approximate formula for estimating the maximum resonant response of beam bridges on viscoelastic supports (VS) under moving loads is proposed. The methodology is based on the discrete approximation of the fundamental vertical mode of a non-proportionally damped Bernoulli–Euler beam, which allows the derivation of closed-form expressions for the fundamental modal characteristics and maximum amplitude of free vibration at the mid-span of VS beams. Finally, an approximate formula to estimate maximum resonant acceleration of VS beams under passage of articulated trains has been proposed. Verification studies prove that the approximate closed-form formula estimates the resonant peaks with good accuracy and is a useful tool for preliminary assessment of railway beam bridges considering the effect of soil-structure interaction at resonance. In combination with the use of full train signatures through the Residual Influence Line (LIR) method, the proposed solution yields good results also in the lower range of speeds, where resonant sub-harmonics are more intensely reduced by damping.

Numerical performance assessment of Tuned Mass Dampers tomitigate traffic-induced vibrations of a steel box-girder bridge

In this paper, the effects of Tuned Mass dampers (TMDs) on the reduction of the vertical vibrations of a real horizontally curved steel box-girder bridge due to different traffic loads are numerically investigated. The performance of TMDs to reduce the bridge vibrations can be affected by the parameters such as dynamic characteristics of TMDs, the location of TMDs, the speed and weight of vehicles. In the first part of this study, the effects of mass ratio, damping percentage, frequency ratio, and location of TMDs on the performance of TMDs to decrease vertical vibrations of different sections of bridge deck are evaluated. In the second part, the performance of TMD is investigated for different speeds and weights of traffic loads. Results show that the mass ratio of TMDs is the more effective parameter in reducing imposed vertical vibration in comparison with the damping ratio. Furthermore, it is found that TMD is very sensitive to its tuned frequency, i.e., with a little deviation from a suitable frequency, the expected performance of TMD significantly decreased. TMDs have a positive and considerable performance at certain vehicle speeds and this performance declines when the weight of traffic loads is increased. Besides, the results reveal that the highest impact of TMD on the reduction of the vertical vibrations is when free vibrations occur for the bridge deck. In that case, maximum reductions of 24% and 59% are reported in the vertical acceleration of the bridge deck for the forced and free vibration amplitudes, respectively. The maximum reduction of 13% is also obtained for the maximum displacement of the bridge deck. The results are mainly related to the resonance condition.

Time delay stability analysis for vibration suppression of a smart cantilever beam with hysteresis property

A stability analysis for a smart beam with an adaptive controller is presented in the paper when considering the time delay phenomenon. With the Lagrange equation and the assumed modes method, a dynamical model is constructed to describe the hysteresis nonlinearity of the smart beam. By simulation and experiment, the nonlinear model is proved effectively using the strain response near the root of the beam when the piezoelectric actuator is applied on with a chirp voltage. Based on the dynamical model, a stability analysis method is proposed with an eigenmatrix in the discrete control system. Through some simulation verifications, it is concluded that a proper time delay will be useful to improve the stability of the smart beam with an adaptive controller. Furthermore, it is verified by the experiments that the free vibration amplitude of the smart beam with an artificial time delay 0.05 s is smaller compared with that at no time delay.

Numerical investigation of cavitation generated by an ultrasonic dental scaler tip vibrating in a compressible liquid.

Bacterial biofilm accumulation around dental implants is a significant problem leading to peri-implant diseases and implant failure. Cavitation occurring in the cooling water around ultrasonic scaler tips can be used as a novel solution to remove debris without any surface damage. However, current clinically available instruments provide insufficient cavitation around the activated tip surface. To solve this problem a critical understanding of the vibro-acoustic behaviour of the scaler tip and the associated cavitation dynamics is necessary. In this research, we carried out a numerical study for an ultrasound dental scaler with a curved shape tip vibrating in water, using ABAQUS based on the finite element method. We simulated the three-dimensional, nonlinear and transient interaction between the vibration and deformation of the scaler tip, the water flow around the scaler and the cavitation formation and dynamics. The numerical model was well validated with the experiments and there was excellent agreement for displacement at the free end of the scaler. A systematic parametric study has been carried out for the cavitation volume around the scaler tip in terms of the frequency, amplitude and power of the tip vibration. The numerical results indicate that the amount of cavitation around the scaler tip increases with the frequency and amplitude of the vibration. However, if the frequency is far from the natural frequency, the cavitation volume around the free end decreases due to reduced free end vibration amplitude.

Adaptive modal vibration control for smart flexible beam with two piezoelectric actuators by multivariable self-tuning control

It has been popular for decades that the vibrations of space structures are suppressed with smart actuators. However, the higher mode vibrations are often motivated when a control strategy is applied to attenuate the vibration for the smart structures. Moreover, if the multi-mode vibration of a smart structure is suppressed with multi-actuators, a proper multivariable control law will be adopted to solve the coupling problem caused by the multi-actuators of the smart structure. Therefore, in the paper, a decoupling technique for two modal vibrations of a smart flexible beam with two piezoelectric patches is adopted by adaptive control. The proposed control law is designed with a multivariable minimum variance self-tuning control. Considering the first two orders of modal vibrations, two piezoelectric patches are configured on the flexible beam according to the strain of the first two orders of modal vibrations along the longitudinal direction of the beam. A dynamical model for the flexible beam with two piezoelectric actuators is constructed by the mode superposition method. With the dynamical model, simulations are implemented to suppress the free vibration of the flexible beam. Moreover, experiments are carried out to verify the effectiveness of the multivariable minimum variance self-tuning control for vibration suppression of the flexible structure. The control results clearly show that the free vibration amplitude of the cantilevered beam with two control voltages applied to the two piezoelectric patches is less than that with one control voltage applied to the first piezoelectric actuator. Thus, multivariable minimum variance self-tuning control is a more efficient approach for suppressing multimodal vibration for a smart flexible beam with two piezoelectric actuators compared with the conventional velocity feedback control.

Ring-shaped traveling wave ultrasonic motor for high-output power density with suspension stator

A ring-shaped traveling wave ultrasonic motor with a suspension stator is proposed for improving output power density. Piezoelectric stacks working in d33 mode are involved in the stator, whereas piezoelectric plates employed in classic ring-shaped traveling wave motors often work in d31 mode. Spring-mass systems are used to suspend the stator from the base that supports the motor and provide preload force. The volume of piezoelectric material and the power density of the motor can be easily increased through the suspension structure. Large vibration amplitude of the stator can be generated on the coupling surface. Simulink analysis and finite element analysis are conducted to verify the theory and determine the optimum parameters of the suspension stator with four piezoelectric stacks. The maximum free vibration amplitude of 4.25 µm of the stator is observed, which is nearly 4.7 times of that without suspension. The prototype can work at a maximum no-load speed of 62 rpm and produce a stall torque of 49.5 mN m under a driving signal of 30 Vpp when the mass block is 0.30 g. Furthermore, the higher output power can be expected because more extra stacks can be added in this suspension structure.

Nonlocal nonlinear model of Bernoulli–Euler nanobeam with small initial curvature and its application to single-walled carbon nanotubes

Although the small-scale effect and initial curvature have significant influence on the nonlinear mechanical property of the nanobeam, there are few researches to consider both factors. On the basis of the nonlocal differential constitutive relation, this paper, for the first time, presents a nonlinear partial differential–integral equation model of Bernoulli–Euler nanobeam with a small initial curvature. Then the model is applied to research the static bending and the frequency of free vibration for the single-walled carbon nanotubes (SWCNTs). This study indicates that the static deformations are relate to the load direction due to the initial curvature. In addition, the initial curvature complicates the relation between the free vibration frequencies and vibration amplitudes.

Vibration damping in road bridges – two case studies of full scale experiments

The paper presents the results of a vibration damping analysis of two road viaducts. The analysis was based on displacement signals recorded during the dynamic load tests carried out before an acceptance process of the viaducts. To create an additional excitation, a 5 cm high threshold was located on the road during low-velocity passages. The Logarithmic Decrement (LD) was calculated using an exponential curve fit to free vibration amplitudes. A fundamental frequency of vibration was considered. To minimize the influence of signal imperfections, a filtration process was carried out using bandpass Infinite Impulse Response (IIR) Bessel filter. The results were correlated for various degrees of excitation resulting from different velocities of loading vehicles and the presence of the threshold. Examples of appropriate and inadequate signals for the damping analysis were shown.

First two modal adaptive vibration control for a smart beam with two piezoelectric bimorphs by a self-tuning PID control

This paper presents model and simulation verification of vibration suppression to two-input two-output system of a smart cantilever beam bonded with piezoelectric bimorphs by Self-tuning PID controller. The Self-tuning PID controller is designed for the smart cantilever beam with pole-placement method theory and recursive algorithm. The displacement is acquired by the Piezoelectric bimorph on the root of the smart cantilever beam. The control voltage is calculated by the designed Self-tuning PID control parameters. The established model realizes simulation through Simulink of MATLAB. Through some simulation verification results, it is indicated that the suppressed amplitude of free vibration is obvious. Therefore, it is demonstrated that the Self-tuning PID control for two-input two-output smart beam system with Piezoelectric bimorphs is feasible to reduce free vibration.

Prediction and explanation of the aeroelastic behavior of a square-section cylinder via forced vibration

The work presented in this study concerns the existing link between fluctuating transverse force characteristics and aeroelastic instability phenomena, which is a step toward further understanding the complex nature of the interactions between square cylinders and air flow. First, by using experimental data from forced vibration, a predictive calculation of the free vibration of an elastically mounted cylinder is carried out. It is found that the prediction results appeared to be qualitatively in agreement with the experimental measurements. This agreement indicates that the measurements using the forced vibration technique is a valuable tool for analysis of free vibration behavior of an elastically mounted cylinder, particularly in cases where the quasi-steady theory is not entirely valid. Furthermore, a new and simple insight into the link between the unsteady force characteristics and the free vibration amplitudes is proposed in this study. Although this approach does not offer details about the nature of the separated flow field around the cross-sections of cylinders, certain complex free-vibration behaviors of square cylinders can be easily interpreted from this perspective.

Effect of size on the dynamic behaviors of atomic force microscopes

Accurate mathematical modeling and simulation of cantilever dynamics are crucial to design and fabrication of the atomic force microscope (AFM). Thickness of AFM cantilevers is in order of few microns or sub-microns and producers trend to make it even smaller because of more resolution and sensitivity. By reducing the cantilever thickness, size effect may be appeared which changes the AFM dynamics. In this paper, effect of size on dynamic behavior of AFM is investigated based on the modified couple stress theory. The AFM is modeled as an Euler–Bernoulli micro-cantilever and the Galerkin projection method is applied to derive the lumped model. Investigation of free vibration amplitude shows the necessity of considering the size effect. Accuracy of solution is verified by comparing the results with two degree-of-freedom model and analogue equations method. Furthermore, stability analysis and frequency response of AFM based on classic and non-classic theories are investigated and the obtained results are compared with each other. Findings of the present study show that considering size effect have significant effect on reliable estimation of the AFM dynamic.

Thermal Behavior Analysis at Large Free Vibration Amplitudes of Thin Annular FGM Plates with Porosities

Geometrically nonlinear free vibration of Functionally Graded thin Annular Plates (FGAP) with porosities subjected to thermal environment is investigated. A semi-analytical model based on an extension of the Rayleigh Ritz method to nonlinear vibrations is considered. A homogenization procedure has been employed to reduce the problem to that of an isotropic homogeneous annular plate. The material properties are assumed to be temperature-dependent and graded in the thickness direction. The rule of mixture has been modified in order to take into account the effect of porosity and approximate the material properties. The problem is solved by a numerical iterative method. The effects of the porosity volume fraction, the temperature distribution through the plate thickness and temperature-dependency of material properties on the nonlinear free vibrations responses of the FGAP at large amplitudes are examined and discussed in detail.

Identification of the Elastic and Damping Characteristics of Soft Materials Based on the Analysis of Damped Flexural Vibrations of Test Specimens

A method for identification of the elastic and damping properties of soft materials in tension–compression and shear in a composition with a rigid (base) material is proposed. The method is based on the analysis of the lowest free vibration frequencies and amplitude dependences of internal damping parameters of three-layer test specimens of an appropriate structure: the base material is placed in the middle of the specimens for tension–compression, but as outer layers for shear. Identification of the elastic properties in tension−compression and shear is based on a comparison of calculated and experimental frequencies of corresponding test specimens. It is shown that the elastic properties found for a technical rubber depends on vibration frequencies of the test specimen. A quadratic functional containing experimental and calculated parameters of internal damping of test specimens is employed to identify the damping properties of soft materials. A three-layer finite element developed for this purpose is proposed for a numerical evaluation of the design parameters of internal damping of a three-layer test specimen. Calculations were carried out to identify the damping characteristics of the technical rubber in tension–compression and shear from the parameters of internal damping of test specimens with a D16AT aluminum alloy as the base material.

Excluding Contact Electrification in Surface Potential Measurement Using Kelvin Probe Force Microscopy.

Kelvin probe force microscopy (KPFM), a characterization method that could image surface potentials of materials at the nanoscale, has extensive applications in characterizing the electric and electronic properties of metal, semiconductor, and insulator materials. However, it requires deep understanding of the physics of the measuring process and being able to rule out factors that may cause artifacts to obtain accurate results. In the most commonly used dual-pass KPFM, the probe works in tapping mode to obtain surface topography information in a first pass before lifting to a certain height to measure the surface potential. In this paper, we have demonstrated that the tapping-mode topography scan pass during the typical dual-pass KPFM measurement may trigger contact electrification between the probe and the sample, which leads to a charged sample surface and thus can introduce a significant error to the surface potential measurement. Contact electrification will happen when the probe enters into the repulsive force regime of a tip-sample interaction, and this can be detected by the phase shift of the probe vibration. In addition, the influences of scanning parameters, sample properties, and the probe's attributes have also been examined, in which lower free cantilever vibration amplitude, larger adhesion between the probe tip and the sample, and lower cantilever spring constant of the probe are less likely to trigger contact electrification. Finally, we have put forward a guideline to rationally decouple contact electrification from the surface potential measurement. They are decreasing the free amplitude, increasing the set-point amplitude, and using probes with a lower spring constant.

集中系モデルによるスロッシング現象の解析（第1報 微小振幅時に対する線形モデルの提案および自由振動解析）

集中系モデルによるスロッシング現象の解析（第1報 微小振幅時に対する線形モデルの提案および自由振動解析）

A framework for backbone experimental tracking : Piezoelectric actuators, stop-sine signal and Kalman filtering

This paper deals with the use of piezoelectric patches for nonlinear dynamic identification. The patches are glued on the structure to identify amplitude-dependent damping and natural frequency; their positions are defined in order to perform the excitation concentrated on the first bending mode. Their locations on the structure allow to perform “stop sines” tests, as, unlike electrodynamic shakers, piezos are embedded on structures and do not modify the studied structure after the excitation signal is switched off. Although, despite the piezo and the stop-sine, the signal is still modulated by other frequency components or polluted by random signals, a post processing with the extended Kalman Filter allows a very good determination of the modal damping and the natural frequency, especially when they depends on the free vibration amplitude.

Vibration of simply supported beams under a single moving load: A detailed study of cancellation phenomenon

Dynamic behaviour of simply supported uniform beams subjected to a single moving point load is analysed in this paper. A simple closed-form expression for free vibration response, valid for both lightly and heavily damped beams, is formulated. A detailed investigation of the cancellations of free responses is carried out. New interpretations for the cancellation mechanism, from the perspectives of free vibration amplitude and phase angle, are presented. Expressions for cancellation speed ratios are formulated based on the initial velocity and displacement conditions for free vibration. The effect of damping on the cancellations of free responses is also studied.

Free Vibration of High-Rise Chemical Tower Controlled by Super-Elastic Shape Memory Alloy Cables

In this paper, the super-elastic shape memory alloy (SMA) composite cables are used for vibration control of high-rise chemical towers during the free vibration. The displacement and velocity response to initial displacements were studied by the lumped mass method combined with Newmark integration method. It is found that super-elastic SMA cables can reduce the free vibration amplitudes and shorten the attenuation period of high-rise chemical towers effectively.