Simplified procedures for vibration serviceability analysis of footbridges subjected to realistic walking loads

This paper deals with the vibration serviceability analysis of footbridges subjected to realistic pedestrian traffic conditions, based on a probabilistic characterization of pedestrian-induced forces. The dynamic response to three different loading conditions is analysed through a non-dimensional approach, which permits the identification of the essential non-dimensional parameters governing the dynamic behaviour. Two simplified procedures are then proposed, founded on the sound definition of two coefficients, the Equivalent Amplification Factor and the Equivalent Synchronization Factor, which allow the evaluation of the vibration serviceability without requiring numerical analyses. Final applications confirm the efficiency of the proposed methods.     

母杜柴登矿立井井塔结构振动分析

母杜柴登矿立井井塔在68.37m楼层上安装有一套提升系统,当提升机组以13m/s全速运转时,井塔第7层西区楼板的中部及第6层南区、北区楼板的中部楼板体系产生了较大的振动。针对上述问题,采用振动动态测试方法对提升机组、井塔不同位置的时域和频域信号进行了测量和分析,结果表明,井塔第6层、第7层楼板的自振频率非常接近提升机组电动机的固有振动频率(22.1Hz),需调整提升设备的动力系统或井塔的第6层、第7层楼板体系的刚度,避免提升机-井塔结构耦合体系发生共振;随着提升速度的增加,第6层、第7层楼板的振动烈度逐渐变大,需提高提升设备机座与基梁间的装配精度,降低楼板振动位移。     

Dynamic response of orthotropic curved bridge decks due to moving loads

The dynamic response of horizontally curved bridge decks simply supported along the radial edges under the action of the moving vehicle is investigated. The bridge deck is idealised as a number of finite strips with orthotropic elastic properties. The stiffness and mass matrix of an individual element were derived using a homogeneous differential equation of an orthotropic plate in polar co-ordinates. The vehicle is idealized as a sprung mass moving at a constant speed in a circular path parallel to the central line of the bridge. The unsprung mass of the vehicle is assumed to be always in contact with the bridge surface during its motion. Viscous damping is taken into account for both bridge and vehicle. Dynamic deflections and moments are presented for the mid-point of the bridge deck and the values have been compared with the available analytical solution.     

Biodynamic response analysis of semi-supine human under varying vertical excitations

The biodynamic responses of semi-supine humans exposed to varying vertical vibration magnitudes (0.125–1.0 m/s² r.m.s.) are studied employing a multi-body modeling approach. The model comprises five rigid segments: the head, upper torso, lower torso, thigh, and leg. The viscoelastic property of tissues at joints and body-support interface are incorporated using the Kelvin-Voigt model. The dynamic model parameters identified through optimization are employed to capture the transmissibility responses of different body segments at varying vibration magnitudes. The Monte-Carlo simulation is performed to ascertain the effect of uncertainty of the model parameter and body mass on the biodynamic responses at different vibration magnitudes. The calibrated model accurately predicts the decrease in the primary resonance frequency with the increase in vibration magnitude. This nonlinearity is also apparent in vertical transmissibility responses of all the body segments. The effect of uncertainty of model parameters and body mass on the transmissibility responses is prominent near resonance frequency, while their effect on the apparent mass response is consistent across the entire frequency spectrum. The Monte-Carlo simulation illustrates higher dispersion in the transmissibility responses of the head and thorax at 1.0 m/s² r.m.s. compared to at 0.125 m/s² r.m.s. Therefore effective restraint systems are required at the head and thorax to counter the impact of high vibration magnitudes experienced during spaceflight.     

Finite difference analysis of plate response to random loads

The application of the finite difference method to analyse the response of plates subjected to stationary random loading is presented. The discrete forced dynamical system generated by the finite difference approximations is analysed by a generalised harmonic analysis. The power spectral density (PSD) for displacement at each node is calculated directly for particular frequencies and subsequently these PSDs are integrated numerically over the frequency range to yield the mean square response. Both viscous and structural damping have been considered. For illustrative purposes the random excitation is taken to be clipped white noise with uniform spatial correlation. To validate the numerical procedure, further verification was obtained by comparing the numerical results with an analytic and with another numerical solution.     

Nonlocal thermoelastic model for temperature-dependent thermal conductivity nanobeams due to dynamic varying loads

Microsystem Technologies - The present paper produces a new nonlocal model for thermoelastic nanobeams of temperature-dependent thermal conductivity. A nanobeam excited by harmonically varying heat...     

Simulation of inelastic deformation in road structures due to cyclic mechanical and thermal loads

The paper presents modeling and simulation of inelastic deformation in road structures leading to rutting. Two material models, one for asphalt-concrete and another for unbound materials, have been calibrated to laboratory test data. The models account for the time and temperature dependent deformation of the asphalt-concrete as well as the friction and cyclic compaction of the unbound layers. The models have been used in simulations of a complete road structure exposed to cyclic mechanical and thermal loads. The simulation results are qualitatively similar to the rutting observed in reality. The simulations can either trace the complete history of the individual load cycles, or can be performed to directly obtain the accumulated effect after a certain number of load cycles. This makes it possible to get quickly the result due to a large number of loadings as desired in engineering design practice.     

Numerical analysis of anisotropic rotational shells subjected to nonsymmetric loads

Through the use of an integral transform, the present paper extends the applicability of the multisegment numerical integration technique to include the solution of general macroscopically anisotropic multilayered shells of revolution. It is found that compared with orthotropic shells, material anisotropy induces a doubling in the number of transformed fundamental equations characterizing the static response. Employing the transform together with the multisegment integration technique and several concepts from the direct stiffness method of structural analysis, procedures are developed which can handle branched anisotropic multilayered shells of revolution in a more effective manner than was previously possible. Based on the procedures outlined in the paper, numerical studies are presented which show the effect of segment size on the solution accuracy and the effects of material anisotropy on selected shell configurations.     

Probabilistic free vibration analysis of beams subjected to axial loads

A stochastic finite-element-based algorithm for the probabilistic free vibration analysis of beams subjected to axial forces is proposed in this paper through combination of the advantages of the response surface method, finite element method and Monte Carlo simulation. Uncertainties in the structural parameters can be taken into account in this algorithm. Three response surface models are proposed. Model I: star experiment design using a quadratic polynomial without cross-terms; Model II: minimum experiment design using a quadratic polynomial with cross-terms; Model III: composite experiment design using a quadratic polynomial with cross-terms.A separate set of finite element data is generated to verify the models. The results show that the Model II is the most promising one in view of its accuracy and efficiency. Probabilistic free vibration analysis of a simply supported beam is performed to investigate the effects of various parameters on the statistical moments of the frequency response of beams. It is found that the geometric properties of beams have significant effects on the variation of frequency response.     

The estimation and control of terrestrial inertial navigation system errors due to vertical deflections

Deflections of the vertical introduce errors into terrestrial inertial navigation systems. In many situations, these errors prove to be intolerable. However, if vertical deflection data are available prior to a mission, this information can in principle be used to reduce the navigation system errors. It is assumed that measurements of vertical deflections plus noise are available at equally spaced points on a square grid. The accuracy to which the Schuler loop errors can be controlled, given this set of measurements, is bounded by the accuracy to which the uncontrolled Schuler loop errors can be estimated given the same set of measurements. Thus lower bounds on the accuracy of the compensated system may be established by obtaining the optimal error covariances of the equivalent estimation problem. It is shown that the estimation problem can be modeled as a linear smoothing problem if the vehicle travels at a constant heading and at a constant velocity. The appropriate error covariances are found using the known techniques of optimal linear estimation theory, Kalman filtering and smoothing, both at and between the grid points.     

Postbuckling analysis of functionally graded plates subject to compressive and thermal loads

Postbuckling analysis of functionally graded ceramic–metal plates under edge compression and temperature field conditions is presented using the element-free kp-Ritz method. The first-order shear deformation plate theory is employed to account for the transverse shear strains, and the von Kármán-type nonlinear strain–displacement relationship is adopted. The effective material properties of the functionally graded plates are assumed to vary through their thickness direction according to the power-law distribution of the volume fractions of the constituents. The displacement fields are approximated in terms of a set of mesh-free kernel particle functions. Bending stiffness is estimated using a stabilised conforming nodal integration approach, and, to eliminate the membrane and shear locking effects for thin plates, the shear and membrane terms are evaluated using a direct nodal integration technique. The solutions are obtained using the arc–length iterative algorithm in combination with the modified Newton–Raphson method. The effects of the volume fraction exponent, boundary conditions and temperature distribution on postbuckling behaviour are examined.     

Recent advances in maneuver loads analysis

The conceptual design of an aircraft system requires a number of analysis cycles involving the study of various configurations for which aerodynamic and structural properties are not well defined. The aeroelastic stability and structural strength considerations are very important factors in the determination of the aerodynamic and the structural configurations. Therefore, this paper briefly reviews the specifications leading to the design loads criteria and the current analysis methods. Suggestions for research activities required in the development of a computational fluid dynamics (CFD) code and its application to predict the design loads are also included.     

Flow due to a sink near a vertical wall, in infinitely deep fluid

Flow caused by a point sink in an otherwise stagnant fluid is studied using numerical methods based on integral-equation techniques and an asymptotic solution for small Froude number. There is a vertical wall present on a plane close to the sink, so that the flow is fully three dimensional. The fluid is of infinite depth, but a free-surface bounds it above. Steady solutions are presented for various Froude numbers and distances of the source from the wall. It is shown that the numerical results and asymptotic formula are in good agreement for small Froude numbers, but the results suggest that the non-linear solution ultimately forms some limiting structure at sufficiently large Froude number.     

Analysis of non-linear response of the human body to vertical whole-body vibration

The human response to vibration is typically studied using linear estimators of the frequency response function, although different literature works evidenced the presence of non-linear effects in whole-body vibration response. This paper analyses the apparent mass of standing subjects using the conditioned response techniques in order to understand the causes of the non-linear behaviour. The conditioned apparent masses were derived considering models of increasing complexity. The multiple coherence function was used as a figure of merit for the comparison between the linear and the non-linear models. The apparent mass of eight male subjects was studied in six configurations (combinations of three vibration magnitudes and two postures). The contribution of the non-linear terms was negligible and was endorsed to the change of modal parameters during the test. Since the effect of the inter-subject variability was larger than that due to the increase in vibration magnitude, the biodynamic response should be more meaningfully modelled using a linear estimator with uncertainty rather than looking for a non-linear modelling.     

Elasto-plastic analysis of axisymmetric structures subject to arbitrary loads by hybrid-stress finite elements

A semi-analytic finite element method in conjuction with a hybrid-stress functional based on the initial stress approach is presented for elasto-plastic analysis. A three-dimensional solid element based on hybrid-stress model is also implemented for the elasto-plastic analysis. A procedure to compute the non-linear effects in terms of Fourier series in the hybrid-stress model is described. The accuracy and efficiency of the semi-analytic method is evaluated via numerical examples by comparing the solution with a full 3-D solution. The semi-analytic method is observed to be a viable alternative to 3-D analysis in elasto-plastic analysis of axisymmetric structures subject to arbitrary loads.     

Finite element analysis of spiral strands with different shapes subjected to axial loads

In this paper a new mathematical geometric model of spiral one or two-layered oval wire strands are proposed and an accurate computational two-layered oval strand 3D solid model, which is used for a finite element analysis, is presented. The three dimensional curve geometry of wires axes in the individual layers of the oval strand consists of straight linear and helical segments. The present geometric model fully considers the spatial configuration of individual wires in the right and left hand lay strand. Derived geometric equations were used for the generation of accurate 3D geometric and computational models for different types of strands. This study develops 3D finite element models of two-layer spiral round, triangular and oval strands subjected to axial loads using ABAQUS/Explicit software. Accurate modelling and understanding of their mechanical behaviour is complicated due to the complex contact interactions and conditions that exist between individual spirally wound wires. Comparisons of predicted responses for the strands with different shapes and constructions are presented. Resultant stress and/or deformation behaviours are discussed.     

Vibration analysis of waffle floors

Two-way grillage or waffle floors are used extensively in semiconductor factories as they provide high impedance mounts for manufacturing equipment that is extremely vibration sensitive. This paper presents a mathematical model for the analysis of vibration at the center of a bay and the transmission of vibration along a waffle floor. The mathematical model is compared with finite element models and experimental results from several manufacturing buildings, and shows good agreement. Trends are shown for the displacement and resonance frequency of the floor as the thickness of the floor, size of the bays and the stiffness of the columns are varied.     

Nonlinear dynamic modeling and body injuries analysis of human/seat system under vertical impact

Predicting the responses and injuries of seated pilots caused by emergency landing or ejection is significant for the design of ejection seats. A nonlinear two-dimensional multi-body human/seat model is proposed to predict the responses and body injuries exposed to vertical impact. Then a new force identification method is presented and applied to obtain the external excitation of the system. In addition, the parameters of this model are optimized based on the Error Assessment of Response Time Histories (EARTH) metric and Non-dominated Sorting Genetic Algorithm II (NSGA-II). Furthermore, utilizing the proposed model, this research predicts body injuries with different impact intensities. With body injuries as output, the influence of input parameters is assessed by global sensitivity analysis (GSA) methods. The result shows that the backrest angle plays a crucial role in body injuries. Finally, the influence of backrest angle is further analyzed to obtain the variation of body injuries with backrest angle. This research provides guiding principles for the subsequent design of ejection seats.