Velocity Of Moving Load Research Articles

Moving Load Spectrum for Analyzing the Extreme Response of Bridge Free Vibration

In order to more effectively establish the relationship between moving load speed and the extreme response of bridge free vibration, a novel analysis method is presented based on the moving load spectrum, which is deduced from Fourier transform in this paper. By analyzing the moving load spectrum in detail, the moving load velocities which lead to the extreme responses of bridge free vibration under single moving constant force or harmonic force are obtained, and the corresponding formula for calculating the moving load velocity which leads to the maximum response of bridge free vibration is put forward. Finally, the moving load spectrum for analyzing the extreme response of bridge free vibration is validated by a large number of calculations in the time domain in this paper. The results show that the moving velocities corresponding to the extreme points in the moving load spectrum are consistent with the velocities corresponding to the extreme points of the bridge vibration response obtained in the time domain, and the forced and free vibration displacement responses of bridge are not the largest when the single moving constant force or harmonic force passes through the bridge at the resonant velocity compared to other speeds.

Some closed-form solutions for static, buckling, free and forced vibration of functionally graded (FG) nanobeams using nonlocal strain gradient theory

In this paper, static bending, buckling, free and forced vibration of functionally graded (FG) nanobeams are studied within the framework of the recently proposed nonlocal strain gradient theory and the Euler-Bernoulli beam theory. The material properties of nanobeam are presumed to be graded in the thickness direction according to a simple power-law distribution in terms of the volume fraction of the constituents. The governing equation and the related boundary conditions are derived via the principle of the calculus of variation. In order to eliminate the axial displacement in the formulation, the concept of the neutral surface is adopted. Some analytical solutions are obtained for the static displacement, critical buckling load, free vibration frequencies and the dynamic displacement for the case of the simply-supported end condition. In the dynamic analysis, three different loading cases, a moving load with constant velocity, point and distributed harmonic loads, are considered, and Duhamel’s integration is utilized for obtaining the corresponding dynamic deflections. Several numerical examples are presented in figures and tables in order to examine the effects of the strain gradient and the nonlocal parameters, the gradient index, the excitation frequency and the moving load velocity on the mechanical behavior of FG nanobeam.

A Finite Element Model for Dynamic Analysis of Triple-Layer Composite Plates with Layers Connected by Shear Connectors Subjected to Moving Load.

Triple-layered composite plates are created by joining three composite layers using shear connectors. These layers, which are assumed to be always in contact and able to move relatively to each other during deformation, could be the same or different in geometric dimensions and material. They are applied in various engineering fields such as ship-building, aircraft wing manufacturing, etc. However, there are only a few publications regarding the calculation of this kind of plate. This paper proposes novel equations, which utilize Mindlin’s theory and finite element modelling to simulate the forced vibration of triple-layered composite plates with layers connected by shear connectors subjected to a moving load. Moreover, a Matlab computation program is introduced to verify the reliability of the proposed equations, as well as the influence of some parameters, such as boundary conditions, the rigidity of the shear connector, thickness-to-length ratio, and the moving load velocity on the dynamic response of the composite plate.

Piezoelectric Energy Harvesting from a Bridge Subjected to Time-Dependent Moving Loads Using Finite Elements

The present paper addresses vibration energy harvesting from a bridge subjected to time-dependent moving loads thanks to a cantilever piezoelectric harvester fixed beneath the bridge. A finite element model of the bridge based on Kirchhoff plate assumptions, Hamilton principle and Newmark integration scheme, for time domain analysis, is considered. The time-varying acceleration of the bridge, submitted to a moving load, is then applied as a base excitation to an electromechanical model of the harvester. Different types of moving loads are considered (constant, harmonic, broadband and narrow-band). In the case of constant or harmonic moving loads, the obtained results confirm previous findings in the literature: for a moving load frequency equal to the natural frequency of the bridge, the harvested energy is maximal when the harvester is located at the maximum amplitude of the bridge’s corresponding mode shape. These results are not confirmed in the case of realistic moving loads with broadband or narrow-banded frequency spectrum pointing out the weakness of the harmonic analysis and the dependence of the harvested energy on the frequency spectrum of the moving load which appears to be with the moving load velocity the two key parameters for energy harvesting.

An exact solution to the problems of flexo-poro-elastic structures rested on elastic beds acted upon by moving loads

This paper aims to examine flexural vibrations of fully saturated poroelastic structureson an elastic bed subjected to moving point loads via an analytical solution. Using aflexural beam model in conjunction with the Biot’s poro-elasticity theory, the equationsof motion of the porous structure are derived. Using assumed mode method and Laplacetransform, the explicit expressions of displacement and pore pressure are obtained carefully.For a particular case, the predicted results are also compared with those of another workand a reasonably good agreement is achieved. The influences of the moving load velocity,permeability ratio, transverse stiffness of the foundation, viscosity of the pore fluid, andporosity on the maximum elasto-dynamic fields and pore pressure are conclusively discussed.The velocity pertinent to the maximum possible dynamic response is graphically determinedand the roles of influential parameters on this crucial factor are displayed. The present modelcould be easily extended to multi-layered poroelastic structures under moving loads.

Optimisation analysis of nanocomposite pipes with internal fluid flow under external excitation

The harmony search algorithm is applied to optimum designs of a functionally graded (FG)-carbon nanotubes (CNTs)-reinforced pipes conveying fluid subjected to moving load. The structure is modelled by Reddy cylindrical shell theory and the final equations are obtained by principal of Hamilton. Based on differential quadrature method (DQM), the dynamic displacement of system is derived. The length, thickness, diameter, velocity of load and acceleration of load, temperature of fluid, velocity of fluid, and the volume fraction of CNT are considered for design variables. The results illustrates that the optimum diameter of the pipe is decreased by increasing the CNTs volume percent. In addition, with increasing the moving load velocity and acceleration, the FS is decreased.

Optimisation analysis of nanocomposite pipes with internal fluid flow under external excitation

The harmony search algorithm is applied to optimum designs of a functionally graded (FG)-carbon nanotubes (CNTs)-reinforced pipes conveying fluid subjected to moving load. The structure is modelled by Reddy cylindrical shell theory and the final equations are obtained by principal of Hamilton. Based on differential quadrature method (DQM), the dynamic displacement of system is derived. The length, thickness, diameter, velocity of load and acceleration of load, temperature of fluid, velocity of fluid, and the volume fraction of CNT are considered for design variables. The results illustrates that the optimum diameter of the pipe is decreased by increasing the CNTs volume percent. In addition, with increasing the moving load velocity and acceleration, the FS is decreased.

THE INFLUENCE OF MASS ON VELOCITY AND ACCELERATION BASED ON NEWTON’S SECOND LAW BY USING LINIER AIR TRACK

The research aims to see whether there is influence of distance on time, mass effect on velocity, and mass effect on acceleration. Variables in this study consisted of manipulation variables of load and distance mass, response variables i.e. time taken and moving load velocity. The results showed that the effect of distance to time can be seen from the correlation coefficient value R 2 = 0.999 for the mass of 128 g and 400.46 g which means that there is influence of 99.9%. And there is the effect of mass on the velocity and acceleration that is the velocity and acceleration of the load mass of 128 g of 0.062 m/s and 0.00625 m/s 2 greater than the velocity and acceleration with mass load 400.46 g of 0.056 m/s and 0.0518 m/s 2 . It is proven by Newton's law of velocity and acceleration is inversely proportional to mass, meaning that the greater the load mass, the speed and acceleration of the object will be smaller, and vice versa. Keywords: Acceleration, linier air track, load mass, Newton’s second law, and velocity.

Analysis of dynamic stress path in inhomogenous subgrade under moving aircraft load

Considering the cut and fill alternating characteristic of airport subgrade in mountainous area, especially in the runway direction, a semi-analytic finite element method was proposed to analyze the dynamic response of inhomogenous subgrade under moving aircraft load. This method can decrease the computational cost effectively by using the Fourier Transform in the transverse direction of the runway to reduce the dimension of the 3D problem and account for the traveling wave effect of moving load. The dynamic responses of a soil element in homogenous and inhomogeneous subgrade subjected to single-wheel aircraft load were analyzed comparatively. The results show that the dynamic stresses generated in soil element are mainly vertical normal stress and in-plane shear stress, forming stress paths with the characteristic of complex principal cyclic stress axis rotation. Due to the traveling wave effect, the dynamic responses of soil are not antisymmetric when the moving load approaches and leaves the observation point. In the homogeneous subgrade, the dynamic stress path in the plane of the two shear stress components is egg-shaped with a tilting angle. As the moving load velocity grows, the long axis of the egg-shaped stress path rotates counterclockwise. In the inhomogeneous subgrade, the dynamic stress is concentrated near the junction of cut and fill areas, and the peak value of the vertical dynamic stress is 1.35 times that in the homogeneous subgrade. Moreover, the stress path near the junction tends to be more prolate and spindle-shaped.

Dynamic response of porous functionally graded material nanobeams subjected to moving nanoparticle based on nonlocal strain gradient theory

Up to now, nonlocal strain gradient theory (NSGT) is broadly applied to examine free vibration, static bending and buckling of nanobeams. This theory captures nonlocal stress field effects together with the microstructure-dependent strain gradient effects. In this study, forced vibrations of NSGT nanobeams on elastic substrate subjected to moving loads are examined. The nanobeam is made of functionally graded material (FGM) with even and uneven porosity distributions inside the material structure. The graded material properties with porosities are described by a modified power-law model. Dynamic deflection of the nanobeam is obtained via Galerkin and inverse Laplace transform methods. The importance of nonlocal parameter, strain gradient parameter, moving load velocity, porosity volume fraction, type of porosity distribution and elastic foundation on forced vibration behavior of nanobeams are discussed.

Dynamic Analysis of an Infinitely Long Beam Resting on a Kelvin Foundation under Moving Random Loads

Nonstationary random vibration analysis of an infinitely long beam resting on a Kelvin foundation subjected to moving random loads is studied in this paper. Based on the pseudo excitation method (PEM) combined with the Fourier transform (FT), a closed-form solution of the power spectral responses of the nonstationary random vibration of the system is derived in the frequency-wavenumber domain. On the numerical integration scheme a fast Fourier transform is developed for moving load problems through a parameter substitution, which is found to be superior to Simpson’s rule. The results obtained by using the PEM-FT method are verified using Monte Carlo method and good agreement between these two sets of results is achieved. Special attention is paid to investigation of the effects of the moving load velocity, a few key system parameters, and coherence of loads on the random vibration responses. The relationship between the critical speed and resonance is also explored.

Optimum Design of FGX-CNT-Reinforced Reddy Pipes Conveying Fluid Subjected to Moving Load

The harmony search algorithm is applied to the optimum designs of functionally graded (FG)-carbon nanotubes (CNTs)-reinforced pipes conveying fluid which are subjected to a moving load. The structure is modeled by the Reddy cylindrical shell theory, and the motion equations are derived by Hamilton's principle. The dynamic displacement of the system is derived based on the differential quadrature method (DQM). Moreover, the length, thickness, diameter, velocity, and acceleration of the load, the temperature and velocity of the fluid, and the volume fraction of CNT are considered for the design variables. The results illustrate that the optimum diameter of the pipe is decreased by increasing the volume percentage of CNTs. In addition, by increasing the moving load velocity and acceleration, the FS is decreased.

Dynamic response of functionally graded beams in a thermal environment under a moving load

ABSTRACTThe dynamic response of functionally graded (FG) beams in thermal environment subjected to moving load is investigated based on the first-order shear deformation theory (FSDT). The initial thermal stresses are determined by solving the thermoelastic equilibrium equations. The finite element method (FEM) is adopted to develop a solution procedure for FG beams with general loading and boundary conditions. The convergence behavior and accuracy of the method are shown through the different numerical examples. Finally, the influences of temperature rise, material graded index, moving load velocity, and boundary conditions on the dynamic behavior of FG beams in thermal environment is presented.

Nonlinear response of functionally graded plates under moving load

The nonlinear response of functionally graded (FG) plates under moving load is studied based on the classical plate theory (CPT). The geometrical nonlinearity due to large deformation is modeled using Green's strain tensor under von Kármán assumptions. The material properties vary continuously through the plate thickness and are obtained according to the rule of mixture. The finite element method (FEM) in conjunction with Newmark’s time integration scheme and Newton–Raphson method are employed to solve the nonlinear system of equations of motion subjected to the different boundary conditions. The formulation and method of solution are validated by studying their convergence behavior and performing the comparison studies with existing results in the literature in the limit cases. Finally, comparison studies between the nonlinear and linear response of FG plates under moving load are carried out and the influences of the material graded index, moving load velocity and plate aspect ratio are investigated.

Size-dependent vibration of a microplate under the action of a moving load based on the modified couple stress theory

This study deals with forced vibration analysis of a microplate subjected to a moving load. The formulation is developed based on the modified couple stress theory in conjunction with Kirchhoff–Love plate theory. The equations of motion of the problem are derived using Lagrange’s equations. In order to obtain the response of the microplate, the trial function for the dynamic deflection is expressed in the polynomial form. The equations of motion are solved by using the implicit time integration Newmark-β method, and then displacements, velocities and accelerations of the microplate at the considered point and time are determined. Five different sets of boundary condition are considered. For this purpose, boundary conditions are satisfied by adding some auxiliary functions to the trial functions. A parametric study is conducted to study the effects of the material length scale parameter, plate aspect ratio, boundary conditions and the moving load velocity on the dynamic response of the microplate. Also, in order to validate the present formulation and solution method, some comparisons with those available in the literature are performed. Good agreement is found. The results show that the dynamic deflections are significantly affected by the scale parameter and the load velocity.

Bi-directional functionally graded materials (BDFGMs) for free and forced vibration of Timoshenko beams with various boundary conditions

This paper investigates free and forced vibration of bi-directional functionally graded (BDFG) Timoshenko beam under the action of a moving load. The material properties of the beam vary exponentially in both axial and thickness directions. The equations of motion are derived by means of Lagrange equations based on Timoshenko beam theory (TBT) as well as Euler–Bernoulli beam (EBBT) theory. In order to obtain free and forced vibration responses, the trial functions for axial, transverse deflections and rotation of the cross-sections are expressed in polynomial forms. Various boundary conditions considered in the study are satisfied by adding auxiliary functions to the displacement functions. The resulting time-dependent equations of motion are solved with the help of the implicit time integration Newmark-β method. At the same time, free vibration frequencies are presented. Some numerical results are provided in tabular form and in figures to examine the effects of the material gradation, moving load velocity, aspect ratio and different boundary conditions on the dynamic responses of BDFG beam.

On the role of shear deformation in dynamic behavior of a fully saturated poroelastic beam traversed by a moving load

Dynamic response of poroelastic beams acted upon by a moving point load accounting for shear deformation is of concern. The porous medium is fully saturated and only longitudinal diffusion is allowed. To this end, based on the Biot׳s consolidation theory and Timoshenko beam model, the transverse equations of motion of the poroelastic beam-like structures are derived. For simply supported beam-like structures, the explicit expressions of the transverse displacement and pore pressure are obtained. The effects of length to thickness ratio, moving load velocity, permeability coefficient, and fluid viscosity on the maximum dynamic response are comprehensively examined. The roles of the crucial factors on the discrepancies between the predicted results by the Euler–Bernoulli beam theory and those of the Timoshenko beam theory are also displayed and discussed. The obtained results display the importance of the shear deformation for deep poroelastic beams acted upon by the moving loads with high velocities.

Modeling and active vibration suppression of a single-walled carbon nanotube subjected to a moving harmonic load based on a nonlocal elasticity theory

This paper investigates active vibration suppression of a single-walled carbon nanotube (SWCNT) under the action of a moving harmonic load using Eringen’s nonlocal elasticity theory. The SWCNT is modeled according to the nonlocal Euler–Bernoulli beam theory. A Dirac-delta function is used to describe the position of the moving load along the SWCNT. Next, a linear classical optimal control algorithm with displacement-velocity feedback is used to suppress vibration in the SWCNT with control forces acting as actuators. The effects of a small-scale parameter, slenderness ratio, moving load velocity, and the excitation frequency of a moving load on the dynamic deflection of the SWCNT are examined. Finally, the ability of the control algorithm to suppress the response of the SWCNT under the effects of a moving load with a number of controlled modes and control forces is surveyed.

Dynamic analysis of functionally graded truncated conical shells subjected to asymmetric moving loads

The dynamic behavior of functionally graded (FG) truncated conical shells subjected to asymmetric internal ring-shaped moving loads is studied. The material properties are assumed to have continuous variations in the shell thickness direction. The equations of motion are derived based on the first-order shear deformation theory (FSDT) using Hamilton׳s principle. The finite element method (FEM) together with Newmark׳s time integration scheme is employed to discretize the equations of motion in the spatial and temporal domain, respectively. The formulation and method of solution are validated by studying their convergence behavior and carrying out the comparison studies in the limit cases with existing solutions in the literature. Then, the influences of material graded index, radius-to-length ratio, semi-vertex angle, thickness, boundary conditions and moving load velocity on the dynamic behavior of the FG truncated conical shells are studied. In addition, the difference between the responses of the FG shells under symmetric and asymmetric loadings is compared.

Dynamic response of functionally graded plates in thermal environment under moving load

As a first endeavor, the dynamic response of functionally graded (FG) plates in thermal environment under a moving load is investigated. The formulation is derived based on the first-order shear deformation theory (FSDT), which includes the effects of initial thermal stresses induced by the thermal environment and also the elastic foundation. The material properties are assumed to be temperature-dependent and graded in the thickness direction. The initial thermal stresses are evaluated by means of the thermoelasticity theory. In order to develop a general solution procedure which can be employed for FG plates with general loading and boundary conditions, the finite element method (FEM) together with Newmark’s time integration scheme is adopted. The formulation and method of solution are validated by studying their convergence behavior and performing the comparison studies with existing results in the literature in the limit cases. Finally, the influences of temperature rise, material graded index, moving load velocity, elastic foundation parameters and boundary conditions on the dynamic behavior of FG plates in thermal environment and subjected to moving load is presented.