3D Dynamic Response Research Articles

Remote 3D Displacement Sensing for Large Structures with Stereo Digital Image Correlation

The work performance of stereo digital image correlation (stereo-DIC) technologies, especially the operating accuracy and reliability in field applications, is not fully understood. In this study, the key technologies of the field remote 3D displacement sensing of civil structures based on stereo-DIC have been proposed. An image correlation algorithm is incorporated in improving the matching accuracy of control points. An adaptive stereo-DIC extrinsic parameter calibration method is developed by fusing epipolar-geometry-based and homography-based methods. Furthermore, a reliable reference frame that does not require artificial markers is established based on Euclidean transformation, which facilitates in-plane and out-of-plane displacement monitoring for civil structures. Moreover, a camera motion correction is introduced by considering background points according to the camera motion model. With an experiment, the feasibility and accuracy of the proposed system are validated. Moreover, the system is applied to sense the dynamic operating displacement of a 2 MW wind turbine’s blades. The results show the potential capability of the proposed stereo-DIC system in remote capturing the full-field 3D dynamic responses and health status of large-scale structures.

3D elastodynamic solutions to layered transversely isotropic soils considering the groundwater level

The semi-dry or moist sediment above the groundwater level forms the vadose zone, while the continuous groundwater system below the groundwater level forms the aquifer. It is generally believed that the vadose zone is composed of unsaturated soils, while the aquifer is composed of saturated soils. The groundwater level would affect the distribution of unsaturated soils and saturated soil along the depth direction, and further change the dynamic behavior of soils under external excitation. Thus, this paper aims to investigate the 3D dynamic response of layered soils considering the influence of groundwater level. The investigated model is established based on dynamic governing equations of unsaturated soils and saturated soils. The precise integration method is combined with Fourier transform to solve the investigated model. To verify the feasibility, the proposed model is achieved and solved by the user-defined PDE module in COMSOL. The two results are in good agreement. Finally, several parametric analyses are provided to discuss the influence of key parameters on dynamic response of layered soils considering the groundwater level.

High-Speed Videogrammetry for Seismic Performance of the Spherical Reticulated Shell Structure on the Shaking Table

Spherical reticulated shell structure is an important structural form of large-span space buildings. It is of great significance to monitor three-dimensional (3D) dynamic responses of spherical reticulated shell structure to better understand its seismic performances, which will be helpful in the future to ensure the healthy condition of large-span space buildings during their lifespan. In this study, with the advantages of non-contact and high accuracy, a high-speed videogrammetric measurement method is proposed for monitoring the 3D dynamic responses of the seismically isolated, spherical, reticulated shell structural model. Two issues—the high-speed videogrammetric acquisition system and network configuration, as well as image sequence target tracking and positioning—are emphasized to achieve a cache of high-speed images and to improve the accuracy of tracking and positioning target points. The experimental results on the shaking table from the proposed method have been compared with those from traditional Optotrak Certus and accelerometers. The results prove that the proposed method is capable and useful for analyzing the seismic performance of spherical reticulated shell structures, as the dynamic responses monitoring accuracy of the method can reach the submillimeter level, with root mean square error values of 0.32 mm, 0.7 mm and 0.06 mm in the X, Y and Z directions, respectively.

Numerical investigation of the contribution of metallic dowels to the stability of multi-drum columns

Remnants of Greek Temples are found all over the Mediterranean, surviving in most cases in the form of free-standing columns. In many cases the drums are placed on top of each other without any connection, whereas in some cases there exist metallic dowels between the drums. The aim of this work is to investigate the contribution of these dowels to the overall stability of multi-drum columns. For that, the paper studies numerically the complex 3D dynamic response of multi-drum columns with dowels between the drums, by using the FE code MARC. The studied columns are part of the colonnade system of the ancient Messene Gymnasium in Greece. In the 3D models, which are based on archaeological data, special attention is given to the modelling of the metallic dowels which were used to connect adjacent drums. The columns are subjected to sinusoidal base excitations having different acceleration amplitudes and different frequencies.

3D structure-soil-structure interaction in an arbitrary layered half-space

The aim of the study is to evaluate the 3D dynamic response of a finite geological region containing two structures and rested on a semi-infinite elastic layered half-space with a dynamic source radiating transient waves. The hybrid modelling approach is applied. It is based on the decomposition of the whole domain under consideration into two sub-regions: a finite-sized near-field elastic isotropic zone with two containment structures and the open semi-infinite far-field layered region. The far-field zone is a semi-infinite elastic isotropic arbitrary layered medium where the near-field finite geological region is located on. The 3D hybrid computational tool is based on the boundary element method (BEM) for the far-field layered zone and the finite element method (FEM) for the finite near-field domain. The model for the semi-infinite layered zone is further extended by the incorporation of a new condensation algorithm which makes it possible to handle 3D wave propagation through arbitrary layered half-space. The condensation algorithm is developed to avoid high computational memory cost while retaining the compatibility with the hybrid FEM-hosted procedure which facilitates the useful solution for the practical three-dimensional engineering problems. The BEM model of the dynamically active far-field zone is inserted as a macro-finite element (MFE) in the FEM commercial program ABAQUS. The accuracy and convergence study of the hybrid numerical scheme is presented. Numerical simulations convincingly illustrate that the dynamic response of structure-soil-structure system depends on different key factors and their mutual interplay. These factors are arbitrary layering of the far-field geological zone, the characteristics of the dynamic source, the site effects phenomena, the structure-soil-structure dynamic interaction, the type and geometrical disposition of foundations and structures and the 3D features of the dynamic motion.

Characterizing dynamic deformation of marine propeller blades with stroboscopic stereo digital image correlation

Stereo digital image correlation (stereo-DIC) technique shows a powerful capacity on full-field three-dimensional (3D) deformation measurement of rotary machine structures. However, it remains a challenge for underwater applications due to difficulties in imaging, stereo calibration, light refraction, and so on. In this paper, its potential in characterizing 3D dynamic deformation of the underwater rotor blades is shown by solving these problems. A stroboscopic stereo-DIC system is established to capture clear speckle images of a blade that rotates in the windowed cavitation tunnel under different flow speeds. To calibrate the stereo camera for underwater object measurement, an improved planar pattern-based calibration method and a globally optimal relative pose estimation algorithm are proposed to calibrate the intrinsic and extrinsic parameters of the stereo-DIC system separately. In particular, a novel refractive 3D reconstruction method for underwater objects is presented to recover the true 3D shape according to flat refraction geometry, ensuring the correctness and reliability of the measured 3D displacement fields. Several experiments demonstrated that the proposed stereo-DIC system and methods are feasible and accurate. Based on this, the measured dynamic displacement fields of a propeller blade are presented and discussed. Results herald a possibility for monitoring the full-field 3D dynamic response and structural health of underwater rotating structures by the proposed technique.

Structural health monitoring and seismic response assessment of bridge structures using target-tracking digital image correlation

Our nation’s infrastructure is aging and deteriorating which increases the need for condition assessment and structural health monitoring. For this purpose, there is a growing interest in using non-contact monitoring methods because of the challenges associated with deploying and installing conventional instrumentation. Target-tracking digital image correlation (DIC) is among these methods and is the focus of this paper. Several research activities have been conducted at the University of Nevada, Reno in the field of dynamic monitoring using DIC and presented here. The first part of the paper is concerned with a large-scale laboratory application where target-tracking DIC was utilized to monitor the response of a bridge structure tested under bidirectional earthquake shaking. The 3D dynamic response of the bridge, along with modal properties, i.e. natural frequency, damping ratio, and mode shapes, were measured or determined using both DIC and conventional instrumentation then compared for validation purposes. The second part of the paper presents results from field monitoring of an actual footbridge under pedestrian loading to determine the vibration frequencies of the bridge, and again compare it against results from conventional accelerometers for validation. From both applications, the DIC is demonstrated to successfully capture (1) peak and residual bridge deck rotation and deformation under different earthquake intensity levels and (2) modal properties for system identification. Practical DIC sampling rates were used to accurately monitor and capture the dynamic response of bridges, which shows a high potential for using DIC for larger structural health monitoring applications and future reconnaissance works.

Analysis of the Rayleigh wave field due to a tangential load applied on the surface of a coated elastic half-space

The paper deals with 3D dynamic response of a coated elastic half space subject to in-plane surface loading. The problem is formulated by a pair of elliptic equations over the interior and a two dimensional singularly perturbed hyperbolic equation expressed in terms of shear wave potentials along the interface. As an example, a point force acting one of the in-plane axis is considered and the integral solution of the normal displacement along the interface is derived through the use of the relation between the wave potentials.

Crack front waves: A 3D dynamic response to a local perturbation of tensile and shear cracks

Crack front waves are long-lived perturbations propagating along the crack front. They are triggered by heterogeneities on the crack plane, as for instance tough asperities, which disturb the crack front shape. Crack front waves are thought to leave a trace on fracture surfaces, and are important elements for post mortem analysis. This paper presents a numerical analysis of crack front waves for tensile and shear cracks in the subsonic regime. The elastodynamics calculations are conducted with a boundary integral method. They reveal that the propagation velocity of these waves is independent of the fracture mode. Moreover, using a Lorentz transformation, we demonstrate that their speed is constant within the crack front moving frame, with a value slightly lower than the Rayleigh wave speed. Finally, we shed a new light on how, in response to the interaction with an asperity of prescribed size and toughness contrast, these waves select a localized perturbation in the velocity profile of characteristic shape, width and amplitude.

3D dynamic responses of a multi-layered transversely isotropic saturated half-space under concentrated forces and pore pressure

Dynamic Green's function plays an important role in the study of various wave radiation, scattering and soil-structure interaction problems. However, little research has been done on the response of transversely isotropic saturated layered media. In this paper, the 3D dynamic responses of a multi-layered transversely isotropic saturated half-space subjected to concentrated forces and pore pressure are investigated. First, utilizing Fourier expansion in circumferential direction accompanied by Hankel integral transform in radial direction, the wave equations for transversely isotropic saturated medium in cylindrical coordinate system are solved. Next, with the aid of the exact dynamic stiffness matrix for in-plane and out-of-plane motions, the solutions for multi-layered transversely isotropic saturated half-space under concentrated forces and pore pressure are obtained by direct stiffness method. A FORTRAN computer code is developed to achieve numerical evaluation of the proposed method, and its accuracy is validated through comparison with existing solutions that are special cases of the more general problems addressed. In addition, selected numerical results for a homogeneous and a layered material model are performed to illustrate the effects of material anisotropy, load frequency, drainage condition and layering on the dynamic responses. The presented solutions form a complete set of Green's functions for concentrated forces (including horizontal load in x(y)-direction, vertical load in z-direction) as well as pore pressure, which lays the foundation for further exploring wave propagation of complex local site in a layered transversely isotropic saturated half-space by using the BEMs.

Dynamic analysis of layered systems under a moving harmonic rectangular load based on the spectral element method

In order to design high-performance roadways, a robust tool which can compute the structural response caused by moving vehicles is necessary. Therefore, this paper proposes a spectral element method-based model to accurately and effectively predict the 3D dynamic response of layered systems under a moving load. A layer spectral element and a semi-infinite spectral element are developed to respectively model a layer and a half-space, and the combinations of these two elements can simulate layered systems. The detailed mathematical derivation and numerical validation of the proposed model are included. Additionally, this model is used to investigate the dynamic characteristics of a pavement structure under a moving harmonic rectangular load. The results show that the proposed model can accurately predict the dynamic response of layered systems caused by a moving load. It is also found that the vertical displacement amplitude curves of surface points caused by a moving harmonic load are asymmetric along the moving direction, and this property is more dominant at higher velocities. In addition, the amplitudes of these vertical displacements are smaller if the loading frequency is higher or the loss factor is bigger. Finally, the loading area and Poisson's ratio only have effect on the displacement amplitudes of points in the close vicinity of the loading area. The proposed model is beneficial to the development of engineering methods for pavement design and is a promising parameter back-calculation engine for pavement quality evaluation.

3D dynamic responses of a 2D hill in a layered half-space subjected to obliquely incident plane P-, SV- and SH-waves

An indirect boundary element method (IBEM) is proposed to investigate the three-dimensional (3D) dynamic responses of a two-dimensional (2D) hill in a layered elastic half-space subjected to obliquely incident plane P-, SV-, and SH-waves. The proposed IBEM is characterized by adopting the full-space Green's function of moving distributed loads to construct the scattered field in the closed regions, while using the half-space Green's function of moving distributed loads to simulate the scattered field in the opened half-space region. This new method thus combines the merits of these two Green's function and is especially suitable for addressing 2.5D multi-domain coupled multilayered wave scattering problems with the advantages of singularity-free, low computational cost and flexibility. The accuracy and validity of the method is verified by comparing its results with a number of existing solutions. Numerical calculations are performed by taking semi-circular as well as semi-elliptical hills as examples, and the effects of the hill height, frequency of excitation, incident angle, and layering on the dynamic responses are analyzed in detail. It is found that the proposed method can treat the oblate as well as prolate hills, which demonstrate that the new IBEM has good adaptability to the shape of hills. In addition, numerical results show that significant focusing effects and standing-wave patterns are formed inside the hills under incident plane waves; the presence of the hill amplifies the ground motion significantly, which is highly related to the hill height, frequency of excitation, incident angle and dynamic characteristics of the site; And there exist pronounced dynamic interaction between the hill and the layer, which leads to the much more complex topographic effects.

Experimental and numerical investigation on the dynamic response of steel chamber under internal blast

The present work aims at investigating the dynamic response of steel chamber under internal blast loading through both experiments and numerical simulations. In the experiment, digital image correlation (DIC) technique is applied to record the three-dimensional (3D) displacement and dynamic response process. A series of steel chamber specimens with different size were designed to conduct internal blast tests, and then numerical models were built by using ANSYS/LS-DYNA. The 3D deformation features were analyzed through both experimental and numerical results. The results show that outward bulging occurs in all side plates and in-plane buckling takes place in all boundary plates. Furthermore, plastic hinge lines along the two diagonals of the target side plate are observed. In addition, 3D dynamic response processes were analyzed through both the DIC technique and numerical results. “Five mountains” deformation shape was observed during the response process because of the confinement of chamber corner to the blast wave. The dynamic response results indicate that the response process of the side plate includes two stages: the whole plate plastic response stage and the central area oscillating stage. In a word, the results confirm that DIC technique is capable of accurately measuring full-field dynamic response of structures under blast loading, and the numerical method established in the present study is efficient and effective in modeling dynamic problems.

3D dynamic response of a transversely isotropic multilayered medium subjected to a moving load

SummaryThe dynamic problem of a transversely isotropic multilayered medium is reducible to quasi‐static problem by introducing a moving system that travels synchronously with the load. Based on the governing equations in the moving system, the ordinary differential equations in the Fourier transformed domain are deduced. An extended precise integration method is adopted to solve the ordinary differential equations, and the solution in the physical domain is recovered by the inverse Fourier transform. Numerical examples are performed to verify the accuracy of the presented method and to analyze the influence of material properties and the load characteristic.

3D dynamic response of a multi-layered transversely isotropic half-space subjected to a moving point load along a horizontal straight line with constant speed

The steady-state dynamic response of a multi-layered transversely isotropic (TI) half-space generated by a point load moving along a horizontal straight line with constant speed is investigated in this paper. To solve this problem, the direct stiffness method combined with the inverse Fourier transform is employed. First, the dynamic equilibrium equations for the TI medium are solved in the frequency and wavenumber domains and the exact three-dimensional (3D) dynamic stiffness matrix for the layered TI half-space is established. Then, the solution in the frequency and wavenumber domains is obtained through the direct stiffness method. Finally, the dynamic response in the time and space domains is obtained using the double inverse Fourier transform with respect to the frequency and one horizontal wavenumber. The accuracy of the method is verified through comparisons with the results for the limiting isotropic case (de Barros and Luco, 1994) as well as the results for the non-moving 3D point load being applied in a multi-layered TI half-space (Khojasteh et al., 2011). Numerical results for both the uniform TI half-space and multi-layered TI half-space are presented, and the effects of the moving speed and especially the material anisotropy on the dynamic response are analyzed. Numerical results show that the dynamic response in a TI medium can be significantly different from that in an isotropic medium, and material anisotropy is very important for the accurate assessment of the dynamic response due to a point load moving in a TI half-space.

An exact solution for three-dimensional (3D) dynamic response of a cylindrical lined tunnel in saturated soil to an internal blast load

The dynamic response of tunnel under internal explosion in reality is a three dimensional geotechnical problem, however, it is often simplified as a plane strain problem in 2D model which can only deal with the dynamic responses of tunnel at the source of explosion. This note proposes a set of exact solutions for three-dimensional (3D) dynamic responses of a cylindrical lined tunnel in saturated soil due to internal blast loading are derived by using Fourier transform and Laplace transform. The surrounding soil is modeled as a saturated medium on the basis of Biot's theory and the lining structure modeled as an elastic medium. By utilizing a reliable and efficient numerical method of inverse Laplace transform and Fourier transform, the numerical solutions for the dynamic response of the lining and surrounding soil are obtained. The 3D dynamic responses of the lined tunnel and the surrounding saturated soil medium due to internal blast loading are then presented and discussed. The results demonstrate that the proposed solutions can help to evaluate the damage of the explosion to surrounding areas of the tunnel in 3D condition at any given elapsed time apart from the section at the source of explosion.

3D scattering of obliquely incident plane SV waves by an alluvial valley embedded in a fluid-saturated, poroelastic layered half-space

The indirect boundary element method is used to study the 3D dynamic response of an infinitely long alluvial valley embedded in a saturated layered half-space for obliquely incident SV waves. A wave-number transform is first applied along the valley’s axis to reduce a 3D problem to a 2D plane strain problem. The problem is then solved in the section perpendicular to the axis of the valley. Finally, the 3D dynamic responses of the valley are obtained by an inverse wave-number transform. The validity of the method is confirmed by comparison with relevant results. The differences between the responses around the valley embedded in dry and in saturated poroelastic medium are studied, and the effects of drainage conditions, porosity, soil layer stiffness, and soil layer thickness on the dynamic response are discussed in detail resulting in some conclusions.

On a 3D moving load problem for an elastic half space

The paper deals with 3D dynamic response of an elastic half-space loaded by a point force moving at a constant speed along a straight line on the surface. The problem is formulated within the framework of the asymptotic hyperbolic–elliptic model developed earlier by two of the authors. The validity of the model is restricted to the range of speeds close to the Rayleigh wave speed. Steady-state near-field solutions are derived in terms of elementary functions. Transient analysis of surface motion illustrates peculiarities of the resonance associated with the Rayleigh wave.

Analysis of 3D Dynamic Response for TC4 Blades by the FEM

TC4 blades are one of the major parts of the aero engine, and the examples of engine invalid and even wrecked are common. In this paper, a 3D analysis system of the vibration behaviors of the TC4 blades is given. The 3D analysis model of blade was described using 20 nodes elements. The finite element procedure was worked out using the blade vibration behaviors analysis of the aero engine. At last, the modal shapes and stress nephograms of the first six frequencies are gotten which influenced the blade vibration characteristics. Results show that the program has offered an effective, flexible research means for analyzing dynamic response of TC4 blades.

Feasibility of monitoring large wind turbines using photogrammetry

Abstract Photogrammetry, which is a proven measurement technique based on determination of the 3D coordinates of the points on an object by using two or more images taken from different positions, is proposed to be a promising and cost efficient alternative for monitoring the dynamic behavior of wind turbines. The pros and cons of utilizing this measurement technique for several applications such as dynamic testing or health monitoring of large wind turbines are discussed by presenting the results of the infield tests performed on a 2.5 MW - 80 m diameter - wind turbine. Within the scope of the work, the 3D dynamic response of the rotor is captured at 33 different locations simultaneously by using 4 CCD (charge coupled device) cameras while the turbine is rotating. Initial results show that the deformations on the turbine can be measured with an average accuracy of ±25 mm from a measurement distance of 220 m. Preliminary analyses of the measurements also show that some of the important turbine modes can be identified from photogrammetric measurement data.