Deflection Components Research Articles

Predicting bathymetry using multisource differential marine geodetic data with multilayer perceptron neural network

ABSTRACT We propose a method for enhancing the accuracy of bathymetry models based on a multilayer perceptron (MLP) neural network that integrates the differences in multisource marine geodetic data (MMGD) (longitude, latitude, reference bathymetry, slope, the meridional and prime components of vertical deflection, gravity anomaly, vertical gravity gradient, and mean dynamic topography). First, we use the MMGD differences between the shipborne sounding control points within 8′ × 8′ grid points and shipborne sounding control points as input data, as well as the differences between the topo_24.1 model and the measured bathymetric values at the control points as output data to train the MLP model. Second, we feed the input data from the central point of a 1′ × 1′ grid into the MLP model to obtain predictions, and then use the topo_24.1 model to recover the predicted bathymetry at the prediction point. We focus on the Caribbean Sea, and construct a Caribbean Bathymetric Chart of the Oceans (CBCO1) model using MLP neural network. The reliability of MMGD, a CBCO2 model using MMGD, and the reliability and effectiveness of the overall method are demonstrated through comparisons with the CBCO2, GEBCO_2022, topo_24.1, DTU18 models at the checkpoints.

NAVIER SOLUTION FOR DEFLECTION AND STRESSES ANALYSIS OF FGM SANDWICH PLATE RESTING ON PASTERNAK ELASTIC FOUNDATION

In this article, the first-order shear deformation theory (FSDT) and Navier’s solution are used to establish analytical solutions for analyzing the deflection and stresses of FGM sandwich plate structures resting on a Pasternak elastic foundation. The top and bottom layers consist of functionally graded materials (P-FGM) that vary according to the exponential law along the thickness direction, while the core layer is composed of a porous material. The boundary condition of the plate is simply supported on all the edges, and the plate is subjected to a sinusoidal distributed load perpendicular to the mid-surface. The reliability of the model is validated through comparison with findings published in reputable journals. The effects of material parameters, geometric dimensions, foundation coefficients, and face-core-face thickness ratios on deflection and stress components of rectangular FGM sandwich plates are investigated in detail in parametric studies.

A new C0 continuous refined zigzag {1,2} finite element formulation for flexural and free vibration analyses of laminated composite beams

This study presents a novel C0 continuous refined zigzag finite element formulation {1,2}, namely RZE{1,2}, for the bending and free vibration analyses of laminated composite beams. The Refined Zigzag Theory (RZT) effectively combines accuracy and computational efficiency, making it a robust approach for thin and thick laminated composite structures. The RZT eliminates the need for shear correction factors, thereby enhancing the overall streamline of the analysis process. The present RZE{1,2} formulation takes into account the transverse stretching by introducing quadratic through-thickness variations of deflection components. The governing equations of the RZT are derived by means of Hamilton’s principle. The through-the-thickness variations of the transverse shear and normal stresses are calculated by integrating the stress equilibrium equations in a post-processing step. Therefore, the Peridynamic Least Squares Minimization (PDLSM) approach is utilized to obtain precise derivatives of axial stresses in the stress equilibrium equations. A new finite element formulation is built up with 3-nodes with a total of 15 DOF. In order to study the influence of transverse stretching, different types of boundary conditions and material variations are applied for laminated composite beams for the bending and free vibration analyses. The distribution of displacements as well as the axial and transverse stresses of the thick beams are extensively examined. The outcomes of RZT are in good agreement with the reference solutions in the literature. The findings of the present study reveal that the presence of the transverse stretching produces more realistic predictions for thick beams where the shear deformations are influential.

Preliminary Results of Marine Gravity Recovery by Tiangong-2 Interferometric Imaging Radar Altimeter

This paper presents for the first time the results of marine gravity recovery using the ocean observation data acquired by Tiangong-2 interferometric imaging radar altimeter (TG2 InIRA) which demonstrate not only the balanced accuracies of the north and east components of deflection of the vertical (DOV) as envisaged, but also the improved spatial resolutions of DOV compared with that by conventional altimeters (CAs). Moreover, much higher measurement efficiency owing to the wide-swath capability and the great potential in accuracy improvement of marine gravity field are also demonstrated. TG2 InIRA adopts the interferometry with short baseline and takes small incidence angles, by which wide-swath sea surface height (SSH) can be measured with high accuracy. Gravity recovery experiments in the Western Pacific area are conducted to demonstrate the performance, advantages and capability of TG2 InIRA. SSH data processing algorithms and DOV calculation have been designed by taking the wide-swath feature into account, based on which, the gravity anomalies are then calculated using the inverse Vening Meinesz formula. The derived gravity anomalies are compared with both the published gravity models and the shipborne gravity measurements. The results show that the accuracy of TG2 InIRA is equivalent to, or even a little better than, that of CAs. The fused gravity result using equal TG2 InIRA data and CAs data performs better than those using TG2 InIRA data alone or CAs data alone. Due to the signal bandwidth of TG2 InIRA is only 40 MHz which is much smaller than that of CAs, much higher accuracy can be hopefully achieved for future missions if larger signal bandwidth is used.

Free Vibration of Rectangular Composite Cantilever Plate and Its Application in Material Degradation Assessment

Many composite cantilever plate-like structures have found engineering applications in different industries. For attaining a meaningful assessment of the plate vibration characteristics, it is important to have efficient and effective methods for determining the natural frequencies/mode shapes of composite cantilever plates. In this paper, a method formulated on the basis of the Ritz method and a simple first-order shear deformation theory (SFSDT) is presented to analyze the free vibration of thin as well as thick rectangular composite cantilever plates for determining their natural frequencies. In the SFSDT, the total deflection is the sum of two deflection components, namely, bending and through-thickness shear-deformation-induced deflections. The successful application of the Ritz method together with the SFSDT for the free vibration analysis of thick composite plates relies on the selection of two independent sets of characteristic functions for the bending and through-thickness shear-deformation-induced deflections, respectively, to satisfy the requirements for the displacement and force conditions at the fixed edge of the plate. The novelty of the proposed method is that two independent sets of characteristic functions, namely, polynomials and trigonometric functions, which satisfy the displacement and force conditions at the fixed edge have been identified and used in the variational method to construct the eigenvalue problem for extracting the modal characteristics (natural frequencies and mode shapes) of the plate. It has been shown that the uses of the selected characteristic functions can produce excellent natural frequencies for both thin and thick composite cantilever plates. Some existing theoretical and experimental natural frequencies of thin as well as thick composite plates have been used to demonstrate the accuracy of the proposed method in predicting natural frequencies. The significant effects of through-thickness shear deformation on the natural frequencies of composite cantilever plates are studied to show the merit of the present method. Finally, for illustrating the application of the proposed method in free vibration analysis, a novel procedure established on the basis of the sensitivity analysis of natural frequencies is presented to assess the material degradation of composite cantilever plates. The numerical examples have shown that fewer than 10 iterations are required in the identification process to produce a good estimation of the current value for each material constant.

Experimental investigations of wave interaction with semi-submerged horizontal rectangular cylinder of elastic bottom

Laboratory experiments were conducted to investigate the interaction of gravity waves with a semi-submerged rectangular cylinder of elastic bottom. Laboratory investigations were conducted for a wide range of wave parameters and a structure of different drafts. The analysis of results focuses on wave transmission at the structure, wave-induced pressures excreted on the plate, plate deflections, etc. The results shows that the nonlinear pressure and plate deflection components arising from the interaction of incoming waves with the structure are often significant. The results show that the nonlinear components often exceed their linear counterparts even for waves of low steepness. This is an original and surprising outcome of significant practical importance as the large nonlinear pressure and plate deflection components may spark a resonance. The problem is serious because plate natural vibration frequencies are often lower than the frequency of fundamental waves or their nonlinear components and the vibration of a plate may be amplified by incoming waves or their nonlinear products. The occurrence of a resonance amplified by incoming waves may lead to the failure of a structure. This outcome is of significant practical importance because it may occur for a wide range of wave parameters.

Drive-By Fleet Monitoring to Detect Bearing Damage in Bridges Using a Moving Reference Influence Function

This paper introduces a new bridge damage indicator, the moving reference influence function (MRIF), to detect bridge bearing damage using deflections inferred from vehicle accelerations. Recently, vehicle acceleration has been used to find the apparent profile (AP) of a bridge when a vehicle passes. This AP consists of bridge profile elevations and bridge deflection components. To describe the relationship between these deflection components and load, a MRIF is proposed for the first time in this paper. An error minimization process is used to find the MRIF and the road surface profile on the bridge. The vehicle acceleration signals used in the paper are assumed to be collected from a partially instrumented vehicle fleet. In the fleet, only the first axle acceleration is collected from each vehicle. To simplify the minimization process, both the MRIF and the bridge profile are represented by kernel density functions. The results show that the bridge profile can be accurately obtained and that bridge bearing damage can be identified from the MRIF. Both area and skewness of the MRIF are damage sensitive and can be used together to find the location and severity of bridge bearing damage.

Reference Point-Free Measurement of Bridge Dynamic Deflection by Fusing Hydraulic Leveling and Accelerometer Signals

Structural health monitoring (SHM) is widely applied to assess the service condition of bridges. Deflection measurements are essential to determine a bridge’s performance, and in particular, dynamic deflection is increasingly required in SHM. However, continuous and high-precision measurements of the absolute dynamic deflection are challenging without a reference point placed at a distance from the bridge. We proposed a reference point-free dynamic deflection measurement system consisting of a level sensor and an accelerometer. The level sensor measures the low-frequency deflection components, while the accelerometer measures the high-frequency deflection components. We redesigned the level sensor from the hydrostatic level sensor and further provided a correction method to achieve the dynamic deflection measurement. A numerical algorithm fuses the signals from the level sensor and accelerometer to obtain the absolute dynamic deflection, and key parameters are calculated. The accuracy of the measurement system was tested in the laboratory, and the sensor results were similar to the ones obtained by the laser test under simple harmonic and random excitations. Field tests conducted on a T-shaped rigid frame bridge with random traffic flow indicate that the system can achieve continuous high-precision deflection measurements of bridges loaded by traffic flow.

The effects of two temperature and laser pulse on modified couple stress thermoelastic diffusion beam

In this work, we studied the problem of thermoelastic diffusion beams on the basis of modified couple stress theory under the effects of two temperature and laser pulse. The Euler-Bernoulli beam theory and the Laplace transform technique are applied to solve the basic equations of thermoelastic diffusion in the non-dimensional form. The transformed components of displacement, lateral deflection, axial stress, temperature change, concentration, and chemical potential are calculated mathematically to solve the problem. Copper material is used to prepare the mathematical model. The general algorithm of the inverse Laplace transform technique has been calculated numerically. MATLAB software is used to find the results numerically and depict them graphically. The effects of two temperature, laser pulse, and couple stress are presented graphically on the physical quantities. Particular cases are also discussed in the present problem. Laser pulse has many applications in Heat treatment, cutting of plastics, glasses, ceramics, semiconductors and metals, surgery, Lithography, and welding.

Some features of flat fiberglass specimens’ behavior under three-point bending

The authors carried out the experimental works devoted to the problem of describing the processes occurring under long-term loading of composite materials. They studied a glass-reinforced plastic (GP) flat specimen under three-point bending and assumed the deformations normal to the section are purely elastic, and the transverse shear deformation consists of two parts –elastic, and creep deformations and damages formed as a result of accumulation. The authors considered a variant of the creep ratios according to the hardening theory. In previous research authors determined its parameters based on the analysis of the tubular samples operation. It was found that even for thin beams, in contrast to a purely elastic problem, taking into account creep under transverse shear leads to inelastic deflection components that are comparable with their elastic values. The authors presented the results of numerical calculations. It is concluded that at large time and loads, deformations appear in the sample caused by the accumulation of damage.

Correlation model of deflection, vehicle load, and temperature for in‐service bridge using deep learning and structural health monitoring

Deflection is an important issue in bridge structural health monitoring. An accurate deflection–vehicle load–temperature correlation model is critical to abnormal data identification, deflection prediction under extreme conditions, and bridge structural assessment. However, because of the discrete distribution in time domain of vehicle load and the extreme complexity of the deflection–vehicle load–temperature correlation, the correlation modeling method needs further studies. A novel deflection–vehicle load–temperature correlation modeling method is developed in this study. Based on the concept of deflection influence line (DIL), the raw vehicle load monitoring data are transformed into time-continuous vehicle influence coefficient (VIC). By using gated recurrent unit (GRU) neural network, a correlation model with inputs of VIC and environmental temperature data and output of deflection data is established. Taking a suspension bridge in China as an example, the prediction accuracy of short-, medium-, and long-term correlation models is tested. Moreover, based on the correlation model, a decomposition method of temperature- and vehicle-induced deflection components is proposed. The results show that the predicted deflection of the short-term correlation model is basically consistent with the real-time monitoring data, while the medium- and long-term correlation models have accurate prediction ability for the deflection extreme values in a certain time window. The temperature- and vehicle-induced deflection components separated by using the correlation model are in good agreement with the wavelet decomposition (WD) results, with clear physical meaning and independent of empirical judgment.

Development of a Lightweight Inertial Gravimeter for Use on Board an Autonomous Underwater Vehicle: Measurement Principle, System Design and Sea Trial Mission

The purpose of this paper is to present the design, development and testing of an innovative instrument called GraviMob, which allows performing dynamic measurements of underwater gravity anomalies. After recalling the interest in underwater gravimetry, we describe the system, the core of which consists of triads of accelerometers rigidly attached to an Autonomous Underwater Vehicle (AUV). The article also presents the mathematical methods for estimating the east, north and vertical components of the local gravity vector. An unscented Kalman filter, integrating AUV position and orientation data, performs estimation of gravity in a frame adapted to its interpretation. To assess its performance, GraviMob was tested in the Mediterranean Sea during the year 2016. A comparison of the surface gravimetric signal previously acquired by the French Navy indicates that the maximum discrepancy between the vertical gravity component and its reference is below 4 mGal. Components of the vertical deflection calculated from GraviMob’s measurements were compared with those calculated from recent gravity field models. While a remarkable agreement was found on the north component, there remains a discrepancy (7 arcsec) on the east component which can be largely reduced by refining the estimation of the orientation of GraviMob’s sensitive axes in the AUV.

Railway Bridge Condition Monitoring Using Numerically Calculated Responses from Batches of Trains

This study introduces a novel method to determine apparent profile of the track and detect railway bridge condition using sensors on in-service trains. The concept uses a type of Inverse Newmark-β integration scheme on data from a batch of trains. In a self-calibration process, an optimization algorithm is used to find vehicle dynamic properties and speed. For bridge health monitoring, the apparent profile of the bridge is first determined, i.e., the true profile plus components of ballast and bridge deflection under the moving train. The apparent profile is used, in turn, to calculate the moving reference deflection influence line, i.e., the deflection due to a moving (static) unit load. The moving reference influence line is shown to be a good indicator of bridge stiffness. This numerical approach is assessed using an elaborate finite element model operated by an independent research group. The results show that the moving reference influence line can be found accurately and that it constitutes an effective indicator of the condition of a bridge.

Bathymetry inversion using the deflection of the vertical: A case study in South China Sea

The deflection of the vertical is one of the essential products of altimetry. However, unlike gravity and vertical gravity gradients, it is seldom used in bathymetry inversion. In this study, an algorithm for bathymetry inversion using the deflection of the vertical is proposed. First, we separately derive the formulas for the bathymetry inversion from the north and east components of the vertical deflection and introduce the data processing. Then a local area in the South China Sea is selected as an example to test the method. The bathymetry inversion based on gravity anomaly is also conducted for comparison. Assuming the ship-borne depths are the true values, the error standard deviations (STDs) of the bathymetry derived by north and east components of the vertical deflection are 156.64 m and 165.57 m, respectively. It indicates that the north component has a better performance in bathymetry inversion than the east component. The inversion results from the combination of both components show a higher accuracy of bathymetry than that from a single component. The difference between the error STD of the combination results and that of the gravity anomaly is less than 0.2 m. The experiment's results also show that the precision of the derived bathymetry can be improved if the parameters of linear regression are adjusted according to water depths. In summary, among the gravity field products used in this study, the gravity anomaly yielded the best performance in the bathymetry inversion. However, since additional data and computation time are required to derive gravity anomalies from altimetric observations, the vertical defections can still be used as supplements, especially in areas where accurate vertical deflections exist.

A series of elasticity solutions for flexural responses of functionally graded annular sector plates

This paper aims at investigating the flexural responses of transversely isotropic functionally graded (FG) annular sector plates subjected to biharmonic loads, where the material parameters are assumed to vary arbitrarily along the thickness direction and the cylindrical boundaries is simply supported at the two radial edges and arbitrary at the two circumferential edges. Based on the extended England-Spencer plate theory, a series of analytical solutions to FG annular sector plates are derived by virtue of the mid-plane displacements of the plate, which can be expressed by four analytic functions of the complex variable, and the corresponding unknown constants can be determined by the boundary conditions at two circumferential edges. In order to validate the proposed analytical solutions, a finite element (FE) model is built to obtain numerical solutions for comparison, which shows that the obtained deflection and stress components are coherent with those from the FE results. Furthermore, two typical biharmonic loads are taken in the numerical examples to discuss the effects of material gradient index, boundary conditions and thickness-to-radius ratio on the flexural responses of the plate in detail. This work gives exact 3D analytical solutions for the FG annular sector plates, which not only provide an in-depth understanding of their mechanical behaviors and a new theoretical route for the analysis of engineering structures, but also serve as benchmark to check analytical solutions based on any simplified plate theories or numerical solutions to the same problem.

Triangular C0 continuous finite elements based on refined zigzag theory {2,2} for free and forced vibration analyses of laminated plates

This study presents a finite element formulation to perform vibration analysis of laminated composite plates based on the Refined Zigzag Theory of order {2,2}, namely RZT-{2,2}. This theory considers the transverse stretching by introducing quadratic through-thickness variations of both in-plane and transverse displacement components. Also, it eliminates the use of shear correction factors and is highly suitable for the analyses of thick and heterogeneous laminated plates. The governing equations of the RZT-{2,2} are derived based on Hamilton’s principle. The stiffness matrix, consistent mass matrix, and load vector of the governing equations are constructed by adopting anisoparametric interpolation functions associated with a triangular element that involves three corner nodes and three mid-side nodes along its edges. The corner nodes consist of eleven kinematic variables while each mid-side node possesses only three deflection components. An adaptive time-stepping algorithm is employed with an optimum time increment determined automatically at each time step, thus, eliminating the stability concerns. The capability of the present approach is demonstrated by considering several benchmark cases regarding free vibration analysis. The effect of transverse stretching is revealed through the dynamic characteristics of the laminated composite plates. In the case of forced vibration analysis, the accuracy of the present approach is established through comparison with three-dimensional finite element models.

Результаты сравнения астрономо-геодезического и навигационно-геодезического методов определения составляющих уклонения отвесной линии

The authors present the results of comparing the components of deflection of vertical obtained through astronomical-geodetic and navigational-geodetic methods. The first one is based on comparing astronomical and geodetic coordinates of a location. This method has recently been widely implemented in a digital zenith camera systems using a small-sized digital telescope with an astronomical camera based on CCD or CMOS technologies, a high-precision inclinometer and satellite navigation system receiver. In this case, the combination of a telescope, an astronomical camera and an inclinometer enables determining the local direction of the plumb line, expressed by astronomical coordinates, from observations of stars at the zenith and using high-precision star catalogs. The navigational-geodetic method is based on comparing the results of the normal heights’ increments, defined through geometric leveling, and geodetic heights, computed with the relative method of satellite coordinate determinations. For each method, random and systematic components of the error and its confidence bounds were calculated; the absolute values of the deflection of vertical components at two geographically separated points were compared.

The fractal behaviour of gravity field elements: case study in Egypt

ABSTRACT The fractal behaviour of gravity field elements was investigated. Particularly, the geoidal heights, gravity anomalies and vertical deflection components were considered. Such data were synthesized from the ultra-high degree SGG-UGM-1 geopotential model. The Egyptian Territory was selected as the study area. To supplement the results, parallel fractal analyses were performed on the GTM3A, Earth2012 and SRTM30 terrain data. The regularization, variogram and global Power Spectral Density (PSD) concepts were applied as different tools for fractal analysis. Consistent fractal dimensions resulted from the regularization and variogram algorithms. These two algorithms ensured the fractalness of the gravitational signals, including the geoidal height. The global PSD algorithm failed to give meaningful fractal dimensions for the topography and geoidal heights. However, it yielded realistic dimensions for the other elements. So, fractal dimensions could characterize the roughness and spatial precisions of different gravitational data. Also, multifractal modeling of the geopotential might be a promising task.

Estimation the components of deflection of the vertical for a point in Baghdad City - Iraq

In the age of the satellite geodesy, the GNSS is widely used in development of geodetic networks and that give much application, for that reason the study is to estimate deflection of the vertical of a point in Baghdad City in Iraq, the estimated depends on the orthometric height, which computed through the levelling and the ellipsoidal height, which computed from the GPS observations. Due to the lack of survey data and the difficulty of taking terrestrial measurements as a result of the security situation the authors used only 5 points for the national network in Baghdad. The deflection of the vertical component component ξ in the north-south direction calculated as ξ=2.5”±0.001” and the prime vertical component η in the east-west direction calculated as η=5.23” ±1.5”. The results were obtained showing that it can calculate the deflection of the vertical at sufficient accuracy.

ANALYSIS OF HYGRO-MECHANICAL BEHAVIOR OF WOOD IN BENDING

The empirical test developed as validation for a new beam element model that can account for both mechanical and environmental load action in finite element analysis is presented. The testing protocol allows for the identification and analysis of contributing deflection components in bending under varying MC conditions, including mechano-sorption. The components of deflection in the shear-free span of a four-point bending test and their responses to varying moisture are evaluated with an analytical procedure. The experiment was conducted on clear-straight-grained sapwood and heartwood specimens of Norway spruce (Picea Abies)(30 x 15 x 640 mm3). The program consisted of three phases: (1.) long term (LT) experiments under constant temperature of 60oC and relative humidity (RH) cycles between 40% and 80%, (2.) a short term static experiment to determine the variation in the sample set and the load-level of the LT experiment on end-matched specimens, and (3) creep tests at 60o and constant humidity at either 40% or 80% to determine the effect of moisture on the viscoelastic creep. Mass changes and hygro-expansion measured on matched specimens were used in the analytical method. Constitutive models used for describing the material-level response to loads and moisture changes were applied to the shear-free segment of the specimens disregarding actual moisture gradients and fiber orientation inside the test specimens. A successful identification of each deflection component and isolation of mechano-sorption component was accomplished. In the 90 da of testing, the dominant component of the total deflection was the elastic component, followed by the mechano-sorptive component. Creep was found to be nonnegligible and important in the correct description of mechano-sorption. The effect of moisture on the viscoelastic behavior showed most important during loading and first stages of decreasing deflection rate phase.