Amplitude-dependent Characteristics Research Articles

Bandgap enhancement of a piezoelectric metamaterial beam shunted with circuits incorporating fractional and cubic nonlinearities

Nonlinear metamaterials have been widely studied for their potential to broaden the bandgap for vibration suppression. However, the bandgap widening effect induced by nonlinearity vanishes when the excitation amplitude is insufficient to trigger the nonlinear behavior. In order to broaden the applicable range of excitation amplitude for nonlinear metamaterials, a novel design of a piezoelectric metamaterial beam shunted with combined nonlinear circuits is presented in this work, which incorporates fractional and cubic nonlinearities in circuits to achieve bandgap enhancement under both low and high excitation amplitudes. Theoretical and numerical models are established for predicting the nonlinear dynamics behaviors of the piezoelectric metamaterial beam, and their computational results are in good agreement. The amplitude-dependent bandgap of the metamaterial beam induced by combined nonlinearity is analyzed through the effective bending stiffness of a unit cell and validated through the frequency response of a piezoelectric metamaterial beam. It is found that based on the complementary nature of fractional and cubic nonlinearities in the amplitude-dependent characteristics, combined nonlinearity of the circuits can effectively improve the bandgap width of the beam under both low and high excitation amplitudes. In addition, the effects of the two nonlinearities on the amplitude-dependent characteristics of the bandgap are studied, and the interplay between the two nonlinearities within the combination is analyzed. The results show that the amplitude-dependent characteristics of the combined nonlinear design can be precisely tuned by adjusting the nonlinear coefficients of the circuits. Overall, a piezoelectric metamaterial beam with both fractional and cubic nonlinearities in circuits possesses superior vibration control performance than those with single nonlinear counterparts in circuits.

Nonlinear vibration analysis of Z-shaped pipes with CLD considering amplitude-dependent characteristics of clamps

Under external excitation, the clamp-pipe structures may exhibit nonlinear vibration behavior due to stiffness softening and damping energy dissipation of the clamp. To implement vibration suppression on pipes, a semi-analytical modeling method is proposed for the Z-shaped pipe structure with partial constrained damping layer (CLD) treatment under the constraint of the clamp. The nonlinear vibration characteristics of the Z-shaped pipe with CLD in both in-plane and out-of-plane directions are further investigated by considering the nonlinear mechanical properties of the clamp. Specifically, the energy expressions of the laminated straight and curved pipe segments are deduced based on the Timoshenko beam theory. The coupling of pipe segments is introduced by the improving artificial spring technology. A novel equivalent mechanical model is developed to simulate the nonlinear mechanical properties of the clamp, which are expressed by nonlinear stiffness and damping with the amplitude-dependent characteristic. Next, an effective algorithm is presented for solving nonlinear dynamic equations in the frequency domain with the amplitude-dependent characteristic. The proposed linear and nonlinear models are verified by the FE analysis and experimental test results. The comparison demonstrates that the proposed method can accurately replicate the nonlinear vibration of the Z-shaped pipe with CLD treatment. Finally, the suppression mechanism of the CLD on the vibration of Z-shaped pipes and the nature of the amplitude-dependent characteristic are further investigated, which can guide the design and vibration reduction of pipes.

Amplitude dependence of natural frequency and damping ratio for 5 supertall buildings with moderate-to-strong typhoon-induced vibrations

Modal parameters play a significant role in the wind-resistant design and vibration control of high-rise buildings. Results from previous studies demonstrate that the natural frequency and damping ratio of high-rise buildings usually exhibit nonlinear variation characteristics with the increase of structural amplitude. However, due to lacking relevant field measurements, the features of natural frequency and damping ratio for super-tall buildings under large wind-induced amplitudes have been less explored. This paper presents a field study on typhoon-induced structural responses of five supertall buildings whose structural heights all exceed 300 m. The peak acceleration responses at the measurement height of most buildings exceeded 10 cm/s2 (gal), with the maximum response reaching 20 gal. Two frequently used methods, i.e., the stochastic subspace identification (SSI) and random decrement technique (RDT) methods are utilized to compare and analyze the amplitude-dependent characteristics of target modal parameters. It is found that with the increase of wind-induced structural vibration amplitude, the fundamental natural frequency generally first decreased and then leveled off, while the damping ratio for the first-order mode of the buildings except the one equipped with a tuned mass damper (TMD) system first increased while then tended to decrease. More interestingly, the critical normalized structural vibration amplitude associated with the maximum damping ratio is found to be in the range of 10−4∼10−5, which agrees well with the theory of “critical tip drift ratio”. Potential explanations for the above phenomena are presented. Furthermore, the obtained results are further compared with existing statistical models, and associated discrepancies suggest the complexities of the dynamic features of supertall buildings.

Observational study of typhoon effects on the oval-shaped 330 m high Zhuhai Center Tower

This paper investigates typhoon-induced wind effects on a skyscraper based on 72-h-long field measurement records. In this large-scale monitoring study, the wind field characteristics surrounding the monitored building are first investigated using climate records collected by a moveable laser radar wind profiler that was temporarily fixed next to the tall building during Typhoon Cempaka, which could avoid adverse impacts caused by interference at the building top or the terrain effects through measurements from an anemometer atop the building or a meteorological observation tower that could be far away from the monitored building. Subsequently, the wind-excited cladding pressures and structural responses of the monitored skyscrapers are analysed according to measurements by pressure transducers, accelerometers and velocimeters, and the pressure distribution characteristics and structural dynamic properties are estimated by spectral analysis and the random decrement technique. Ultimately, provided the oval-shaped appearance and spiral configuration of the Zhuhai Center Tower, the results derived in this study are compared with those of other supertall buildings in terms of several aspects of concern, including the distribution features of wind pressures and acceleration response and amplitude-dependent characteristics of modal parameters, which would further the understanding of wind effects on tall buildings with various cross sections and building shapes. This study aims to provide comprehensive reference information for the wind-resistant design of high-rise buildings in tropical cyclone-prone regions.

Influence of Fluid Viscosity and Compressibility on Nonlinearities in Generalized Aerodynamic Forces for T-Tail Flutter

The numerical assessment of T-tail flutter requires a nonlinear description of the structural deformations when the unsteady aerodynamic forces comprise terms from lifting surface roll motion. For linear flutter, a linear deformation description of the vertical tail plane (VTP) out-of-plane bending results in a spurious stiffening proportional to the steady lift forces, which is corrected by incorporating second-order deformation terms in the equations of motion. While the effect of these nonlinear deformation components on the stiffness of the VTP out-of-plane bending mode shape is known from the literature, their impact on the aerodynamic coupling terms involved in T-tail flutter has not been studied so far, especially regarding amplitude-dependent characteristics. This term affects numerical results targeting common flutter analysis, as well as the study of amplitude-dependent dynamic aeroelastic stability phenomena, e.g., Limit Cycle Oscillations (LCOs). As LCOs might occur below the linear flutter boundary, fundamental knowledge about the structural and aerodynamic nonlinearities occurring in the dynamical system is essential. This paper gives an insight into the aerodynamic nonlinearities for representative structural deformations usually encountered in T-tail flutter mechanisms using a CFD approach in the time domain. It further outlines the impact of geometrically nonlinear deformations on the aerodynamic nonlinearities. For this, the horizontal tail plane (HTP) is considered in isolated form to exclude aerodynamic interference effects from the studies and subjected to rigid body roll and yaw motion as an approximation to the structural mode shapes. The complexity of the aerodynamics is increased successively from subsonic inviscid flow to transonic viscous flow. At a subsonic Mach number, a distinct aerodynamic nonlinearity in stiffness and damping in the aerodynamic coupling term HTP roll on yaw is shown. Geometric nonlinearities result in an almost entire cancellation of the stiffness nonlinearity and an increase in damping nonlinearity. The viscous forces result in a stiffness offset with respect to the inviscid results, but do not alter the observed nonlinearities, as well as the impact of geometric nonlinearities. At a transonic Mach number, the aerodynamic stiffness nonlinearity is amplified further and the damping nonlinearity is reduced considerably. Here, the geometrically nonlinear motion description reduces the aerodynamic stiffness nonlinearity as well, but does not cancel it.

A hybrid neural network model based modelling methodology for the rubber bushing

To fully consider the influences of the exciting frequency (0–20 Hz) and the environmental temperature (−50–20°C) on the dynamic characteristics of the rubber bushing in the railway vehicle, a hybrid neural network model is applied to develop the detailed model of the rubber bushing. The nonlinearities of the rubber bushing existing in the elastic element, the friction element and the viscous element are involved in the model to reflect the frequency- and amplitude-dependent characteristics of the rubber bushing. The experimental data are collected and exploited to find out the relationship between the input and output with the help of the neural network model. Furthermore, the influences of the environmental temperature on the dynamic parameters of the rubber bushing are considered. By testing the dynamic performance of the rubber bushing under the excitation with different frequencies, amplitudes and temperatures, the hybrid neural network model is trained and its critical parameters are identified. In this way, the trained hybrid neural network model for the rubber bushing can accurately reflect the dynamic performance in the presence of various excitation and environment temperatures.

Nonlinear vibrations of fiber-reinforced composite cylindrical shells with bolt loosening boundary conditions

In this paper, nonlinear vibrations of fiber-reinforced composite cylindrical shells (FRCCSs) with bolted joint boundary conditions are studied both theoretically and experimentally, where the nonlinear amplitude-dependent material property of fiber-reinforce composites (FRCs) and partial bolt loosening boundary conditions are taken into account. By representing the nonlinear material property via Jones-Nelson theory, Love shell theory is used to calculate the elastic strain energy of shells. The bolt loosening boundary conditions are achieved using artificial spring-damper technique. The Rayleigh-Ritz method is employed to derive the equations of motion for FRCCSs, from which the natural frequencies, damping ratios, and forced response can be obtained. Then, a series of vibration tests are carried out on a FRCCS specimen to validate the modeling approach proposed here. Based on the validated model, vibrations of FRCCS structures accounting for amplitude dependence of FRCs with different partial bolt loosening boundary conditions are investigated. It is found that increasing bolt loosening degree and loose bolt number leads to decrement of natural frequencies, and increment of modal damping ratios and resonant response amplitudes due to the coupling effect of declined boundary stiffness and increased boundary damping at bolted constraint edges. As the excitation level rises, the amplitude-dependent characteristics of natural frequencies and damping parameters of FRCCSs gradually become weak, while the increasing rates of resonant response amplitudes show an upward trend.

Modeling and Control of Piezoelectric Hysteresis: A Polynomial-Based Fractional Order Disturbance Compensation Approach

Piezoelectric hysteresis is a critical issue that significantly degrades the motion accuracy of piezo-actuated nanopositioners. Such an issue is difficult to be precisely modeled and compensated for, primarily due to its asymmetric, rate, and input amplitude-dependent characteristics. This article proposes a novel method to deal with this challenge. Specifically, a polynomial-based fractional order disturbance model is proposed to accommodate and characterize the complex hysteresis effect. In this model, the rate dependence is captured by a general method of implementing curve fitting in Bode magnitude plot. The inverse model for control purposes is immediately available from the original one. The proposed method does not require expensive computational resources. In fact, this article shows that this controller can be easily implemented in an analog manner, which brings the advantages of high bandwidth and low cost. Extensive modeling and tracking experiments are carried out to demonstrate the effectiveness of the proposed method. It is shown that the piezoelectric hysteresis nonlinearity can be significantly suppressed over a wide bandwidth.

Identification of Nonlinear Damping of Fiber-reinforced Composite Thin Plate with Vibration Amplitude Dependent Characteristics Based on Refined Resonance Method

Identification of Nonlinear Damping of Fiber-reinforced Composite Thin Plate with Vibration Amplitude Dependent Characteristics Based on Refined Resonance Method

Experimental study of high/low temperature effects on the dynamic performance of rubber spring for railway vehicles

For the layer rubber spring of a high-speed bogie, lab tests were conducted to obtain the dynamic parameters under extremely high and low temperatures (-60°C∼60°C) to obtain the nonlinear stiffness and damping parameters relevant to the frequency, amplitude and temperature changes. It starts from introducing the rubber element dynamic parameter test equipment, test plan and test methods. The applied loads and the temperatures are discussed. Then both the static and dynamic tests were performed for the layer spring of axle box, along the axial and radial directions. It shows that the common results can only reflect frequency- and amplitude-dependent characteristics of rubber, but the corresponding parameter change associated with each frequency and amplitude is highly dependent on the temperature. This phenomenon is quite severe in the low and extremely low temperature cases. Therefore, it is essential and necessary to carry out environmental temperature tests as well as basic theory study and simulations on all rubber components in order to know the parameter variation domain of the suspension system of a railway vehicle.

On the verification of superposition method of kinematic interaction and inertial interaction in dynamic response analysis of soil-pile-structure systems

A simplified analytical formulation has been used to verify the superposition method of two components of soil-structure interactions (SSI), namely-the kinematic interaction and the inertial interaction for estimating the dynamic response of soil-pile-structure systems (SPSS). The dynamic response analysis is conducted in the frequency domain and the soil behavior ranging from elastic-to-inelastic state is covered. The effective foundation input motion (EFIM) is obtained from shaking table model testing under 1g conditions for the kinematic interaction and the pile head impedance functions (IFs) are estimated from pile-head loading test for the inertial interaction, respectively. The EFIM and pile head IFs both have frequency and loading amplitude dependent characteristics. These experimentally recorded EFIM and pile head IFs are used as inputs in the analytical formulations to compute the dynamic response of the SPSS by superimposing the kinematic and inertial interaction. Superimposing adopts a linear interpolation method for appropriate use of the pile head IFs. The analytical (superimposed) dynamic response is then compared with experimentally measured dynamic response for verification purpose of superposition method and the comparison shows good agreement indicating that with appropriate use of EFIM and IFs, superposition method is reasonably good to produce the frequency and amplitude dependent dynamic response characteristics of SPSS. Certain discrepancies in amplification ratio and in resonant frequency particularly around the dominant vibrating modes have been observed in the comparison. The reason for such observed disagreements is possibly the difference between soil damping (hysteretic and radiation) and the difference between soil-pile stiffness.

Monitoring of wind effects on 600 m high Ping-An Finance Center during Typhoon Haima

This paper presents analyzed results of field measurements of wind-induced pressures on building claddings and structural responses of 600 m high Ping-An Finance Center (PAFC) in Shenzhen, China during the passage of Typhoon Haima. The characteristics of cladding pressures during the typhoon were investigated with highlights on energy distribution, non-Gaussian probability and coherence features. Then, the natural frequencies, damping ratios and mode shapes of the skyscraper were presented. Based on the field measurements, the amplitude-dependent characteristics of the modal parameters were discussed and the range of selection of damping ratio for the wind-resistant design of super-tall buildings was recommended. Finally, the serviceability of the skyscraper under typhoon condition was assessed. This paper aims to further understand the wind effects on super-tall buildings and provide useful information for the design of skyscrapers in tropic cyclone prone regions.

Effects of Precast Cladding Systems on Dynamic Characteristics of Steel Frame Buildings by Ambient and Free Vibration Tests

Full-scale tests on a one-story steel frame structure with a typical precast cladding system using ambient and free vibration methods are described in detail. The cladding system is primarily composed of ALC (Autoclaved Lightweight Concrete) external wall cladding panels, gypsum plasterboard interior linings, and window glazing systems. Ten test cases including the bare steel frame and the steel frame with addition of different parts of the precast cladding system are prepared for detailed investigations. The amplitude-dependent dynamic characteristics of the test cases including natural frequencies and damping ratios determined from the tests are presented. The effects of the ALC external wall cladding panels, the gypsum plasterboard interior linings, and the window glazing systems on the stiffness and structural damping of the steel frame are discussed in detail. The effect of the precast cladding systems on the amplitude dependency of the dynamic characteristics and the tendencies of the dynamic parameters with respect to the structural response amplitude are investigated over a wide range. Furthermore, results estimated from the ambient vibration method are compared with those from the free vibration tests to evaluate the feasibility of the ambient vibration method.

Reduced Order Models for Dynamic Behavior of Elastomer Damping Devices

In the context of passive damping, various mechanical systems from the space industry use elastomer components (shock absorbers, silent blocks, flexible joints...). The material of these devices has frequency, temperature and amplitude dependent characteristics. The associated numerical models, using viscoelastic and hyperelastic constitutive behaviour, may become computationally too expensive during a design process. The aim of this work is to propose efficient reduced viscoelastic models of rubber devices. The first step is to choose an accurate material model that represent the viscoelasticity. The second step is to reduce the rubber device finite element model to a super-element that keeps the frequency dependence. This reduced model is first built by taking into account the fact that the device's interfaces are much more rigid than the rubber core. To make use of this difference, kinematical constraints enforce the rigid body motion of these interfaces reducing the rubber device model to twelve dofs only on the interfaces (three rotations and three translations per face). Then, the superelement is built by using a component mode synthesis method. As an application, the dynamic behavior of a structure supported by four hourglass shaped rubber devices under harmonic loads is analysed to show the efficiency of the proposed approach.

Monitoring of dynamic behaviour of super-tall buildings during typhoons

This paper presents the field measurement results of the wind effects on two super-tall buildings (having height over 400 m) in Hong Kong during the passage of Typhoon Nesat in 2011. The field data such as wind speed, wind direction, structural acceleration and displacement responses were simultaneously recorded during the typhoon. Detailed analysis of the field data was conducted to investigate the wind field over an urban area, structural dynamic properties and wind-induced responses of the super-tall buildings. The typhoon-generated wind characteristics including turbulence intensity, gust factor and power spectral density of fluctuating wind speed were presented and discussed. The acceleration responses were analysed by Fourier transform to represent an averaged perspective over the records. Then, the wavelet transform was used to present time-frequency energy distributions of the structural vibrations. Instantaneous spectra were also presented for further discussions of the non-stationary signals. A high-pass Kaiser FIR digital filter was adopted to eliminate the multipath effects on the displacement responses recorded by global positioning system. Then, the resonant and background responses as well as their contributions to the total displacements were identified. Damping ratios of the high-rise structures were evaluated by the random decrement technique, which demonstrated amplitude-dependent characteristics. Finally, the serviceability performance of the super-tall buildings under wind actions with different return periods was estimated.

常時微動計測・振動実験・強震観測に基づく超高層建物の振動特性とその変化

Vibration characteristics of a high-rise building has examined by microtremor observation, free vibration test and earthquake observation. Natural frequencies and damping ratios for lower modes are estimated by microtremor tests, free vibration tests with AMD and man-powered excitations. Natural frequencies are shown to be lowered approximately 2% comparing to the situation soon after the construction. Relatively low damping ratios less than 1% are stably obtained. Amplitude dependent characteristics are slightly observed in estimated natural frequencies. Vibration characteristics during low-level earthquake response are estimated. Obtained properties during several years are effective for structural health evaluation after the large earthquake response.

Monitoring of typhoon effects on a super-tall building in Hong Kong

SUMMARY A super-tall building with height of 420 m and 88 floors is located in central Hong Kong. Field monitoring of wind effects on the high-rise structure was conducted during the passage of several typhoons on the basis of a wind and movement monitoring system installed in the building. Field data such as wind speed, wind direction, pressures on cladding, acceleration and displacement responses were simultaneously recorded during the typhoons and then analyzed. Typhoon wind parameters including turbulence intensity, gust factor, peak factor, turbulence integral length scale and power spectral density were presented and discussed. The dynamic properties of the high-rise structure were determined from the field measurements and compared with those calculated at the design stage. The damping ratios of the super-tall building were evaluated by a random decrement technique, which demonstrates amplitude-dependent characteristics. The relationships between the structural dynamic responses and the approaching wind speed were analyzed. Wind tunnel tests were conducted to investigate the wind effects on the super-tall building. The field-measured acceleration responses were found to be consistent with the model test results. Finally, the serviceability performance of the super-tall building during the typhoons was assessed on the basis of the field measurement results. The findings of the paper are expected to be of considerable interest and practical use to professionals and researchers involved in wind-resistant designs of super-tall buildings. Copyright © 2013 John Wiley & Sons, Ltd.

On the computation of the slow dynamics of nonlinear modes of mechanical systems

A novel method for the numerical prediction of the slowly varying dynamics of nonlinear mechanical systems has been developed. The method is restricted to the regime of an isolated nonlinear mode and consists of a two-step procedure: In the first step, a multiharmonic analysis of the autonomous system is performed to directly compute the amplitude-dependent characteristics of the considered nonlinear mode. In the second step, these modal properties are used to construct a two-dimensional reduced order model (ROM) that facilitates the efficient computation of steady-state and unsteady dynamics provided that nonlinear modal interactions are absent.The proposed methodology is applied to several nonlinear mechanical systems ranging form single degree-of-freedom to Finite Element models. Unsteady vibration phenomena such as approaching behavior towards an equilibrium point or limit cycles, and resonance passages are studied regarding the effect of various nonlinearities such as cubic springs, unilateral contact and friction. It is found that the proposed ROM facilitates very fast and accurate analysis of the slow dynamics of nonlinear systems. Moreover, the ROM concept offers a huge parameter space including additional linear damping, stiffness and near-resonant forcing.

Dynamic characteristics and wind-induced responses of a super-tall building during typhoons

This paper presents the field measurement results of dynamic characteristics and wind-induced responses of a 420m high tall building in Hong Kong during the passage of typhoons. The field data such as wind speed, wind direction, acceleration and displacement responses were simultaneously and continuously recorded from a monitoring system installed in the super-tall building. The outputs of accelerometers and GPS mounted in the building are compared to examine the accuracy of the GPS. The multipath effects are extracted by a combination of Empirical Mode Decomposition (EMD) and wavelet method, and then are removed by a high pass finite impulsive response (FIR) digital filter to improve the performance of the GPS. After obtaining the accurate GPS′s data, the resonant and background responses of the super-tall building as well as their contributions to the total displacements are presented and discussed. Finally, damping ratios of the building are evaluated by the random decrement technique, which demonstrate amplitude-dependent characteristics. The outcomes of this study are expected to be of interest and practical use to engineers and researchers who are involved in the wind-resistant design or structural health monitoring of super-tall buildings.

Joint Equalization/Demodulation for Digital Data Storage on Photographic Film

Data storage on photographic film has become a prospective alternative for long-term digital archiving. The storage capacity of such systems is strongly limited due to intersymbol interference (ISI) which can be significantly reduced by using equalization. This contribution presents two algorithms which jointly perform equalization and demodulation for data storage on film with non-linear, non-Gaussian, and amplitude-dependent characteristics. The performance of both approaches is investigated by means of simulations based on a realistic channel model.