Elastic Support Conditions Research Articles

Surrogate based prediction models for elastically supported beams under the action of opposite moving loads

A hybrid model that incorporates an artificial neural network (ANN) and non-dimensional numerical analysis has been developed to predict the displacement response of an elastically supported (ES) beam under the action of sequential moving loads in opposite directions. The dataset acquired from non-dimensional numerical modeling was utilized for training multi-layered feed-forward ANN, resulting in the development of surrogate models. The input parameters include the beam and load parameters, whereas the beam’s displacement is the output parameter. The robustness and efficiency of the hybrid models have been highlighted using statistical metrics, which show that training and validating data produce promising predictions. Further, the relationship between input and output parameters was represented using Pearson’s correlation. Results indicated that the effectiveness of the ES beam depends on the critical combination of stiffness parameter κ and interspatial distance parameter ϵ under particular speed parameter R. To bypass the computational cost, a user-friendly interface has been developed to assess the displacement response of elastically-supported beams under the action of one-way and two-way moving loads. Further, the proposed methodology has wide application in analyzing and designing short to medium-span bridges in critical locations such as canal/road crossings under the action of opposite moving loads using elastic support conditions.

Vibration analysis of buried pipelines and piles using differential transformation method

Investigating the interaction between structures and their elastic foundations is essential in structures with elastic support conditions, such as buried pipelines and piles. Research investigation was carried out to find the frequency of a buried structure simulated by Euler–Bernoulli beam equations, with distributed damping and general boundary conditions on an elastic foundation. The elastic bed was modelled by a linear spring, and boundary conditions were changeable at two ends of the beam's support with variations in the stiffness of transitional and rotational springs. The differential transformation method (DTM) was then used to solve the equations by correlating the function and its derivatives. The frequency of the structure was obtained for various damping and stiffness values. The increase in the stiffness of the elastic support and the decrease in damping led to a higher frequency. The results of DTM agreed with the results of the exact method.

DYNAMIC MAGNIFICATION OF BIOMECHANICAL SYSTEM MOTION

Methods for estimation of dynamic magnification pertaining to motion in biomechanics have been developed and approbаted in the paper. It has been ascertained that widely-used characteristics for evaluation of motion influence on mechanisms and machinery such as a dynamic coefficient and acceleration capacity factor become irrelevant while investigating human locomotion under elastic support conditions. The reason is an impossibility to compare human motion in case when there is a contact with elastic and rigid supports because while changing rigidity of the support exercise performing technique is also changing. In this case the technique still depends on a current state of a specific sportsman. Such situation is observed in sports gymnastics. Structure of kinematic and dynamic models for human motion has been investigated in the paper. It has been established that properties of an elastic support are reflected in models within two aspects: in an explicit form, when models have parameters of dynamic deformation for a gymnastic apparatus, and in an implicit form, when we have numerically changed parameters of human motion. The first part can be evaluated quantitatively while making comparison with calculations made in accordance with complete models. For this reason notions of selected and complete models have been introduced in the paper. It has been proposed to specify models for support and models of biomechanical system that represent models pertaining only to human locomotor system. It has been revealed that the selected models of support in kinematics and dynamics have structural difference. Kinematics specifies only parameters of elastic support deformation and dynamics specifies support parameters in an explicit form and additionally in models of human motion in an explicit form as well. Quantitative estimation of a dynamic motion magnification in kinematics and dynamics models has been given while using computing experiment for grand circle backward on a gymnastics horizontal bar as an example. It has been shown that an influence of a gymnastic apparatus on motion has numerically the same order as motion of a sportsman without taking into account elastic properties of the support.

Load-Sharing Characteristics of Power-Split Transmission System Based on Deformation Compatibility and Loaded Tooth Contact Analysis

In order to implement the uniform load distribution of the power-split transmission system, a pseudostatic model is built. Based on the loaded tooth contact analysis (LTCA) technique, the actual meshing process of each gear pair is simulated and the fitting curve of time-varying mesh stiffness is obtained. And then, the torsional angle deformation compatibility conditions are proposed according to the closed-loop characteristic of power flow, which will be combined with the torque equilibrium conditions and elastic support conditions to calculate the transfer torque of each gear pair. Finally, the load-sharing coefficient of the power-split transmission system is obtained, and the influences of the installation errors are analyzed. The results show that the above-mentioned installation errors comprehensively influence the load-sharing characteristics, and the reduction of only one error could not effectively achieve perfect load-sharing characteristics. Allowing for the spline clearance floating and constrained by the radial spacing ring, the influence of the floating pinion is analyzed. It shows that the floating pinion can improve the load-sharing characteristics. Through the comparison between the theoretical and related experimental data, the reasonability and feasibility of the above-proposed method and model are verified.

Vibration analysis of multi-walled carbon nanotubes using a spring–mass based finite element model

We report a study of the vibrational characteristics of multi-walled carbon nanotubes modeled exclusively using springs and lumped masses. Based on the atomic microstructure of the nanotube, three-dimensional nanoscale spring elements are utilized to simulate the dynamic behavior of each layer of the multi-walled carbon nanotubes. Appropriate spring elements are also developed to model the interlayer interactions and describe the van der Waals potentials between carbon atoms on different layers. Direct application of the physical variables of molecular mechanics theory to the springs is used to simulate the relative translations and rotations between atoms as well as the masses of the carbon atoms. The stiffness and mass matrices of the problem are used to construct the dynamic equilibrium equation. The natural modes of vibration and the corresponding natural frequencies are derived by solving the eigenvalue problem for different support conditions. The present method suggests novel basic modes of vibration, beyond those reported in the literature pertaining to multi-walled carbon nanotubes. The effects on the basic modes and natural frequencies created by van der Waals interactions and geometric parameters such as number of layers and aspect ratio are investigated in the context of elastic support conditions. Comparisons with other theoretical studies reveal very good correlations in terms of fundamental modes and frequencies.

A SIMPLIFIED METHOD FOR ESTIMATING LONGITUDINAL SEISMIC RESPONSES OF LONG SPAN STEEL CABLE-STAYED BRIDGES WITH LONGITUDINALLY FREE OR ELASTIC SUPPORT CONDITIONS

A SIMPLIFIED METHOD FOR ESTIMATING LONGITUDINAL SEISMIC RESPONSES OF LONG SPAN STEEL CABLE-STAYED BRIDGES WITH LONGITUDINALLY FREE OR ELASTIC SUPPORT CONDITIONS

Stability formulae for shear-wall frame structures

For preliminary design of shear-wall frame structures, the lowest buckling load has to be estimated, preferably using a simple and accurate formula. A simple formula is presented by modeling the structure as a shear-restrained column and solving the associated total energy functional or the governing differential equation by means of the energy approach. The formula is applicable for fixed as well as elastic support conditions and the results agree with the exact analytical transcendental solutions.