Second-order Vibration Research Articles

Fluid–acoustic–structure resonance mechanism of a plane cascade via a low-speed wind tunnel test

Acoustic resonance is an important factor that contributes to aeroengine compressor failure. In this study, a plane cascade of compressor blades was designed to reproduce acoustic resonance via a low-speed wind tunnel test. A high-frequency hot-wire, microphone and strain gauge were used to synchronously measure the fluid, acoustic and structural parameters. We analysed the variation in the amplitude and frequency of the multi-field parameters with increasing mean flow velocity and explored the multi-field interaction mechanism that induces the acoustic resonance of the plane cascade. The plane cascade effectively reproduced the acoustic resonance phenomenon. The first-order acoustic-mode frequency of the plane cascade flow duct, second-order torsional vibration mode frequency of the blade and shedding mode frequency of the tip clearance leakage vortex were equal under acoustic resonance. The fluid, acoustic and structural fields showed a strong interaction effect, achieving the maximum blade vibration amplitude and causing fatigue cracks of torsional vibration at the blade root. The frequency lock-in region of the compressor plane cascade was divided into an ‘acoustic–structure’ interaction region, a ‘fluid–acoustic–structure’ interaction region and a first-order acoustic-mode dominant region with increasing mean flow velocity, which demonstrates an interesting phenomenon in which the fluid–acoustic–structure modes compete: acoustic mode > blade vibration mode > vortex shedding mode. The results demonstrate a unique approach to the study of acoustic resonance that provides insight into the acoustic resonance mechanism in a cascade of compressor blades.

Effect of Stratified Flow on the Vibration of Anchor Cables in a Submerged Floating Tunnel

This study investigates the vertical-type submerged floating tunnel with anchor cables. Based on the characteristics of the anchor cables, the anchor cables are simplified as a nonlinear beam model with hinged ends. Disregarding the axial displacement of the tunnel body, the loads will cause displacements in the x and z directions of the tunnel body. The vibrations of the anchor cables are decomposed into three directions, and the parameter excitation at the connection point between the anchor cables and the tunnel body is taken into account. The equations of motion for the three degrees of freedom of the anchor cables are established using Hamilton’s principle, and then the three equations are solved using the Galerkin method and the fourth-order Runge–Kutta method. The basic characteristics of an internal wave stratified flow acting on the anchor cables are considered, as well as the influence of the incident angle of the ocean currents on the three degrees of freedom of the anchor cables. The results indicate that (1) stratified flow weakens the first- and third-order vortex-induced vibrations of the anchor cables while enhancing the second-order vortex-induced vibrations. When considering the parameter excitation of the anchor cables, the first- and third-order vibrations are weakened, while the second-order vibration remains significant; (2) the first-order vibration of the anchor cables reaches its maximum value when the transverse oscillation frequency of the tunnel body is twice its natural frequency, and the second-order vibration of the anchor cables reaches its maximum value when the transverse oscillation frequency of the tunnel body is twice its natural frequency; (3) the downstream vibration of the anchor cables increases with the increase in the incident angle of the ocean currents, the cross-flow vibration of the anchor cables decreases with the increase in the incident angle of the ocean currents, and the axial vibration of the anchor cables reaches its maximum value when the incident angle of the ocean currents is 60 degrees; (4) stratified flow weakens the lock-in phenomenon of the anchor cables, and the influence of the 1/2 stratified flow on the vibrations of the anchor cables is greater than the influence of the 1/2 stratified flow.

Noise analysis of interior structure under powertrain excitation

To accurately identify the structural noise problem caused by vibration in the cockpit, an experimental study was conducted on a certain type of SUV under uniform acceleration conditions. Based on the planning of the multi-body system dynamics model, a transfer path model with secondary contributions is constructed, and the load is identified using the single degree of freedom model and multi-frequency bandwidth model under the OPAX method based on this path. The results indicate that the second-order vibration of the powertrain is transmitted to the entire suspension system through the X direction of the right suspension. The second-order vibration of the suspension system is then transmitted to the Z direction of the right rear bolt of the subframe, causing the entire subframe vibration and ultimately reaching the target point. This structural path has the greatest impact on the interior noise of the vehicle. This path research method can more accurately determine the main excitation points that cause interior noise problems on a certain path and better understand the overall energy transfer characteristics along the transmission path.

Design and Experimental Evaluation of a Dual-Cantilever Piezoelectric Film Sensor with a Broadband Response and High Sensitivity.

Cantilever-beam-type PVDF (Polyvinylidene Fluoride) piezoelectric film sensors are commonly utilized for vibration signal detection due to their simple structures and ease of processing. Traditional cantilevered PVDF piezoelectric film sensors are susceptible to the influence of the second-order vibration mode and have a low lateral stress distribution at the free end, which limit their measurement bandwidth and sensitivity. This study is on the design of a dual-cantilever PVDF piezoelectric film sensor based on the principle of cantilevered piezoelectric film sensors. The results of the experiments indicate that, compared to a typical single-arm piezoelectric cantilever beam vibration sensor, the developed sensor has a longer second-order natural frequency that ranges from 112 Hz to 453 Hz, while the first-order natural frequency is maintained at around 12 Hz. This leads to a better ratio of the second-order natural frequency to the first-order natural frequency and a wider frequency response range. At the same time, the sensitivity is increased by a factor of 3.48.

Numerical and experimental investigation of a variable-curvature shell class I flextensional transducer.

Class I flextensional transducers cannot form broadband characteristics because of the deep valley between their first- and second-order response curves. This valley arises from the sound pressure cancellation produced by the vibration in different areas of the shell. This paper examines the cause of the deep valley by analyzing the three-dimensional equivalent radiated sound field of the transducer. By solving the three-dimensional vibration equation of the shell of revolution and reducing its dimensionality, it can be concluded that its vibration state is related to the positive and negative curvatures in both main directions. Therefore, a variable-curvature shell class I flextensional transducer is proposed, and the second-order vibration of the transducer is changed by the variable-curvature structure composed of positive and negative Gaussian curvature surfaces. The proposed transducer avoids sound pressure cancellation and achieves broadband characteristics. After optimization, a transducer prototype is fabricated, and a pool test is conducted. The test results show that the transducer couples the first three vibration modes, attaining broadband characteristics with an in-band fluctuation of less than 8 dB and a bandwidth of more than 5.4 kHz in the axial and circumferential directions.

Nonlinear coupling vibration analyses of large-scale wind turbine system

With the development of wind energy, the unit capacity of wind turbine is becoming larger and the height of the support tower is getting higher. Limited by the transport conditions, the diameter of the tubular steel tower cannot further increase with the increase of the tower height, which results in the lower natural frequencies of the tower. The higher and more slender wind turbine towers are more sensitive to the external excitation and many tower collapses have occurred in recent years because of the interplay with the longer rotor blades. A 2 MW wind turbine system with a 120 m full steel tubular tower is taken as an example in this study to research the nonlinear coupling vibration mechanism under the normal operation case and the emergency shut-down case. An integrated model of large-scale wind turbine system including the tower, blades, hub, and nacelle is established by the open-source software FAST to study its nonlinear interaction vibration mechanism. Under the normal operation load case, the acceleration response of the steel wind turbine tower is greatly affected by the rotational frequency of the rotor. The maximum accelerations in the fore-aft and side-side directions both appear around the middle-upper height of the tower. Under the emergency shut-down load case, the maximum fore-aft acceleration response appears at the top of the tower, but the maximum side-side response still appears around the middle-upper height of the tower. The first-order vibration mode plays a dominant role in the top fore-aft acceleration and the second-order vibration mode has great contribution to the side-side acceleration under the emergency shut-down load case. The numerical results of this study can provide insight into the vibration control mechanism of the full steel tower.

A miniature longitudinal-bending hybrid linear ultrasonic motor inspired by the planar hinged five bar mechanism

Inspired by the double crank planar hinged five bar mechanism, a longitudinal-bending hybrid linear ultrasonic motor with compact miniature is proposed and tested. In order to realize miniaturization, it adopts a bonded-type structure. Four lead zirconate titanate (PZT) piezoelectric ceramics are distributed equally into two groups and bonded to the two ends of the metal frame, and then, two voltages with a phase difference of 90° are applied to each of the two groups of PZT ceramics. Subsequently, the first-order longitudinal vibration and second-order bending vibration generated by the motor combine with each other at the tip of the driving foot to form an elliptical motion trajectory. According to the theoretical kinematic analysis of the free beam, the initial structural dimensions of the motor were designed. Then, the initial dimensions of the motor were optimized, and the zero-order optimization algorithm was used to achieve the purpose of longitudinal and bending resonance of the motor, and finally, the optimal dimensions of the motor were obtained. A prototype of the designed motor was made, followed by experimental tests on the performance of the prototype, including mechanical output. The maximum motor speed without load at 69.4kHz is 134.57 mms-1. Under 200 Vpp voltage and 6 N preload, the output thrust of the motor is about 0.4 N at the maximum. The actual mass of the motor is about 1.6g; therefore, the thrust-to-weight ratio was calculated as 25.

Magnetic-Solid Coupling Nonlinear Vibration of an Axially Moving Thin Plate Under Air-Gap Magnetic Field

The nonlinear inherent vibration of an axially moving ferromagnetic thin plate under the action of the armature air-gap magnetic field is investigated. Based on the nonlinear elasticity theory, the energy relationship equations of the thin plate are given. Based on the electromagnetic theory and the solution of Laplace’s magnetic potential equation, magnetic force on the ferromagnetic rectangular plate under air-gap magnetic field environment is deduced. The Hamilton variational principle is applied to derive the magneto-solid coupled nonlinear vibration equation of the axially moving ferromagnetic thin plate. The two-degree-of-freedom nonlinear vibration differential equations containing static load terms with boundary conditions of SSSS and SSCC are obtained by discretizing through the Galerkin method. The multi-scale method is applied to solve the second-order approximation for deriving the first two orders’ intrinsic frequency of the nonlinear system. The variation laws of first two orders’ nonlinear inherent vibration with axial velocity, magnetic potential, initial air-gap thickness, and initial value are given through numerical examples, and the comparative analysis is performed. The results show that the first-order and second-order inherent vibration frequencies decrease with the increase of axial velocity and magnetic potential and increase with the increase of initial air-gap magnetic field thickness. Different materials and different boundary conditions have greater influence on the first-order and second-order inherent frequencies, and show obvious nonlinear characteristics. The results can provide references for analyzing and controlling the vibration behavior of moving structures in electromagnetic environment.

Nonlinear Vibrations of Carbon Nanotubes with Thermal-Electro-Mechanical Coupling

Carbon nanotubes (CNTs) have wide-ranging applications due to their excellent mechanical and electrical properties. However, there is little research on the nonlinear mechanical properties of thermal-electro-mechanical coupling. In this paper, we study the nonlinear vibrations of CNTs by a thermal-electro-mechanical coupling beam theory. The Galerkin method is used to discretize the partial differential equation and obtain two nonlinear ordinary differential equations that describe the first- and second-order mode vibrations. Then, we obtain the approximate analytical solutions of the two equations for the primary resonance and the subharmonic resonance using the multi-scale method. The results indicate the following three points. Firstly, the temperature and electric fields have a significant influence on the first-mode vibration, while they have little influence on the second-mode vibration. Under the primary resonance, when the load amplitude of the second mode is 20 times that of the first mode, the maximal vibrational amplitude of the second is only one-fifth of the first. Under the subharmonic resonance, it is more difficult to excite the subharmonic vibration at the second-order mode than that of the first mode for the same parameters. Secondly, because the coefficient of electrical expansion (CEE) is much bigger than the coefficient of thermal expansion (CTE), CNTs are more sensitive to changes in the electric field than the temperature field. Finally, under the primary resonance, there are two bifurcation points in the frequency response curves and the load-amplitude curves. As a result, they will induce the jump phenomenon of vibrational amplitude. When the subharmonic vibration is excited, the free vibration term does not disappear, and the steady-state vibration includes two compositions.

Modelling and calculation of stumulated oscillation for a crushing plant with vibration

The paper presents the results of the mathematical modelling of external stimuli to improve the efficiency of the removal of grain material from the grinding zone. Thus, the authors proposed to improve the evacuation conditions of the finished product from the working chamber of the crushing plant, as one of these solutions to improve the grinding process in crushers. As a result of creation of external vibrating influence. For this purpose, the calculation chart for modelling the proceeding process of the crushing plant body movement is created which takes into account weight and sizes of the crusher, weight, angular velocity of rotation and eccentric piece location, as well as rigidity of an elastic suspension on which the crusher is established. For the solution of the posed problem, we used methods of analytical mechanics, the Lagrange equation of the second kind, for the mechanical system with two degrees of freedom. As a result of calculations amplitude-frequency characteristics of mechanical system are determined. The conclusion about the choice of the angular velocity of the eccentric rotation for creation of necessary external stimulating influence on the crushing system and improvement of conditions of evacuation of a ready product from a working zone is given. The resonance frequencies of firstand second-order system vibrations and the vibrator frequency are determined to achieve resonance frequencies. Keywords: vibration, modelling, Lagrangian equations of the second kind, grinding, crushing plant.

Numerical and experimental investigation of a negative-curvature variable-shell flextensional transducer.

Type IV flextensional transducers do not have broadband characteristics due to the deep valley between their first- and second-order response curves arising from the sound pressure cancellation produced by the vibration in different areas of the shell. In this paper, the cause of the deep valley is examined by analyzing the equivalent radiated sound field of the transducer. Simplifying the three-dimensional vibration equation to a two-dimensional equation shows that the vibration state of the shell is related to the positive and negative curvature. Therefore, a variable-shell flextensional transducer with a negative curvature is proposed, which changes the second-order vibration of the transducer by introducing a negative curvature structure. The transducer avoids acoustic pressure cancellation, achieves broadband characteristics, and has continuous high efficiency in the frequency band. After optimization, a prototype of the transducer is fabricated and a pool test is completed. The test results show that the transducer realizes the coupling of the first three vibration mode, forming a broad band with an in-band fluctuation of less than 8 dB at 1200-5600 Hz, and the efficiencies of the first to third resonance peaks are 30.2 %, 16.6 %, and 9.4 %, respectively.

Two-Stage Time-Varying Vibration Compensation for Coherent LiDAR Based on the Adaptive Differential Evolution Method

Coherent LiDAR, which is based on triangular frequency modulated continuous wave (T-FMCW), is a promising technology for high-resolution imaging, because it can achieve long-range and high-precision measurements using low power. However, owing to the short wavelength of laser, the system is extremely sensitive to time-varying vibration. Most vibration compensation methods perform well in the scenes that contain strong scatterers using enough data. However, they lose validity in scenes without strong scatterers and sufficient observation time. To address this problem, we develop a second-order vibration error model for coherent LiDAR that divides the Doppler frequency shift caused by time-varying vibrations into quadratic and primary errors. Based on the vibration error model, we propose a two-stage time-varying vibration compensation method using the adaptive differential evolution (ADE) algorithm. In the first stage, we iteratively determine the optimal quadratic vibration coefficients that minimize the spectral entropy of the compensated dechirp signals using the ADE algorithm. Subsequently, we compensate for the quadratic errors using the estimated quadratic vibration coefficients. In the second stage, we use the frequency spectrum cross-correlation method to estimate the primary vibration coefficients and compensate for the primary errors. We perform experiments in the scene containing a point target and the scenes containing multi-component targets and distributed targets without strong scatterers. The results indicate that the proposed method can effectively compensate for time-varying vibration errors using only one-period T-FMCW data in different scenes. Further, the results of the proposed method are more accurate and stable than the Doppler frequency shift method.

Robust and minimum norm stabilization for uncertain singular second-order vibration systems

Robust and minimum norm stabilization for uncertain singular second-order vibration systems

Study of the structural, morphological and optical properties of ZnSe doped with Yb3+

A wurtzite phase of Zn 1−x Yb x Se (0 ≤ x ≤ 1.8) nanoparticles was synthesized through photo assisted chemical bath deposition. Glancing angle X-ray diffraction disclosed a hexagonal wurtzite crystal structure. The crystallite size (D) of undoped ZnSe was estimated 24.40 nm and then gradually decreased to 4.66 nm, after Yb 3+ doping. Scanning electron microscopy images revealed that with an increase in the Yb 3+ concentration, the thin film morphology transformed from Nano-flakes to spherical particles. The expected elements were confirmed by elemental energy X-ray dispersive analysis. Raman spectroscopy revealed the existence of two distinct optical phonon peaks induced by first- and second-order longitudinal vibration peak located at 257 and 500 cm -1 , respectively. UV–visible spectroscopy elucidated that the absorption spectra showed that the band gap energy for undoped ZnSe thin films can be tuned in the range of 2.76 - 3.12 by varying Yb 3+ concentration. Photoluminescence analysis revealed two emission and shoulder peaks located at 3.19 eV, 2.37 eV and 1.70 eV, which were ascribed to the band-to-band and imperfections of ZnSe, respectively. Chromaticity investigations revealed that the blue emission color was dependent on the concentration of Yb 3+ . The results suggest that Zn 1−x Yb x Se (0 ≤ x ≤ 1.8) is a promising candidate for blue-light emitting phosphor. The data that support the findings of this study are available from the corresponding author upon reasonable request.

Acoustic field switching of piezoelectric device for microsphere diameter sorting

To realize non-destructive diameter sorting of the inertial confinement fusion (ICF) microspheres, a novel standing waves piezoelectric sorting device is proposed in this study. Six piezoelectric plates and a container constitute the proposed device. The piezoelectric plates are used to excite the standard second-order bending vibration mode and the non-standard fourth-order bending vibration mode of the container, respectively, thereby two standing waves are produced in the liquid inside the container. Adjusting the working sequence and working duration of the two standing waves to realize the sorting of the ICF microspheres with different diameters. First, the distribution characteristics of the acoustic field produced by the vibration mode are theoretically analyzed. Then, the finite element method is used to analyze the vibration modes of the proposed device and the induced acoustic fields, optimize its dimensions, and verify the feasibility of the proposed sorting principle. In addition, vibration tests are performed on the prototype of the proposed device to analyze its vibration characteristics. Finally, an experimental platform is built to conduct the manipulation and sorting tests for the ICF microspheres. Experimental results show that the maximum average velocities of the ICF microsphere driven by the two vibration modes are 1.49 mm/s and 3.93 mm/s, respectively. And the difference in moving velocity caused by the difference in their diameter is significant. By controlling the excitation signals, the ICF microspheres with diameters of 480 μm and 680 μm can be effectively sorted within 13 s. The proposed standing wave piezoelectric sorting device holds the advantages of non-contact, non-destructive, cross-scale manipulation, and easy manufacturing, presenting the potential application for sorting the ICF microspheres and improving the detection efficiency.

Calculation of spectroscopic parameters of hydrogen and halogen bounded CH3CHO···HF and CH3COH···FH complexes

In this work, equilibrium geometry, bond energy, harmonic and anharmonic spectral parameters of the monomers of CH3CHO, HF molecules and CH3CHO···HF, CH3COH···FH complexes were calculated using the set of bases MP2/6-311++G(3df, 3pd). Anharmonic calculations were performed using second-order vibration theory. The binding energies of CH3CHO ··· HF and CH3COH ··· FH complexes are 10.1 kcal/mol and 1.7 kcal/mol, respectively.

A new operator based on edge detection for monitoring the cable under different illumination

In the field of bridge non-contact monitoring, the variation of illumination is one of the important factors that hinder edge detection technology to monitor bridges in real-time and long-time. In this paper, a new proposed edge detection operator is introduced. This method measures the frequency of the cable by locating the shadow of the bottom of the cable under different illumination. Compared with the Canny operator and current methods, the advantages of the new operator are explained in detail. The precision and robustness of the new operator are tested through a series of experiments in the laboratory. The experimental results show that, in terms of accuracy, the errors in first-order vibration frequency, second-order vibration frequency, first-order amplitude, and second-order amplitude are less than 1 %, 2 %, 6 %, and 26 %, respectively, between the improved operator method and the acceleration sensor. Compared with current technology, the accuracy of the new operator can reach 0.0001 mm. Compared with the Canny operator, this operator has strong robustness under different illumination. It could provide a scientific basis for engineering monitoring.

Research on system identification method of buffer system based on experimental signal pre-processing

In order to obtain the theoretical model of a gun buffer system, the dynamic vibration characteristics of the buffer system were studied by force hammer experiments, and the vibration acceleration response curves of the buffer system after being excited by the impact load were obtained. The acquired signals were processed by noise reduction, detrending, data smoothing and frequency domain integration, and the second-order free vibration model was used to identify the stiffness, damping and other parameters of the system, and compared with the experimental results. The deviation between the calculated results of the identification model and the experimental results is less than 4%, which compared with the general direct identification method, the error is reduced by about 10%. This method can provide a simple and fast technical way for the accurate identification of vibration system models.

A Novel Model of Ultrasonic Fatigue Test in Pure Bending.

The very high cycle fatigue (VHCF) failure of in-service components is mainly caused by the vibration of thin-wall elements at a high frequency. In this work, a novel model of ultrasonic fatigue test was developed to test thin-wall material in bending up to VHCF with an accelerated frequency. The theoretical principle and finite element analysis were introduced for designing a sample that resonated at the frequency of 20 kHz in flexural vibration. In the advantage of the second-order flexural vibration, the gauge section of the sample was in the pure bending condition which prevented the intricate stress condition for thin-wall material as in the root of cantilever or the contact point of three points bending. Moreover, combining the constraint and the loading contact in one small section significantly reduced heating that originated from the friction at an ultrasonic frequency. Both strain gauge and deflection angle methods were applied to verify the controlling of stress amplitude. The fractography observation on Ti6Al4V samples indicated that the characterized fracture obtained from the novel model was the same as that from the conventional bending test.

Study on the Vibration Characteristics of Rape Plants Based on High-Speed Photography and Image Recognition

The transmission characteristics of the vibration excitation of rape plants are of great significance to the study of the harvesting loss and threshing mechanism of rape during harvesting. Aiming to examine the problem that the existing vibration measurement method cannot be well adapted to the vibration measurement of small plants such as rape, this article proposes a vibration measurement method based on high-speed photography and image recognition and uses this measurement method to study the vibration characteristics of rape plants in the three states, i.e., sweep frequency, standing frequency, and free attenuation, with a default hydraulic shaker. The results showed that the average measurement error of the vibration amplitude of this method was 0.0068 mm, and the relative measurement error of the amplitude at 20 Hz was 0.45%, which met the test requirements. Based on this measurement method, a sweep frequency test of rape plants was carried out. It was found that the first-order and second-order vibration modes of rape plants were concentrated in the first 15 Hz. The resonance range of rape plants mainly occurred at 6–7 Hz and 11–12 Hz. The standing frequency vibration test showed that rape plants had strong resonance at 6 Hz and 11 Hz, and grain falling was 1.192% and 0.992%, respectively, which was greater than those of other frequencies. The free attenuation vibration of the rape plant showed that the average attenuation coefficients of the mark points on the lateral branch at 20 cm, 30 cm, and 40 cm from the branch node were 0.542, 0.475, and 0.441, respectively, and the attenuation coefficient decreased as the distance between the mark point and the branch node increased. The amplitude attenuation coefficient of the main branch had little difference, and the average value was 0.797. This research can provide some reference for exploring the threshing mechanism of the rape drum and optimizing the header structure and parameters.