Nodal Accelerations Research Articles

Seismic Damage Identification Using a Combination of Mixture of Gaussian and Harris Hawks Optimization

ABSTRACTThe present study aims to identify damage in structures using seismic responses and a two‐stage method based on mixture of Gaussian (MOG) and Harris hawks optimization (HHO). Two‐dimensional (2‐D) frame structures under seismic loads are simulated using the finite element method (FEM). The placement of sensors is optimized using a combination of an iterated improved reduced system (IIRS) and the binary differential evolution (BDE) algorithm. The MOG classifier is trained to find the damaged story and damaged element type (i.e., whether it is a beam or a column) using the nodal acceleration responses at the optimal sensor placement of the seismically loaded structure. Thus, as the first step, the possibly damaged elements are located through the classifier. Then, in the second step, the damage is accurately located and quantified by HHO algorithm. The performance of the proposed method is assessed using the numerical results of 2‐D frames of 7 and 14 stories in different damage scenarios with and without considering noise. As a result, the efficiency of the proposed method for the seismic damage identification of 2‐D frames is revealed. Sensor positions are well optimized, and it causes the method to be highly effective. Moreover, MOG correctly finds a damaged story and identifies whether a damaged element is a beam or a column. Damage in the presence of noise is also localized and quantified precisely by HHO.

К РАСЧЕТУ ПЛИТНЫХ АЭРОДРОМНЫХ ПОКРЫТИЙ ПРИ ИХ ВЗАИМОДЕЙСТВИИ С ИНЕРЦИОННОЙ НАГРУЗКОЙ ПРИ ДВИЖЕНИИ В РЕЖИМЕ ТОРМОЖЕНИЯ.

The method of calculating plates under the action of inertial loads during their movement with variable velocity is considered. The problem of the interaction of the airfield surface with the aircraft load is solved, at the moment of its movement, in braking mode, when landing on the surface in the form of an extended rectangular freely operable plate lying on an elastic base. When taking into account the nonlinear contacts of the chassis wheels with the plate, piecewise linear characteristics of contact stiffness are used. The vertical dynamics of the spatial model of the aircraft during the run is modeled by a system of rigid bodies with elastic-viscous bonds. To construct the methodology, the methods proposed earlier by the author of the article are used: a step-by-step method for solving problems of the relentless dynamics of structures and a method for calculating structures for the action of inertial and mobile force loads (the method of nodal accelerations).

A comparative study of geosynthetically reinforced earth foundations in multi-utility transportation infrastructure for high-speed railways

A high-quality railway track resting on an excellent foundation is required to support high-speed railway transportation. The foundations of high-speed railway tracks are generally constructed on the lifted embankment with the improved ground using different reinforcement agents like geosynthetics and rigid lateral support. The present study performed dynamic finite element simulations on a ballasted rail track laid over a geosynthetically reinforced embankment with and without facing wall support. Three foundation geometries were analyzed to examine the effect of facing wall support and geosynthetics on the lateral resistance of the foundation. An area loaded with a constant pressure was moved at a constant speed, causing the load motion at different speeds in the 90–360 km/h range. Different parameters were calculated at node paths to help understand the lateral effect of moving load. The results showed that the lateral resistance based on nodal acceleration and velocity increased with facing wall support in the range of 40%–57%. Any increment over the minimum facing wall thickness of 300 mm does not significantly increase lateral resistance. Geosynthetics provided a vital function in the foundations with a less bulk volume of soil and increased the lateral resistance by 10%.

МЕТОД РАСЧЕТА СТЕРЖНЕВЫХ СИСТЕМ НА ВЗАИМОДЕЙСТВИЕ С ИНЕРЦИОННОЙ НАГРУЗКОЙ ПРИ ПЕРЕМЕННОЙ СКОРОСТИ ДВИЖЕНИЯ

The method of calculating rod systems for interaction with a mobile inertial load at a variable speed of motion using the proposed rod boundary elements (GE) is considered. Test problems on the movement of a load with variable speeds along a pivotally supported beam with its discretization by a set of GE are considered. The problem of movement in the braking mode of a high-speed train on a frame overpass is considered. To construct the methodology, the step method proposed earlier by the author of the article is used to solve problems of unsteady dynamics of structures and the method of calculating structures for the action of mobile force and inertial loads (the method of nodal accelerations).

Shaking table tests on the seismic response of truss structure with air spring‐FPS three‐dimensional isolation bearing

AbstractTo investigate the isolation effect of the friction pendulum system (FPS) horizontal isolation bearing and the air spring‐FPS three‐dimensional (3D) isolation bearing in truss structure and the influences of long‐period ground motions on the isolated structure, the shaking table test of a truss structure is designed and conducted. The ordinary ground motions, near‐fault pulse‐like ground motions, and far‐field long‐period ground motions with different spectral characteristics are chosen to input into the structure, and the dynamic characteristics such as the acceleration, displacement, and stress of the truss are compared and analyzed. The horizontal frequency of the horizontal isolated structure is reduced after the horizontal isolation, while the vertical frequency is further reduced after 3D isolation. The isolation effect of nodal acceleration, nodal displacement, and member stress under 3D isolation is better than that of horizontal isolation, especially the vertical seismic response is significantly improved. When the ground motion intensity is small, the FPS horizontal isolation bearing slides little, and reducing the seismic response of the structure is limited. There is a better isolation effect of 3D isolated structure. The vertical frequency ratio Rf under ordinary ground motions is far away from 1 and close to 3, basically avoiding the main energy segment of the ground motions. The advantage of 3D isolated structure is relatively reduced under long‐period ground motions, which lies in the rich low‐frequency components of long‐period ground motions which are difficult to isolate effectively.

Dynamic response optimization of a thermoplastic composite sandwich beam under random vibration

The dynamic response of a thermoplastic composite sandwich structure is optimized under random vibration. First, the experimental modal analysis data of a set of test samples are processed by a sequential set of statistical analysis such as descriptive statistics, factor analysis, and paired sample t-test. Then, the sample with the highest ability to represent the group is taken as the reference data. Three different computational models, which are defined according to whether the solid to be meshed is considered an area or a volume, are constructed. Modal analysis results of the computational models are compared to the reference experimental data to evaluate the performance of the models. To predict the dynamic response of the sandwich beam, it is excited through a random signal in the transverse direction. The nodal acceleration responses are computed in 17 evenly spaced points located on the upper finishing layer of the sandwich beam. Finally, a geometry optimization study is conducted to predict the optimum thicknesses of the 7 layers bonded together to form the sandwich beam. The optimum layer thicknesses that minimize the nodal accelerations at 17 evenly spaced points on the sandwich beam are computed. The current study shows that the shell model has the closest values to the experimental data compared to other models. As far as the dynamic response of a TPC sandwich structure is concerned, it is concluded that the shell model better represents the structure during the modeling phase and leads to concurrently reduced weight and nodal acceleration, when optimized.

Effect of the CHS on Seismic Responses of the Single-Layer Spherical Reticulated Shell under Vertical Seismic Motions

Single-layer spherical reticulated shells are typical roof structures for the gymnasiums. The center-hung scoreboard (CHS) is large weight display device which is usually suspended on the roof of the gymnasium. The effect of the CHS on the dynamic characteristics and seismic responses of the single-layer spherical reticulated shell (SPRS) is not fully clear. In this paper, the effect of the CHS on the SPRS under vertical seismic action is investigated. Two kinds of FE models are built with Abaqus software, including the flexibly suspended model and the simplified model. In a simplified model, the CHS is simplified as four fixed masses on the four CHS suspension nodes. The dynamic explicit method is used for the seismic responses, and the Lanczos method is used for the dynamic characteristics. The influence of the CHS weight and the sling length of on dynamic characteristics and seismic responses are analysed. It turns out that in the flexibly suspended model, the first three vibration modes are free swing of the CHS, and the CHS weight and the sling length have a significant impact on the fourth and subsequent modes. The length of the sling has a large impact on some low-order frequencies, but has little impact on the high-order frequencies. Compared with the simplified model, the axial forces of some structural members and some nodal acceleration in the flexibly suspended model under vertical seismic motions would increase by as high as 523% and 564%, respectively. It turns out that the seismic responses of the SPRS would be underestimated if a simplified model is used for analysis. The region in the central of the SPRS, the hoop members of the SPRS, and the support platform are the most affected regions in terms of both axial force and nodal acceleration.

Effect of the MHS on Earthquake Response of Space Truss Structures under Horizontal Earthquake Motion

Space truss structures are commonly used in long-span roof structures. Recently, middle-hung scoreboards (MHS), a kind of large-scale display device flexibly suspended in the center of the roof, have been widely used in gymnasiums. However, the effect of the MHS on dynamic characteristics and earthquake response of space truss structures needs to be investigated. In this paper, the effect on the MHS under horizontal earthquake motion is studied. The simplified model, where the MHS is simplified to four fixed masses on a structure, and the flexibly suspended model are established with Abaqus software, and the earthquake response is analyzed by the time-history method with the dynamic explicit method. The influence laws of the wire extent and the MHS weight are discussed. Compared with the simplified model, the nodal acceleration and the axial force rise up to 2.123 times and 1.575 times, respectively, in the flexibly suspended model, indicating that the amplification effect of the MHS acts significantly under horizontal earthquake motion. It turns out that the earthquake response of a space truss structure could be underestimated if a simplified model is used. The crest acceleration of both top chord nodes and bottom chords nodes are greatly influenced by the MHS weight but little affected by the wire extent. The influence laws of the MHS weight and the wire extent on crest axial forces of structural members are very complicated. The central regions of both the top chords and the bottom chords are the most affected regions, and the boundary regions parallel to the direction of the earthquake motion are the least affected regions. It is suggested that the envelope value under the conditions of different wire extent and MHS weight are used for structural design.

On the Seismic Performance of the Single-Layer Reticulated Shell with a Center-Hung Scoreboard under Multiple Seismic Excitations

Single-layer reticulated shells are widely used as roof structures of gymnasiums. However, the seismic performance of the single-layer reticulated shell with a center-hung scoreboard (CHS), which is a kind of large-scale display device suspended on the roof center of many gymnasiums, has not been fully studied. In this paper, the influence of the CHS on the seismic response of single-layer reticulated shells is investigated. Single-layer reticulated shells and the CHS-integrated models including flexibly suspended models and simplified models are established, respectively, using the Abaqus software. The responses of integrated models are calculated by an explicit dynamic method under 3D seismic action. The axial forces of the flexibly suspended case and the simplified case where the scoreboard is simplified as fixed masses on the roof structure are compared. Compared with those in the simplified model, the axial forces of some shell members and some nodal acceleration in the flexibly suspended model under multiple seismic excitations would increase by as high as 125% and 315%, respectively. It turns out that seismic responses of the single-layer reticulated shell would be underestimated if a simplified model was used for seismic response analysis. The region near the boundary and the region neighbouring the support platform members are the most affected regions due to the combination of the horizontal swing effect and the vertical impact effect of the CHS under multiple seismic excitations.

МЕТОД РАСЧЕТА ВЗАИМОДЕЙСТВИЯ МОСТОВОГО ПЕРЕХОДА И СКОРОСТНОГО ЖЕЛЕЗНОДОРОЖНОГО СОСТАВА ПРИ ПЕРЕМЕННОЙ СКОРОСТИ ДВИЖЕНИЯ (к формированию норм для ВСМ)

Boundary elements for rods on an elastic base are proposed for the calculation of bridges on the HSR when moving at a variable speed of an inertial load (railway train). A set of linear and trigonometric functions is used to approximate the displacements at the construction of boundary elements. These elements are used to calculate the vibrations of the rail track outside the bridge and the track on the bridge, together with double-track girder superstructures connected through the interlayers at high-speed movement of arbitrary power and inertial loads. To construct the methodology, the step method proposed earlier by the author of the article for solving problems of unsteady dynamics of structures and the method of calculating structures for the action of mobile force and inertial loads (the method of nodal accelerations) are used.

A finite element model for evaluating the effectiveness of the Advanced System for Implant Stability Testing (ASIST)

The Advanced system for Implant Stability Testing (ASIST) was developed to evaluate the stability of osseointegrated implants. ASIST matches the physical response with an analytical model’s prediction to determine the stiffness of the bone implant interface (BII) which is then used to calculate the ASIST Stability Coefficient (ASC). In this investigation, a 3D dynamic finite element (FE) model of the ASIST experimental impact technique for bone anchored hearing aids was created. The objectives were to evaluate the analytical model’s ability to capture the behavior of the implant system and to assess its effectiveness in minimising the effects of the system’s geometry on the ASC scores. The models were developed on ABAQUS®, they consisted of the implant, abutment, screw, base support and impact rod. The models relied on frictional contact definitions between the system’s components. The simplified “three-part” model had the implant, abutment and screw merged as one part while the “five-part” model treated them as separate components. Different interface conditions were simulated (friction coefficient range: 0–0.9) for three abutment lengths (6, 9 and 12 mm). The simulation output was the average nodal acceleration response of the rod, which was imported to the custom ASIST program in Mathematica® to obtain the ASC scores. The overall quality of the curve fits indicate that the analytical model is capable of representing the system’s behavior. Moreover,ASC scores provide a reliable assessment of implant stability as they are sensitive to interface conditions and are minimally influenced by the system’s geometry.

To the question of action on the rods lying on elastic foundation, inertial load with a variable speed of its movement

A method for calculating the rods on elastic foundation under the inertial load action when it moves at a variable speed is proposed. Test problems about a force or load movement with variable speeds along a hinged beam and about the movement with a high-speed railway car deceleration along a track section modeled by a hinged supported beam of great length on an elastic foundation are considered. The selection of the elastic foundation material of the rail track determines the dynamics of the high-speed railway car in different modes of its movement. To construct the methodology, the previously proposed by the author of the article solutions are used: a step-by-step procedure for solving the problems of unsteady dynamics of structures and the method of “nodal accelerations” to take into account the action on structures of a moving inertial load.

Boundary rod elements for modeling the railway at the bridge crossing under the action of the speed railway load

New rod boundary elements on an elastic foundation (finite elements of large length, when approximating the displacements by a set of linear and trigonometric functions) are proposed for calculating the path oscillations outside the bridge and on the bridge, combined with a double-track beam bridge connected through a layer with a high-speed rolling stock movement. The selection of interlayer material is related to the dynamics of the bridge. To build the methodology, the articles published earlier by the author are used: a step-by-step procedure for solving the problems of unsteady dynamics of structures and the method of “nodal accelerations” to take into account the action on the structures of a moving inertial load.

Formulation of equation error estimator using measured displacement de-noised by temporal–spatial filter for system identification of elastic solids

ABSTRACT This paper presents a new class of the equation error estimator using de-noised displacement by the temporal–spatial filter for the system identification in an elastic solid. The finite element method is employed to discretize the equation of motion for an elastic solid, and the Young’s modulus of each finite element is estimated by the proposed approach. The temporal–spatial filter is applied to de-noise measured nodal displacements and to reconstruct nodal accelerations. The equation of motion modified for the de-noised dynamic responses is derived, and the equation error estimator (EEE) for the system identification is defined with the modified equation of motion. The proposed EEE represents the residual error of the modified equation of motion over a measurement interval, and results in a nonlinear equation, which is solved by the successive substitution method. The sensitivity of the temporal–spatial filter required to solve the nonlinear equation is derived by the direction differentiation of the analytical expressions of the filter. The validity and accuracy of the proposed approach are tested through numerical simulation studies. It is shown that the proposed method yields accurate and stable solutions without regularization for all cases tested in this study.

Local Acceleration of Neurofilament Transport at Nodes of Ranvier.

Myelinated axons are constricted at nodes of Ranvier. These constrictions are important physiologically because they increase the speed of saltatory nerve conduction, but they also represent potential bottlenecks for the movement of axonally transported cargoes. One type of cargo are neurofilaments, which are abundant space-filling cytoskeletal polymers that function to increase axon caliber. Neurofilaments move bidirectionally along axons, alternating between rapid movements and prolonged pauses. Strikingly, axon constriction at nodes is accompanied by a reduction in neurofilament number that can be as much as 10-fold in the largest axons. To investigate how neurofilaments navigate these constrictions, we developed a transgenic mouse strain that expresses a photoactivatable fluorescent neurofilament protein in neurons. We used the pulse-escape fluorescence photoactivation technique to analyze neurofilament transport in mature myelinated axons of tibial nerves from male and female mice of this strain ex vivo Fluorescent neurofilaments departed the activated region more rapidly in nodes than in flanking internodes, indicating that neurofilament transport is faster in nodes. By computational modeling, we showed that this nodal acceleration can be explained largely by a local increase in the duty cycle of neurofilament transport (i.e., the proportion of the time that the neurofilaments spend moving). We propose that this transient acceleration functions to maintain a constant neurofilament flux across nodal constrictions, much as the current increases where a river narrows its banks. In this way, neurofilaments are prevented from piling up in the flanking internodes, ensuring a stable neurofilament distribution and uniform axonal morphology across these physiologically important axonal domains.SIGNIFICANCE STATEMENT Myelinated axons are constricted at nodes of Ranvier, resulting in a marked local decrease in neurofilament number. These constrictions are important physiologically because they increase the efficiency of saltatory nerve conduction, but they also represent potential bottlenecks for the axonal transport of neurofilaments, which move along axons in a rapid intermittent manner. Imaging of neurofilament transport in mature myelinated axons ex vivo reveals that neurofilament polymers navigate these nodal axonal constrictions by accelerating transiently, much as the current increases where a river narrows its banks. This local acceleration is necessary to ensure a stable axonal morphology across nodal constrictions, which may explain the vulnerability of nodes of Ranvier to neurofilament accumulations in animal models of neurotoxic neuropathies and neurodegenerative diseases.

Time step estimates for explicit dynamics with reciprocal mass matrices

AbstractIn this contribution, a novel local, node‐based time step estimate for explicit dynamics with reciprocal mass matrices is presented. Reciprocal mass matrices are sparse matrices used in explicit dynamics that allow computation of nodal acceleration from the total force vector. They can be built algebraically and variationally and aim for higher critical time steps or/and accuracy than the lumped mass matrix approximation. Since the element eigenvalue inequality by Fried is not valid for reciprocal mass matrices, element‐based estimates may be not conservative and they are consequently inadequate. Therefore, the nodal time step estimate for diagonally lumped mass matrices based on Gershgorin's theorem is further developed for application to reciprocal mass matrices. Additionally, simplifications of the proposed time step estimate that improve computational efficiency, especially for contact problems with the penalty method, are discussed. These simplifications use subadditivity and submultiplicativity properties of expressions used in the estimate. Finally, efficiency of the proposed estimate is illustrated by a numerical example.

Structural damage detection using time domain responses and an optimization method

ABSTRACTAn efficient method is proposed to determine the location and severity of structural damage using time domain responses and an optimization method. The time domain responses utilized here are the nodal accelerations measured at the limited points of a structure subjected to an impulse load. The nodal accelerations of the structure are obtained by Newmark time integration method. Firstly, using nodal accelerations extracted for the damaged structure and an analytical model of the structure, an objective function is defined for optimization. Then, the optimization-based damaged detection problem is solved via a differential evolution algorithm for finding the location and severity of damage. In order to assess the accuracy of the proposed method, four numerical examples are considered. Simulation results reveal the efficiency of the method for properly identifying damage with considering measurement noise.

Feedback control strategies for active control of noise inside a 3-D vibro-acoustic cavity

This paper presents and compares three feedback control strategies for active control of noise inside a 3-D vibro-acoustic cavity. These are a) control strategy based on direct output feedback (DOFB) b) control strategy based on linear quadratic regulator (LQR) to reduce structural vibrations and c) LQR control strategy with a weighting scheme based on structural-acoustic coupling coefficients. The first two strategies are indirect control strategies in which noise reduction is achieved through active vibration control (AVC), termed as AVC-DOFB and AVC-LQR respectively. The third direct strategy is based on active structural-acoustic control (ASAC). This strategy is an LQR based optimal control strategy in which the coupling between the various structural and the acoustic modes is used to design the controller. The strategy is termed as ASAC-LQR. A numerical model of a 3-D rectangular box cavity with a flexible plate (glued with piezoelectric patches) and with other five surfaces treated rigid is developed using finite element (FE) method. A single pair of collocated piezoelectric patches is used for sensing the vibrations and applying control forces on the structure. A comparison of frequency response function (FRF) of structural nodal acceleration, acoustic nodal pressure, and piezoelectric actuation voltage is carried out. It is found that the AVC-DOFB control strategy gives equal importance to all the modes. The AVC-LQR control strategy tries to consume the control effort to damp all the structural modes. It is seen that the ASAC-LQR control strategy utilizes the control effort more intelligently by adding higher damping to those structural modes that matter more for reducing the interior noise.

Numerical and experimental vibration analysis of olive tree for optimal mechanized harvesting efficiency and productivity

A 3D model of a middle-size olive tree has been analyzed considering various shaking conditions by using an attached trunk shaker to improve the harvesting rate as regards the critical nodal acceleration and displacement. The effects of shaking frequency, loading type as well as temperature and loading height were simulated and investigated on olive-stem-twig joint rupture. Comparing the results of finite element modal analysis in ABAQUS 6.10 with those of field experiments, utilizing a hydraulic eccentric-mass trunk shaker, exhibits less than 5% deviation at frequencies between 10 and 25Hz at the first four vibration modes with damping ratio of 16–30%. The experiments and simulations show the maximum harvested quantity of sample middle-size olive trees is 92% and 96%, respectively. It is acquired at f=20Hz, T=28°C for 45% moisture content of wood in late November 2012, without chemicals. The optimized mechanical harvesting yielded the lower number of workers, time saving (∼12tree/h), and to improve the obtained productivity (293kg/h). The results imply that accurate 3D analysis of mechanized olive harvesting can be an efficacious solution to obtain desired parameters and optimal efficiency, which is comparable to manual method.

Reduction in the dynamic amplitudes of moored cable systems

Cable-body systems are intelligent and cost-effective structures used in ocean engineering and also for many oceanographic missions. The demand for such systems is increasing steadily because of new types of systems like wind farms, ocean energy converters and floating airports. Mooring of such platforms to a fixed point on the earth makes the system secure. Dynamic behaviour of a moored system with a subsurface buoy is studied here. The optimum position of the buoy is found using an analytical approach. The location of the buoy along the cable is a critical aspect in tension reduction. An analytical method is developed for the solution of a typical mooring problem taking into account the presence of a subsurface buoy. The method originally proposed by Walten and Polachek (1959) is modified here to suit the present problem. The nodal accelerations and velocities at the points of lumped mass of subsequent time steps can be expressed as per the Houbolt scheme. Integration of the accelerations and velocities lead to the solutions of the mooring-line dynamic problems subject to constraints to achieve the numerical convergence of solution. Dynamic amplitudes vary with the frequency of excitation at the surface due to external disturbances like waves and current. Wave, current and water depths are considered for the dynamic load built up along the mooring line. A number of cases are worked out, and some important and significant results are presented in this paper. Dynamic tension variations with and without a subsurface buoy are determined. Effect of pre-tension is determined and presented. Dynamic amplitude for different frequency ratios and different amplitudes of motions are determined. The method is useful for deepwater systems in which tension reduction provides better efficiency for the performance of the anchor by providing better seakeeping ability in the case of a ship or a platform.