Displacement Frequency Response Research Articles

Simplified Tunnel–Soil Model Based on Thin-Layer Method–Volume Method–Perfectly Matched Layer Method

In order to analyze the ground vibration responses induced by the dynamic loads in a tunnel, this paper proposes a new simplified tunnel–soil model. Specifically, based on the basic theory of the thin-layer method (TLM), the basic solution of three-dimensional layered foundation soil displacement was derived in the cylindrical coordinate system. The perfectly matched layer (PML) boundary condition was applied to the TLM. Subsequently, a tunnel–soil dynamic interaction analysis model was established using the volume method (VM) in conjunction with the TLM-PML method. The displacement frequency response function of the foundation soil around the tunnel foundation was derived. Finally, a ground vibration test under an impact load in a tunnel was carried out. The test and calculated results were compared. The comparison results show that the ground vibration acceleration response values within 25 m from the load are similar. Compared with the test results, the theoretical calculation results exhibit a decreasing trend in the range of 40–80 Hz between 25 and 60 m, with the maximum reduction being approximately one order of magnitude. In addition, the experimental comparison demonstrates that the model can be used to analyze the ground vibrations caused by underground loads.

Pulse-Width-Modulation-Based Time-Delay Compensation Control for High-Speed On/Off Valves

The dynamic characteristics of high-speed on/off valves (HSVs) are a key factor in measuring their performance, and determining the control accuracy of valve-controlled systems. Furthermore, the hysteresis characteristics of HSVs can seriously affect their dynamic characteristics. This study evaluated the hysteresis characteristics of HSVs in a valve-controlled hydraulic control system, and considered the pressure changes in front of the valve during the opening and closing process of the valve core. A time-delay compensation control (TDCC) based on pulse-width modulation (PWM) was proposed. The reference PWM signal was used to control the opening and closing time of the HSV, while the loading signal was composed of an opening compensation PWM, an excitation PWM, an opening holding PWM, and a closing compensation PWM. Using an opening compensation PWM to start the initial current, combined with current feedback and pressure changes in front of the valve, the amplitude and duty cycle of different PWM signals were determined in real time. This reduced the time delay and working current of the HSV during opening and closing. A simulation comparison analysis was conducted, with a single PWM control and a pre-excitation control algorithm (PECA). The results showed that, compared to a single PWM control, the TDCC can reduce the overall opening and closing time delay by 78.1%, and the energy consumption by 64.7%. Compared with PECA, the overall opening and closing time delay was reduced by 10.9%, and the energy consumption was reduced by 28%. At the same time, the frequency response of the valve core displacement increased by 70%, compared to the single PWM control.

Noise Prediction Study of Traction Arc Tooth Cylindrical Gears for New Generation High-Speed Electric Multiple Units

As the speed of the new generation of high-speed electric multiple units (EMU) increases, the requirements for vibration and noise reduction in traction gear trains are becoming higher and higher. Although most researchers have focused on the vibration mechanics analysis of gears, the actual noise has the most direct impact on passenger experience and safety. To address this problem, a new type of curved cylindrical gear is proposed to analyze the dynamic characteristics of the gear pair and predict its radiated noise based on the acoustic-vibration coupling theory using the finite element-boundary element method. Parametric modeling of the gear pair using CREO and assembly motion analysis were performed. ANSYS was used to analyze the stress distribution, inherent frequency, and inherent vibration pattern of the gear pair, and harmonic response analysis was performed using the modal superposition method to solve the displacement frequency response curve and vibration characteristics. ACTRAN was used to construct the free-field model, create acoustic excitation based on the acoustic-vibration coupling equation, set the field points, and predict radiated noise. The research results show that the noise is mainly concentrated in the tooth meshing area, and the root mean square RMS range of its sound pressure level value is 91–100 dB. Its dynamic characteristics and noise values are in line with the traction requirements of high-speed EMU, providing a new idea for improving the noise prediction of traction gears for new generation high-speed EMU, which in turn strongly support the noise control of high-speed EMU stock and thus improve the passenger experience and driving environment.

A novel lever-arm tuned mass damper inerter (LTMDI) for vibration control of long-span bridges

In this study, the lever mechanism is incorporated with the tuned mass damper inerter (TMDI) to further promote the practical application of TMDI in long-span bridges. Four potential configurations of the lever-arm tuned mass damper inerter (LTMDI) are first established, and the corresponding governing equations are derived. Then, the optimum configuration of LTMDI is identified by minimizing the peak of non-dimensional displacement frequency response function (FRF). Subsequently, the influences design parameters, such as mass ratio, inertance ratio, lever mass ratio, and spanning distance of the inerter are investigated. Based on the results, empirical design formulas of design parameters are proposed and verified. Finally, a cable-stayed bridge is adopted as a numerical case to further illustrate the performance of LTMDI in terms of response reduction and robustness. The results show that the involving of the lever into TMDI is an effective mechanism for implementing the inerter’s spanning in long-span bridges. With this mechanism, it is practically feasible to achieve a high effectiveness, low space requirement and more robustness control device for long-span bridges. The developed design formulas have a high accuracy, which can provide reliable support for the design of the LTMDI in engineering applications.

A grounded inerter-based oscillating TMD for suppressing harmonic and random vibrations

Inspired by the lightweight passive vibration control technology, in this work a new anti-vibration device is proposed to significatively improve the protection for stationary mechanical structures subjected to different kinds of vibratory loads. Such a device is herein termed as the grounded inerter-based two-degree-of-freedom tuned mass damper (GI-TDOF-TMD) composed by a grounded inerter and TDOF-TMD with rotational and translational motions, which controls the primary structure's dominant modal shape by using the synergistic dynamic effects of both devices. In order to fairly evaluate the GI-TDOF-TMD's vibration mitigation effectiveness with respect to other devices, the damped and undamped primary structure's nondimensional compliance and mobility transfer functions are firstly computed from a generalized mathematical model that considers four types of random and harmonic excitation inputs which are the following: force general case, base acceleration excitation, base displacement input and inertial force generated by the unbalance in rotary machinery. For harmonically excited mechanical systems, the H∞ performance measure is applied to minimize the maximum resonant peaks of the displacement and velocity dimensionless frequency response functions (FRFs). As the Extended Fixed-Points Technique (EFPT) is analogous to the H∞ criterion, quasi-optimal solutions are firstly computed to perfectly calibrate the FRF's invariant points. After performing this, the evolution of the FRF's control invariant frequencies revealed that GI-TDOF-TMD performs well at low inertance values. Therefore, the GI-TDOF-TMD's maximum control performance is obtained when the inerter's inertial force is the same as that yielded by the TMD's physical mass. In view of such a dynamic behavior, the GI-TDOF-TMD approximately provides 40% and 17% improvements when compared with respect to the classic dynamic vibration absorber (DVA) and TMD-inerter (TMDI), respectively. Then, the GI-TDOF-TMD's power dissipation capability is demonstrated by applying the H2 norm approach to the randomly excited damped mechanical structures. Additionally, it is also revealed through the stochastic energy balance that the GI-TDOF-TMD's internal power dissipation effectiveness is directly reflected on the minimization of the primary structure's kinetic energy. Moreover, for random inputs, the proposed device can broaden the effective operating bandwidth in approximately 45% and 19% when compared to the classic DVA and TMDI, respectively. Therefore, the GI-TDOF-TMD works better than the TMDI in terms of structural displacement and velocity response mitigation, which can be useful in civil engineering applications.

Graphic Transfer Matrix Method for Kinetostatic and Dynamic Analyses of Compliant Mechanisms

Abstract Kinetostatic and dynamic analyses of compliant mechanisms with complex configurations continue to be an attractive issue for obtaining a process-concise and result-accurate solution. In this paper, the transfer matrix method (TMM) is improved for a unified linear kinetostatics and dynamic modeling of compliant mechanisms with complex serial-parallel configurations in an oriented graphic way. In detail, the transfer matrices of typical building blocks commonly used in compliant mechanisms are summarized and derived. Then, a graphic transfer matrix modeling procedure capturing both the kinetostatics and dynamics of general compliant mechanisms is introduced. The displacement amplification ratio, input/output stiffness, parasitic error, natural frequencies, and frequency response of a typical compliant microgripper and a planar parallel three-degrees-of-freedom (3DOF) nanopositioner are calculated with such a graphic transfer matrix method. The advantages of the proposed modeling method lie in its convenience and uniformity in formulating both the kinetostatic and dynamic behaviors of a class of compliant mechanisms with distributed and lumped compliances in a transfer matrix manner, which has minimal DOF and is easily programmed.

Analysis on seismic control strategies for structural control device: A comparative study

The paper explores various control strategies proposed by researchers from decades ago in controlling the building structural system. It focuses on hybrid mass dampers used by many researchers in their previous work because the implementation of this device needs an excellent control strategy to provide a better performance in suppressing building vibration. The suitable choice of control strategy in structural control is important in giving the best structure response to withstand an earthquake or strong wind. Based on previous structure and control strategies, a simulation for a two-storey building structure system equipped with a hybrid mass damper at the top building has been conducted. Fuzzy logic controller (FLC), Sliding mode controller (SMC) and fuzzy sliding mode controller (FSMC) are used to suppress the building structure vibration during an earthquake by giving input from seismic excitation taken from El Centro earthquake. The simulation result shows that FSMC technique provides better performance compared to FLC and SMC in suppressing the building vibration based on the displacement response and frequency response. This paper concludes with the problems left and recommendations for structural control improvement.

Dynamic Characteristics of Rotor-Squeeze Film Damper-Support System Excited by Base Harmonic Excitations Using MHB-AFT Method

Abstract When operating at high speed, aeroengines mounted on the aircrafts also perform complicated maneuvering flights along with the aircrafts. The engine rotor systems will undergo forced motions excited by base movements and mass unbalance, which may lead to severe vibrations. Squeeze film damper (SFD) is generally used for vibration damping in aeroengine, but it also introduces structural nonlinearity like bistable jump. Moreover, the reliability of SFD is also affected by base excitations. Therefore, it is necessary to investigate the nonlinear dynamic behavior of rotor-SFD-support system excited by base motions. Taking a muti-disk rotor shaft supported by two SFDs with squirrel cages as the research object to simulate a gas generator in a turboshaft engine, the steady-state responses of the rotor system were calculated by multidimensional harmonic balance combined with alternating frequency/time domain method (MHB-AFT). The effects of base harmonic rotations and mass unbalance on steady-state responses of rotor system were investigated. The results indicate that the time-varying parametric excitations of base motions have strong effects on amplitude–frequency response of transverse displacement of rotor system. The critical speeds and resonant amplitudes of responses change with the magnitude and frequency of several base harmonic rotations. The variation of the frequency of base harmonic motion has the most significant impact on the amplitude–frequency response of transverse displacement of rotor system. The increase of base harmonic frequency will lead to multiple local peaks in the response curves, especially in the case of base harmonic rolling motion. In addition, the combination of base harmonic rotation around pitching and yawing axes results in significantly different response characteristics. Therefore, the influence of base harmonic motions should be considered during the structural design and damping optimization of SFDs.

Simulation analysis of electromagnetic noise of shaftless rimless thruster

In this paper, the shaftless rimless propulsion motor is taken as the research object, and the modal analysis of the stator in free state and constrained state is carried out by using the finite element method. The electromagnetic force is solved by numerical method, and then it is loaded on the stator. The harmonic response analysis of the stator is carried out, and the acceleration and displacement frequency response diagrams of the stator surface are obtained, and the vibration nephogram of the stator is analyzed. The results show that the acceleration and displacement in the radial direction are greater than those in the axial direction, which indicates that the vibration frequency in the radial direction is greater than that in the axial direction under the excitation of the radial electromagnetic force. When the frequency of the radial electromagnetic force is close to the natural frequency of the motor, the motor resonates and the vibration frequency increases.

Numerical investigation of vortex induced vibration effects on the heat transfer for various aspect ratios ellipse cylinder

The vortex-induced vibration of various aspect ratio (AR=0.75, 1.0, 1.25 and 1.5) ellipse cylinders with convective heat transfer is investigated at Re=150 and m∗=10 for 3≤Ur≤12, where Ur=U/(fnD) and fn is the natural frequency of cylinder in still air. The amplitude and frequency response of displacement, force and the Nusselt number are presented and discussed, the vorticity, temperature contours and wake patterns are studied to understand the effect of AR and Ur on the 1DOF vibration characteristics and the heat transfer of the isothermal cylinder. The results show that the classical Karman shedding (2S) is observed at relative low displacement and the C(2S) occurs when the cylinder undergoes high-amplitude oscillations for the AR considered, and the P+S wake mode which is composed with a single vortex and one pair of counter-rotating vortices during the transition from the initial branch to the VIV lock-in regime. There are multiple frequencies related to the response of Nusselt number, with the 2StNu dominating. And the maximum value of NuA is 11.07, 11.7, 12.1 and 12.35 for AR=0.75, 1.0, 1.25 and 1.5 respectively, which are increased by 7%, 8.7%, 11% and 13.5%, respectively, compared with the corresponding stationary cylinders, indicting an enhanced heat transfer of VIV cylinder. As increasing of the AR to 1.5, an early exit of the VIV lock-in regime and into the desynchronized regime happens due to the strong 2Stn in the lift frequency response when.

Parametric modeling of steady-state gradient coil vibration: Resonance dynamics under variations in cylinder geometry

Gradient coil (GC) vibration is the root cause of many problems in MRI adversely affecting scanner performance, image quality, and acoustic noise levels. A critical issue is that GC vibration will be significantly increased close to any GC mechanical resonances. It is well known that altering the dimensions of a GC fundamentally affects the mechanical resonances excited by the GC windings. The precise nature of the effects (i.e., how the resonances are affected) is however not well understood. The purpose of the present paper is to study how the mechanical resonances excited by closed whole-body Z-gradient coils are affected by variations in cylinder geometry. A mathematical Z-gradient coil vibration model recently developed and validated by the authors is used to theoretically study the resonance dynamics under variation(s) in cylinder: (i) length, (ii) mean radius, and (iii) radial thickness. The forced-vibration response to Lorentz-force excitation is in each case analyzed in terms of the frequency response of the GC cylinder's displacement. In cases (i) and (ii), the qualitative dynamics are simple: reducing the cylinder length and/or mean radius causes all mechanical resonances to shift to higher frequencies. In case (iii), the qualitative dynamics are much more complicated with different resonances shifting in different directions and additional dependencies on the cylinder length. The more detailed dynamics are intricate owing to the fact that resonances shift at comparatively different rates and this leads to several novel and theoretically interesting predicted effects. Knowledge of these effects advance our understanding of the basic mechanics of GC vibration and offer practically useful insights into how such vibration may be passively reduced.

Design, modeling, and experiment of a multi-bifurcated cantilever piezoelectric energy harvester

A multi-bifurcated cantilever piezoelectric energy harvester (BCPEH) is designed and verified to achieve a wide and adjustable response frequency band. The theoretical model is derived based on the Euler-Bernoulli beam theory and continuity boundary conditions to investigate the dynamic response of the BCPEH. The displacement frequency response function and the voltage frequency response function of the BCPEH are deduced based on the Galerkin method, and the theoretical results of a typical multi-bifurcated cantilever piezoelectric energy harvester, the Y-shaped BCPEH, are verified by the finite element method (FEM) and experiments. In addition, by comparing experimental output power of the Y-shaped BCPEH with that of the traditional cantilever-based piezoelectric energy harvester with the same mass of the bifurcated part at the beam-tip, it demonstrates that the Y-shaped BCPEH has a wider operational frequency band. Moreover, it is found that the Y-shaped BCPEH can be designed with an asymmetric configuration to adjust its response frequency distribution. The number of resonant frequencies and the output power of the asymmetric Y-shaped BCPEH are higher than that of the symmetric Y-shaped BCPEH. And the Y-shaped BCPEH has even better performance than L-shaped BCPEH. This study provides a new design concept for enhanced energy harvester.

Calculating the response of waveguides to base excitation using the wave and finite element method

The prediction of the response of waveguides to time-harmonic base excitations has many applications in mechanical, aerospace and civil engineering. The response to base excitations can be obtained analytically for simple waveguides only. For general waveguides, the response to time-harmonic base excitations can be obtained using the finite element method. In this study, we present a wave and finite element approach to calculate the response of waveguides to time-harmonic base excitations. The wave and finite element method is used to model free wave propagation in the waveguide, and these characteristics are then used to find the amplitude of excited waves in the waveguide. Reflection matrices at the boundaries of the waveguide are then used to find the amplitude of the travelling waves in the waveguide and subsequently the response of the waveguide. This includes the displacement and stress frequency response transfer functions. Numerical examples are presented to demonstrate the approach and to discuss the numerical efficiency of the proposed method.

Investigation of 2D Rainbow Metamaterials for Broadband Vibration Attenuation.

Phononic crystals (PnCs) and metamaterials are widely investigated for vibration suppression owing to the bandgaps, within which, wave propagation is prohibited or the attenuation level is above requirements. The application of PnCs and metamaterials is, however, limited by the widths of bandgaps. The recently developed rainbow structures consisting of spatially varied profiles have been shown to generate wider bandgaps than periodic structures. Inspired by this design strategy, rainbow metamaterials composed of nonperiodic mass blocks in two-dimensional (2D) space were proposed in the present study. The blocks were connected by curved beams and tessellated with internal voids to adjust their masses. In order to demonstrate the effects of the rainbow design, two 2D metamaterials, with periodic and nonperiodic units, respectively, were investigated and manufactured using additive manufacturing technologies. Receptance functions, i.e., displacement frequency response functions, of the manufactured metamaterials were calculated with finite element models and measured with a testing system containing a mechanical shaker, an impedance head, and a laser Doppler vibrometer. The obtained numerical and experimental results showed that the metamaterial with rainbow blocks has extended bandgaps compared with the periodic metamaterial.

Digital Demodulation Using I/Q Signals and Optical Phase Control Applied to a Vibrometer

An efficient and cost effective optical phase detection vibrometer based on a modified closed loop homodyne Michelson interferometer is presented. Real-time phase demodulation is carried out, using an embedded platform that performs data acquisition, signal processing, PI (proportional-integral) control and the generation of signals that drive the electrooptic Pockels cell phase shifter and the piezoelectric actuator under test. Two phase quadrature signals are generated from a single interferometric output, using the interleaving action, in alternation, of a digitally generated modulating signal, and then the well-known differential-cross-multiplication technique is applied to perform the computation of the phase shift of interest. The quadrature condition is reached using the PI loop based on an error signal obtained from a Lissajous figure derived from out-of-phase signals. The vibrometer is capable of measuring nanometric displacements, and is simple, inexpensive, accurate, immune to fading and self-consistent. The new method was used to determine the displacement frequency response curves of two prototypes of multi-actuated flextensional piezoelectric actuators. Measurements were made between 500 Hz and 15 kHz, and the results agreed with those obtained by the standard SCM-Signal Coincidence Method.

A Displacement Frequency Response Function-Based Approach for Locating Damage to Building Structures

Frequency response function (FRF) data can provide considerably more information on damage in the desired frequency range as compared to modal data extracted from a very limited range around resonances. Among structural health monitoring techniques, FRF-based methods have the potential to locate structural damage. Conventional structural damage detection technology collects structural response data using contact systems, such as displacement or acceleration transducers. However, installing these contact systems can be costly in terms of labor, cost, and time. Several noncontact measurement technologies, such as optical, laser, radar, and GPS, have been developed to overcome these obstacles. Given the rapid advances in optical imaging hardware technology, the use of digital photography in structural monitoring systems has attracted considerable attention. This study develops a displacement FRF-based approach to locate damage to building structures. The proposed damage location index, CurveFRFDI, improves the sensitivity of SubFRFDI, which is a substructure FRF-based damage location index proposed by Lin et al. (2012). Moreover, the feasibility of applying the proposed approach to locate damage to building structures using displacement measured by a digital camera combined with digital image correlation techniques is also investigated in this study. A numerical example and an experimental example are presented to demonstrate the feasibility of using the proposed approach to locate damage to building structures for single and multiple nonadjacent damage locations.

Mitigation of Traffic Induced Vibration Using Geocell Inclusions

This paper describes the potential use of geocell reinforcement in mitigating the traffic induced vibration. The vibration caused by the vehicular movement was simulated over the unreinforced and geocell reinforced sections using mechanical oscillator. The displacement amplitude and peak particle velocity were measured to understand the vibration mitigation efficacy of geocell. The effect of depth of placement of geocell on the mitigation of vibration parameters was studied. The inclusion of geocell was found effective in reducing the induced vibration based on the experimental results. The vibration mitigation efficacy of geocell was improved significantly at the shallow depth of placement of geocell mattress. The improvement in elasticity of the subgrade was observed maximum when the geocell was placed at a depth of 0.1B from the ground surface. Further, analytical and numerical approaches were used to predict the displacement amplitude versus frequency response of reinforced soil sections. FLAC3D was used for performing the numerical investigation. The geocell was modelled according to its honeycomb shape to acquire the accurate response of geocell reinforced section. Whereas, mass spring dashpot analogy was followed for the analytical evaluation. In overall, the amplitude response predicted from the numerical and analytical studies were found to be in good agreement with the experimental results.

A life test of ultrasonic motors under different torque loads and the analysis of the characteristics of wearing surfaces

Without a coil and a gearbox, an ultrasonic motor has an important application in space engineering and so forth with advantages of light weight, small volume, less electromagnetic radiation, fast dynamic response, and high energy density. However, the obvious friction and wear between the stator and the friction material (as a part of the shaft assembly) restrict the reliability and life time of the ultrasonic motor. In this paper, a life test of ultrasonic motors is designed and carried out for 3041.7 h, and the eight motors are divided into four groups with torque loads of 0.03 Nm, 0.09 Nm, 0.16 Nm, and 0.21 Nm in the test. The evolution characteristics of the displacement frequency response and the wear on the stator contact surface under different torque loads during the wear process are analyzed. Some start-up problems occur during the early time in the life test are found and explained based on a meshing effect between the stator and the friction material, and some targeted suggestions are proposed to overcome the problems. The study can help to understand the wear failure mechanism and characteristics of ultrasonic motors.

Coupled Dynamics of Cable-Harnessed Structures: Experimental Validation

The experimental study and model validations for the coupled dynamics of a cable-harnessed beam structure are presented. The system under consideration consists of multiple pretensioned cables attached along the length of the host beam structure positioned at an offset distance from the beam centerline. Analytical model presented by the coupled partial differential equations (PDEs) for various coordinates of vibrations is found, and the displacement frequency response functions (FRFs) obtained for both Euler–Bernoulli and Timoshenko-based models are compared to those from the experiments for validation. The results are shown to be in very good agreement with the experiments.

Identification of weak nonlinearities in MDOF systems based on reconstructed constant response tests

A novel strategy to characterize and identify structural nonlinearities in MDOF systems based on reconstructing constant response tests from constant excitation tests is developed in this paper. Constant displacement frequency response functions (FRFs) can be measured by a stepped sine test where the displacement is controlled at every frequency of interest. In these FRFs, the nonlinear restoring force is effectively linearized and natural frequencies can be estimated by linear modal analysis. Using a series of constant displacement tests, the relationship of equivalent stiffness versus displacement can be established by curve fitting, and hence, the nonlinear stiffness characterized. This paper proposes a method to reconstruct the constant displacement FRFs from stepped sine tests with constant excitation; this avoids the requirement to control either the response or force amplitude leads to a faster and more stable testing program. Similarly, damping nonlinearities in structures can be characterized and identified by constant velocity tests reconstructed in a similar way. This approach of FRF reconstruction is mathematically simple and suitable for structures with weak nonlinearities. The method is demonstrated on a framed structure with unknown weak nonlinearities, and the nonlinear stiffness and damping parameters of the structure are identified and validated. The results demonstrate the feasibility and effectiveness of the approach and also show the potential for practical applications in engineering.