3D Vibration Research Articles

Three-dimensional full-field vibration measurements using a handheld single-point laser Doppler vibrometer

The laser Dopper vibrometer (LDV) has become a standard instrument to perform high spatial resolution 3D vibration measurements of complex structures. An important step in the LDV measurement procedure is the estimation of the pose of the instrument relative to the test object. Existing LDV pose estimation methods rely on the use of 3D range sensors to perform this task. These sensors are costly and often their spatial resolution and accuracy is too limited for an accurate LDV pose estimation. But most importantly, existing LDV pose estimation techniques are slow. In this paper, we present a novel LDV pose estimation method based on matching of a 2D camera image and a CAD model of the test object. In contrast to existing pose estimation techniques, our method is able to track the pose of the LDV in real-time (up to about 30 LDV positions per second). This means that our method also allows LDV pose estimation when either the LDV or the object is moving. Using the real-time LDV pose tracking we present a new LDV measurement methodology where we hold instrument in our hand while moving around the test structure. This allows us to perform full-field scanning and 3D velocity measurements with a low-cost single point LDV sensor. We show that the measurement accuracy of a stationary handheld LDV measurement is about 40 dB (which is about 10 dB lower than in the case of measurements on a tripod). Furthermore, we demonstrate that the 3D vibrations measurements using the handheld vibrometer have an error of about 20% compared to classical measurements performed by combining three LDV measurements on a tripod. We illustrate our method on vibration measurements of a composite bicycle frame.

Finite element analysis of resonant properties of silicon nanowires

This paper presents a 3D nanostructure modal vibration analysis by using finite element models. The modal frequencies and corresponding modal shapes of silicon nanowires of various thickness against length ratios are determined by solving a linear structural eigenvalue problem for the 3D solid finite element model, where surface stress effects are taken into account by using the stress stiffness matrix. The cases of fixed/fixed and fixed/free boundary conditions at the nanowire ends are investigated. The results obtained by 3D solid models and models based on the beam bending theory have been compared with each other, as well as with the results obtained elsewhere in the literature computationally and experimentally. It has been shown that the effects caused by surface stresses are insignificant for wires with length-to-width ratio less than 10.

Stability and nonplanar buckling analysis of a current-carrying mircowire in three-dimensional magnetic field

This paper investigates the stability and nonplanar buckling of a current-carrying microwire immersed in a three-dimensional (3D) magnetic field based on modified coupled stress theory and Euler–Bernoulli beam assumptions. Utilizing Hamilton’s principle, the partial differential governing equations for 3D vibrations of the current-carrying microwire are derived. These governing equations are then discretized via the Galerkin’s approach and solved by a fourth-order Runge–Kutta method. Numerical results show that the slenderness ratio and magnetic field have obvious effect on the stability of the microwire. When the applied magnetic field is along the axial direction of the undeformed microwire, the shape of the postbuckling configuration of the microwire is very sensitive to initial conditions employed. If, however, the magnetic field is deviated from the axial direction of the undeformed microwire, it is interesting that the shape of the postbuckling configuration is independent of initial conditions even if the y- and/or z-component of the 3D magnetic field strength is sufficiently small. Another attractive feature of the results is that the lateral deflection of the microwire can be adjusted by changing the magnetic field strength in each direction, which may have potential application to the microelectromechanical systems (MEMS). Finally, the influence of a 3D magnetic field on the axial displacement of the microwire is analyzed, and it is demonstrated that in practice the axial motion of the microwire may be considered negligible.

3D Vibration Analysis of Combined Shells of Revolution

A three-dimensional (3D) method of analysis is presented for determining the natural frequencies and the mode shapes of combined hemispherical–cylindrical shells of revolution with and without a top opening by the Ritz method. Instead of mathematically two-dimensional (2D) conventional thin shell theories or higher-order thick shell theories, the present method is based upon the 3D dynamic equations of elasticity. Mathematically, minimal or orthonormal Legendre polynomials are used as admissible functions in place of ordinary simple algebraic polynomials which are usually applied in the Ritz method. The analysis is based upon the circular cylindrical coordinates instead of the shell coordinates which are normal and tangent to the shell mid-surface. Strain and kinetic energies of the combined shell of revolution with and without a top opening are formulated, and the Ritz method is used to solve the eigenvalue problem, thus yielding upper bound values of the frequencies by minimizing the frequencies. As the degree of the Legendre polynomials is increased, frequencies converge to the exact values. Convergence to four-digit exactitude is demonstrated for the first five frequencies. Numerical results are presented for the combined shells of revolution with or without a top opening, which are completely free and fixed at the bottom of the combined shells. The frequencies from the present 3D Ritz method are compared with those from 2D thin shell theories by previous researchers. The present analysis is applicable to very thick shells as well as very thin shells.

Low-frame-rate single camera system for 3D full-field high-frequency vibration measurements

Abstract A single-camera stereo-digital image correlation (stereo-DIC) system to obtain 3D full-field vibration measurements is proposed. The optical setup is composed of two planar mirrors and a single low frame rate camera, thus resulting in a compact and low-cost equipment. The two mirrors are used to create pseudo-stereo images of a target surface on the camera sensor, which are then correlated by using stereo-DIC. The image acquisition process is carried out at low frame rates and the Nyquist-Shannon frequency limitation is overcome by adopting a down-sampling approach under the hypothesis that the vibration signal is characterized by a single known frequency component. The developed pseudo-stereo DIC system allows to obtain 3D full-field vibration measurements in a frequency range up to 4 kHz even with an available frame rate (at full resolution) of 178 fps. The effectiveness of the described approach has been verified by performing vibration measurements on a cantilever plate and a turbine blade.

Virtual Model of Grip-and-Cut Picking for Simulation of Vibration and Falling of Grape Clusters

Abstract. Current robotic prototypes mainly harvest fruit clusters by gripping and cutting the main rachis. However, severe cluster vibration and fruit falling may occur during speedy harvesting. Determining the characteristics of this vibration and falling is important to achieve optimal control in robotic harvesting. Therefore, a virtual grip-and-cut model of cluster picking was developed, and corresponding cluster vibration and fruit falling simulations were performed for robotic harvesting. Multi-property finite element modeling of the main rachis was based on measurements of the rachis compression, shearing, and bending properties. A simulation model of cluster vibration was then built and combined with an end-effector model to obtain a virtual model of grip-and-cut cluster picking. The 3D vibration simulation model of a fruit cluster coupled with the grip-and-cut end-effector model effectively characterized the complex vibration in multilevel and multicomponent fruit clusters with individual diversity of the components’ properties. With the virtual model for cluster picking, dynamic interactive simulation can be realized of the fruit cluster and the grip-and-cut end-effector. Experiments verified that the average deviation of the average swing angle and fruit falling ratio were 6.09% and 8.71%, respectively. Furthermore, the finger-rachis deviation and grip-and-cut speed had a significant influence on the swing angle and fruit falling ratio. The 3D vibration simulation model of a fruit cluster and the virtual model of cluster picking are useful tools for virtual analysis and design of robotic harvesters. Keywords: Falling, Fruit cluster, Harvesting, Robot, Simulation, Vibration.

Fabrication of hierarchical freeform surfaces by 2D compliant vibration-assisted cutting

In this paper, instead of the commonly used fast tool servo method, a two degrees-of-freedom (2D) vibration-assisted machining method is proposed to enable the efficient generation of freeform surfaces with hierarchical micro/nano-structures. With this method, the freeform component of the surface is realized by 1D vibrations in the depth-of-cut direction, whereas the hierarchical micro/nano-structures are generated by elliptical vibrations at high frequency and small vibration amplitudes. The determination of the tool vibration path, considering tool geometry and the interference between the tool's flank surface and the machined surface, is presented and used as the basis to propose a surface generation algorithm for topography prediction. Using a developed 2D vibration compliant cutting system, experiments were conducted to machine hierarchical sinusoidal and discontinuous cubic surface arrays for demonstration. The results show a high consistency between the simulated and generated topographies demonstrating the effectiveness of the proposed method for the efficient machining of hierarchical freeform surfaces. In addition, wettability tests were undertaken to demonstrate that larger wetting angles can be obtained on hierarchical freeform surfaces as compared to their smooth counterparts.

Numerical realization and structure characterization on random close packings of cuboid particles with different aspect ratios

Packing processes of cuboid particles with different aspect ratios (h/b) under 3D vibrations were numerically reproduced by discrete element method using multi-sphere model. The influences of vibration conditions (e.g. vibration time, frequency, and amplitude) and particle shape on the packing densification were comprehensively analyzed. The macro property such as packing density (ρ) and micro properties such as coordinate number (CN), radial distribution function (RDF), contact types and force networks were systematically characterized and compared, and the densification mechanism was discussed. Meanwhile, the randomness of cuboid packing systems was evaluated by nematic order parameter (S2) and cubic order parameter (S4). The results show that dense packings of cuboids with different aspect ratios can be realized by properly controlling vibration conditions. In ρ ~ h/b curve, three peaks can be identified at h/b = 0.5, 1.0 and 1.5, corresponding to the packing densities of 0.700, 0.736 and 0.707, respectively. After vibration, the nematic order parameter S2 decreases in each case and cuboids with too high or too low aspect ratios are easier to form orientational order, while the cubic order parameter S4 increases but it is not positively correlated to the value of packing density. The formation of more face-to-face contacts leads to higher averaged CN and packing density. RDF indicates that special local structures can be formed during packing densification. Force networks indicate that the vibration energy transferred from the container enables cuboid particles near the bottom to generate orientation ordering, where more strong forces are observed, which can promote the rearrangement of cuboid particles for packing densification.

A self-powered 3D activity inertial sensor using hybrid sensing mechanisms

A self-powered 3D activity inertial sensor (3DAIS) is proposed for multi-axis acceleration and rotation inertial sensing. The 3DAIS consists of magnetic buckyballs encapsulated inside a 3D–printed spherical shell, with multi-layers of PTFE, PVDF and Al films fabricated on the inner walls of the shell and wire coils winded on the outside. The device demonstrated good performance in hand motion recognition and human activity state monitoring application. When operating as a 6-axis inertial sensor, the 3DAIS is able to sense X, Y and Z-acceleration during linear motion as well as detect roll, pitch and yaw angular velocity during rotational motion. The device possesses self-powering ability as well and is able to harvest energy through hybrid mechanisms of piezoelectric, electromagnetic and triboelectric from various energy sources such as 3D vibration, rotation and human motion, etc. The proposed 3DAIS can potentially pave the way to an advance motion sensing system with self-powering capability for wearables and healthcare telemedicine applications.

Influences of train speed and concrete Young's modulus on random responses of a 3D train-track-girder-pier coupled system investigated by using PEM

In this paper, a refined three-dimensional (3D) vibration model for a train-track-girder-pier coupled system is established and solved using a pseudo-excitation method (PEM). Considering the excitation of random track irregularities, a high-speed railway case study is presented to verify the effectiveness of the model and the method by comparing the results with those given by a Monte Carlo method. A pre-stressed concrete box girder for a high-speed railway bridge with excitation of random track irregularities is used to investigate the influences of train speed and concrete Young's modulus on the random dynamic responses of the coupled system. The results show that the PEM is 1-2 orders of magnitude more computationally efficient for the random dynamic analysis of the train-track-girder-pier systems compared with the Monte Carlo method. The power spectral densities (PSDs) of vertical accelerations of coach body change only slightly with time, but they change significantly with track irregularity frequency. All the first peaks of the PSD curves for the coach body vertical acceleration are shown to appear at around the same fundamental frequency. The concrete Young's modulus of the girder has a large influence on the PSDs of the vertical acceleration of the bridge, but the distribution of vibration energy in the frequency domain varies very little. The results can be applied to railway design and maintenance.

3D free vibration analysis of multi-directional FGM parallelepipeds using the quadrature element method

• A novel element for analyzing 3D vibration of multidirectional FGM solid is established. • Stiffness matrix is explicitly given when integration points do not coincide with nodes to achieve higher accuracy. • Comparisons show the accuracy of the proposed multidirectional FGM parallelepiped element. In this paper, the existing quadrature element method (QEM) is extended to analyze the three-dimensional (3D) free vibration of multi-directional functionally graded material (FGM) parallelepipeds under general boundary conditions. The material properties vary continuously in multiple directions according to a power-law form. Formulations of the multi-directional FGM parallelepiped element are given. Since the element nodes do not coincide with the integration points, a different way is used to compute the strains at integration points to derive explicit element stiffness matrix. A number of case studies on multi-directional FGM square and rhombic thick plates with general boundary conditions and different power-law exponents have been conducted. The effect of power-law exponents and boundary conditions on the free vibration behavior of FGM plates is investigated. The natural frequencies are in excellent agreement with either existing results or data obtained by ABAQUS using fine meshes. It is demonstrated that the extended QEM is simple in formulations and capable of capturing the 3D vibration behavior of the multi-directional FGM plates with high precision. New results are presented and may be used as benchmark solutions for future researches.

Research on a 3-DOF Motion Device Based on the Flexible Mechanism Driven by the Piezoelectric Actuators.

This paper describes the innovative design of a three-dimensional (3D) motion device based on a flexible mechanism, which is used primarily to produce accurate and fast micro-displacement. For example, the rapid contact and separation of the tool and the workpiece are realized by the operation of the 3D motion device in the machining process. This paper mainly concerns the device performance. A theoretical model for the static performance of the device was established using the matrix-based compliance modeling (MCM) method, and the static characteristics of the device were numerically simulated by finite element analysis (FEA). The Lagrangian principle and the finite element analysis method for device dynamics are used for prediction to obtain the natural frequency of the device. Under no-load conditions, the dynamic response performance and linear motion performance of the three directions were tested and analyzed with different input signals, and three sets of vibration trajectories were obtained. Finally, the scratching experiment was carried out. The detection of the workpiece reveals a pronounced periodic texture on the surface, which verifies that the vibration device can generate an ideal 3D vibration trajectory.

Three‐dimensional vibration analysis of simply supported laminated cylindrical shells and panels by a strong SaS formulation

AbstractIn this paper, the strong sampling surfaces (SaS) formulation developed earlier by the authors to solve the statics problems for plates and shells is extended to the three‐dimensional (3D) vibration analysis of laminated composite shells. The SaS formulation is based on choosing the arbitrary number of SaS parallel to the middle surface in order to introduce the displacements of these surfaces as basic shell unknowns. Such choice of unknowns with the use of Lagrange polynomials in approximations of displacements and strains through the layer thicknesses leads to a robust laminated shell formulation. The feature of the proposed strong SaS formulation is that all SaS are located inside the layers at Chebyshev polynomial nodes. The use of outer surfaces and interfaces is avoided that makes possible to minimize uniformly the error due to Lagrange interpolation. Therefore, the strong SaS formulation based on direct integration of equations of motion of the elastic body can be applied efficiently for the 3D vibration analysis of laminated cylindrical shells and panels.

Numerical free vibration analysis of homogeneous or composite beam using a refined beam theory built on Saint Venant’s solution

Free vibration problem of an arbitrary cross-sectional homogeneous or composite beam is investigated using a refined 1D beam theory (RBT). This theory includes a set of 3D displacement modes of the cross-section (CS) which reflects its mechanical behavior: the main part of these sectional modes is extracted from the 3D Saint Venant’s solution and another part is related to the CS dynamic behavior. These sectional modes, which are first derived from a CS analysis, lead to a consistent 1D beam model which really fits the section nature (shape and materials), and hence the beam problem.The numerical strategy to apply such general approach, is based on a first set of CS problems solved by 2D-FEM computations to get the sectional modes, and then the dynamic beam problem is solved by 1D-FEM computation according to RBT displacement model to provide (in fine) the first natural frequencies and 3D vibration mode shapes of the beam. To do so and in order to easily apply such method, a user friendly Matlab numerical tool named CSB (Cross-Section and Beam analysis) has been developed.To illustrate the capabilities and the accuracy of the method to catch the main 3D-effects, such as elastic/inertial coupling effects and 3D local/global mode shapes, a significant set of beam cross-section configurations with isotropic and anisotropic materials are analyzed. The first ten natural frequencies and 3D mode shapes are systematically compared to those obtained by full 3D-FEM computations, and some of them to literature.

Trinity of Three-Dimensional (3D) Scaffold, Vibration, and 3D Printing on Cell Culture Application: A Systematic Review and Indicating Future Direction.

Cell culture and cell scaffold engineering have previously developed in two directions. First can be ‘static into dynamic’, with proven effects that dynamic cultures have benefits over static ones. Researches in this direction have used several mechanical means, like external vibrators or shakers, to approximate the dynamic environments in real tissue, though such approaches could only partly address the issue. Second, can be ‘2D into 3D’, that is, artificially created three-dimensional (3D) passive (also called ‘static’) scaffolds have been utilized for 3D cell culture, helping external culturing conditions mimic real tissue 3D environments in a better way as compared with traditional two-dimensional (2D) culturing. In terms of the fabrication of 3D scaffolds, 3D printing (3DP) has witnessed its high popularity in recent years with ascending applicability, and this tendency might continue to grow along with the rapid development in scaffold engineering. In this review, we first introduce cell culturing, then focus 3D cell culture scaffold, vibration stimulation for dynamic culture, and 3DP technologies fabricating 3D scaffold. Potential interconnection of these realms will be analyzed, as well as the limitations of current 3D scaffold and vibration mechanisms. In the recommendation part, further discussion on future scaffold engineering regarding 3D vibratory scaffold will be addressed, indicating 3DP as a positive bridging technology for future scaffold with integrated and localized vibratory functions.

Dynamics of Multipoint Thread Turning—Part I: General Formulation

This paper formulates the generalized dynamics and stability of thread turning operations with custom multipoint inserts. The closed-loop chip regeneration mechanism is modeled by evaluating the effect of the current vibrations and the vibration marks left from the previous tooth. Using the developed chip discretization method, the dynamic cutting and process damping forces are obtained at each point along the cutting edge by projecting the three-dimensional (3D) vibrations of the tool and workpiece in the direction of local chip thickness. The equation of motion is derived in both physical and modal spaces, and stability is analyzed in frequency domain using Nyquist criterion. An iterative process optimization algorithm has been developed to maximize productivity while respecting machine tool's torque and power limits. Extension of the model to thin-walled workpieces along with the validating experiments on real-scale oil pipes is presented in Part II of this paper.

Three-Dimensional Vibration of the Crankshaft of a Large Marine Diesel Engine Under a Mixed Thermo-Elastic-Hydro-Dynamic Lubrication Coupling Between Flexible Crankshaft and Engine Block

Abstract To predict the vibration characteristics of the crankshaft of the larger marine diesel engine accurately and comprehensively, based on the finite element models of the crankshaft and the engine block reduced by a component mode synthesis (CMS) method as well as extended Reynolds equation and Greenwood-Tripp theory, a mixed thermo-elasto-hydro-dynamic lubrication coupling model between a whole flexible engine block and a rotating flexible crankshaft is set up. According to this strongly coupled nonlinear model, the torsional-axial-lateral three-dimensional (3D) vibration of the crankshaft can be calculated simultaneously. The method is verified through comparison with other computational methods. Also, the vibrations are compared under different support models and whether to consider the effect of temperature. Specific 3D vibrations are displayed, and some stage nonlinear characteristics are shown in 3D direction. The modeling method will contribute to reveal the vibration mechanism and optimize the design of the shafting system.

Experimental study on the packing densification of mixtures of spherical and cylindrical particles subjected to 3D vibrations

ABSTRACTTo identify the dense packing of cylinder–sphere binary mixtures (spheres as filling objects), the densification process of such binary mixtures subjected to three-dimensional (3D) mechanical vibrations was experimentally studied. Various influential factors including vibration parameters (such as vibration time t, vibration amplitude A, frequency ω, vibration acceleration Γ) as well as particle size ratio r (small sphere vs. large cylinder), composition of the binary mixtures XL (volume fraction of cylinders), and container size D (container diameter) on the packing density ρ were systematically investigated. The results show that the optimal vibration parameters for different binary cylinder–sphere mixtures are different. The smaller the size ratio, the less vibration acceleration is needed to form a stable dense packing. For each binary mixture, high packing density can be obtained when the volume fraction of large cylindrical particles is dominant. Meanwhile, increasing the container size can decrease the container wall effect and get higher packing density. The proposed analytical model has been proved to be valid in predicting the packing densification of current cylinder–sphere binary mixtures.

Identification of Dynamic Characteristics of Bridge for FE Modeling Based on Measurement of 3D Shape and Vibration

Identification of Dynamic Characteristics of Bridge for FE Modeling Based on Measurement of 3D Shape and Vibration

3D vibration measurements by a virtual-stereo-camera system based on a single low frame rate camera

A 3D full-field optical system for high frequency vibration measurement is proposed. The system is composed of a single low-frame-rate camera and two planar mirrors. This compact optical setup overcomes the typical drawback of capturing synchronous acquisitions in the case of a camera pair. Moreover, planar mirrors allow for the use of the classical pinhole model and, thus, conventional stereo-calibration techniques. The use of a low-frame-rate camera provides on the one hand a high-resolution sensor with a relatively low-cost hardware but imposes, on the other, the adoption of a down-sampling approach, which is applicable only when a single (known) sinusoidal load is applied to the structure. The effectiveness of the proposed setup has been verified by the 3D vibration measurement of two different targets up to a frequency of 1 kHz, corresponding to a displacement amplitude of 0.01 mm.