Maximum Dynamic Deflection Research Articles

Vehicle–Bridge Coupling Vibration of Long-Span Concrete-Filled Steel Tubular Arch Bridge

An increase in the nonlinearity of the bridge will lead to a more obvious vehicle–bridge interaction effect and affect the vehicle response and driving comfort as the span increases. This paper establishes a refined finite element model of vehicle–bridge coupling for the 575 m long-span concrete-filled steel tubular arch bridge, Pingnan Third Bridge. Coupling vibration responses under different vehicle speeds, vehicle weights and road conditions of this bridge is analyzed. Then its comfort is assessed according to the comfort criterion. The results show that the vehicle–bridge coupling model has good agreement with the field test. The dynamic response of the bridge within the speed limit has no significant linear relationship with the magnitude of the vehicle speed without considering the pavement class. When the vehicle exceeds the speed limit, the dynamic response increases sharply with the increase in speed. The increase in vehicle weight leads to an increase in the maximum dynamic deflection of the bridge and a decrease in the impact coefficient, but the actual total response of the bridge does not decrease. The worse the road surface condition, the more dramatic the dynamic response of the bridge structure, taking into account the road surface level.

An analytical study on vortex-induced vibrations of cylinders with variable cross-section in the range of low Reynolds numbers

In the current paper, vortex-induced oscillations of circular cylinders with variable have been investigated. Considering the von-Kármán nonlinear strain-displacement relations and using the displacement coupling model to simulate the system and fluid-structure interaction, the nonlinear differential equations governing the motion have been derived using Hamilton’s principle. To apply the effect of vortices on the system vibrations, the nonlinear Van der Pol oscillator equation has been used. Then, using the Galerkin method, differential equations with partial derivatives are discretized, and nonlinear differential relations are solved by the Runge-Kutta approach. Finally, the response of the system, the phase curves, and the changes in the maximum amplitude according to the fluid velocity are obtained for various parameters, and the results have been discussed. Regarding the obtained results, changes in the cross-section of the beam have a significant effect on the lock-in region and also the maximum deflection of the beam. The maximum dynamic deflection for θ = 2° occurs at the velocity u = 2 , which is equal to 0.927. Also, the lock-in phenomenon is created for the beam with θ = 2.5° and θ = 3° at the velocities u = 2.78 and u = 4.23 , respectively.

Dynamic Response of an Elastic Tube-like Nanostructure Embedded in a Vibrating Medium and under the Action of Moving Nano-Objects

In recent years, researchers have looked at how tube-like nanostructures respond to moving loads and masses. However, no one has explored the scenario of a nanostructure embedded in a vibrating medium used for moving nano-objects. In this study, the governing equations of the problem are methodically derived using the nonlocal elasticity of Eringen as well as the Rayleigh and Reddy–Bickford beam theories. Analytical and numerical solutions are developed for capturing the nonlocal dynamic deflection of the nanostructure based on the moving nanoforce approach (excluding the inertia effect) and the moving nanomass approach (including the inertia effect), respectively. The results predicted by the established models are successfully verified with those of other researchers in some special cases. The results reveal that for low velocities of the moving nano-object in the absence of the medium excitation, the midspan deflection of the simply supported nanotube exhibits an almost symmetric time-history curve; however, by increasing the nano-object velocity or the medium excitation amplitude, such symmetry is violated, mainly due to the lateral inertia of the moving nano-object, as displayed by the corresponding three-dimensional plots. The study addresses the effects of the mass and velocity of the moving nano-object, amplitude, and frequency of the medium excitation, and the lateral and rotational stiffness of the nearby medium in contact with the nanostructure on the maximum dynamic deflection. The achieved results underscore the significance of considering both the inertial effect of the moving nano-object and the shear effect of stocky nanotubes embedded in vibrating media. This research can serve as a strong basis for conducting further investigations into the vibrational properties of more intricate tube-shaped nanosystems that are embedded in a vibrating medium, with the aim of delivering nano-objects.

Bridge Performance Recovery Test after Strengthening with a Prestressed CFRP Laminate

This paper introduces the strengthening of a concrete bridge using a CFRP laminate anchorage system and describes the static and dynamic test process, including the loading method and the test results. This paper compares the stress, strain, and deformation of each key section before and after reinforcement under static loads, moving loads, braking vehicles, and jumping vehicles to demonstrate the strengthening effect of the bridge and the performance of the CFRP laminate. The CFRP laminate anchorage system effectively restores the structural elastic properties of the bridge, enabling the prestressed CFRP laminates and the bridge structure to synergistically function as a composite, exhibiting exceptional operational performance. After reinforcement, the maximum dynamic deflection in the middle span after reinforcement decreases by 25.73%, and the maximum dynamic strain in the middle span decreases by 18.00%; under the jumping vehicle, the damping ratio decreases by 43.69%. By strengthening with prestressed CFRP, the original damaged bridge can have its performance restored and its service life extended, and the need for bridge demolition and reconstruction is avoided. This brings about social benefits by saving raw materials, reducing demolition waste, and protecting the environment.

Sensitivity analysis of vibration response of timoshenko beam to mass ratio and velocity of moving mass and boundary conditions: Semi-analytical approach

In real-world physics phenomena, the boundary conditions of structural members in the structural beam systems affect the system response. Also, moving load or mass problems are used widely in many engineering fields, such as structural, transportation, mechanical engineering, etc. Therefore, it is necessary to study the effect of boundary conditions on beam vibrations. Hence, a semi-analytical approach for the Timoshenko beam with various boundary conditions under moving mass is presented in this paper. Dynamic Green Function is introduced for modeling the beam under moving mass. An accurate formulation is illustrated for modeling a Timoshenko beam under moving mass with different boundary conditions. Finally, some examples demonstrate to assess of the effect of different boundary conditions, the mass ratio of moving mass, and the speed of moving mass. The numerical results are shown the efficiency and simplicity of the present approach. Based on the results, it is found that the mass ratio affects the dynamic response shape. For moving mass, the delay of the maximum dynamic deflection with respect to the mass position, increases with the speed at the higher speeds. But for smaller values of the speed, the same results of the maximum dynamic deflection for the moving load model along with the moving mass model are obtained. On the other hand, the maximum dynamic deflection points of the curves move slightly towards the right end of the beam with an increasing mass ratio. Also, the location of the constraint in the asymmetric beams is more significant in dynamic response. It is found that the dynamic behavior of the beam under moving mass changes dramatically based on the type of boundary conditions. Furthermore, the displacement obtained for each boundary condition decreases with increasing mass speed.

ОПРЕДЕЛЕНИЕ ВЯЗКОУПРУГИХ ХАРАКТЕРИСТИК ЭЛЕМЕНТОВ МНОГОСЛОЙНЫХ КОНСТРУКЦИЙ НА ОСНОВЕ АНАЛИЗА ДИССИПАЦИИ ЭНЕРГИИ

The deteriorating operating conditions of roads is one of the most important problems facing specialists in the road industry. It is mainly associated with a reduction in the rigidity of road pavements made as extended multi-layer structures. To identify the causes of rigidity reduction, non-destructive testing is used, which is based on solving the inverse coefficient problem of restoring the elastic constants based on the response on the surface. Purpose of the study: We aimed to provide a rationale for a new pavement condition indicator that would take into account the history of deformation and loading from a source on the surface, based on which it would be possible to solve the inverse problem of restoring the elastic and viscous characteristics of pavement layers. Methods: To do that, we performed mathematical modeling of the stress-strain state of a multi-layer medium based on the solution of a system of dynamic Lame equations. Viscosity is taken into account by introducing tangents of the angles of wave energy losses in the materials of layers. Results: The results obtained in modeling for the first time made it possible to establish the relationship between changes in the modulus of elasticity as well as tangents of the angles of energy losses in pavement layers and the amount of energy dissipation in the structure. Discussion: It should be noted that it is possible to switch from the bowl of maximum dynamic deflections as the main pavement condition indicator to the analysis of hysteresis loops on the road structure surface, recorded at different distances from the point of load application and being an analogue of the full bowl of dynamic deflections showing the history of the test object loading.

Energy absorption and vibration of smart auxetic FG porous curved conical panels resting on the frictional viscoelastic torsional substrate

In recent years, the utilization of various methods to absorb vibration in widely-used structures has gained significant attention to control and reduce the destructive effect of the resonance phenomenon. The increased useful lifetime and reduced maintenance and repair costs are the advantages of vibration absorption. Besides, utilization of energy absorbers is one of the most effective strategies for reducing energy supply costs for different parts of the structure, such as sensors. In this regard, a numerical study is performed in this research to evaluate the energy absorption by vibrations' absorption in a conical three-layered panel located on a viscoelastic substrate. This three-layered panel is composed of three parts: piezoelectric upper layer reinforced with Graphene nanoplatelets (GPLs), auxetic core, and functionally graded material (FGM) porous lower layer. The substrate includes spring element, shear, torsion, and substrate-structure friction factor. Hamilton's principle and energy method have been used to extract the governing equations to model the first-order shear deformation theory (FSDT) for the presented structure. The Differential Cubature Method (DCM) and the Newmark method have been used to solve the governing equations. Results show that by applying the negative voltage to the sandwich conical panel, the in-plane compression forces and natural frequency are increased, while the maximum dynamic deflection is decreased. Furthermore, increasing the inherent damping coefficient increases the damping decrement. Meanwhile, the nonlinear scattering and increased dispersion concentration of GPLs near the upper and lower surfaces of the piezoelectric layer will increase the frequency and energy absorption. Besides, the increased friction factor of the viscoelastic substrate and sandwich cone leads to more absorption energy.

Rear-End Impacts - Part 2: Sled Pulse Effect on Front-Seat Occupant Responses

<div class="section abstract"><div class="htmlview paragraph">This study was conducted to assess the effects of differing rear impact pulse characteristics on restraint performance, front-seat occupant kinematics, biomechanical responses, and seat yielding. Five rear sled tests were conducted at 40.2 km/h using a modern seat. The sled buck was representative of a generic sport utility vehicle. A 50<sup>th</sup> percentile Hybrid III ATD was used. The peak accelerations, acceleration profiles and durations were varied. Three of the pulses were selected based on published information and two were modeled to assess the effects of peak acceleration occurring early and later within the pulse duration using a front and rear biased trapezoidal characteristic shape.</div><div class="htmlview paragraph">The seatback angle at maximum rearward deformation varied from 46 to 67 degrees. It was lowest in Pulse 1 which simulates an 80 km/h car-to-car rear impact. The seatback plastic deformation was greater in the pulse with the rear biased trapezoidal acceleration profile, Pulse 4, than in the front biased trapezoidal acceleration profile, Pulse 5 (46 degrees v 41 degrees). Coincidingly, the longitudinal head displacement was slightly greater in the Pulse 4. There was limited relative motion between the ATD torsos and the seatbacks. The relative motion between the ATD torso and the seatback was less than 7 cm in all tests. The head, chest and pelvis peak acceleration and timing varied depending on the pulse. All peak head, chest, pelvis and upper and lower-neck moments occurred prior to maximum seatback dynamic deflection. The biomechanical responses were all well below injury assessment reference values. The seatback structural restitution was the highest in Pulse 1 which had the lowest amount of dynamic and plastic seatback deformation and had the highest lap belt load. All peak belt loads occurred in the rebound phase of the ATD.</div><div class="htmlview paragraph">The sled coordinate-based data was used to determine the effective restraint stiffness. The results were used to develop a spring-mass model. The model will help understand the effects of pulse characteristics on predicted chest acceleration for future research.</div><div class="htmlview paragraph">In conclusion, the results from this study show that pulse shape has a measurable effect of seat and ATD kinematics in high-speed rear impacts and should considered for future research and testing.</div></div>

The forced vibration of infinitely long cylinders reinforced by carbon nanotubes subjected to combined internal and ring‐shaped compressive pressures

In this study, the forced vibration of cylinders reinforced by carbon nanotubes (CNTs) under a moving load is estimated based on the theory of oscillations. The composite cylinders reinforced with CNTs of infinite length subjected to combined action of the internal pressure and ring‐shaped compressive pressure with constant velocity. Here, we consider uniform and nonuniform reinforcement distributions, with the mechanical properties varying linearly throughout the thickness and the effective material properties are estimated by employing the extended rule of mixture. Following the formulation of the problem, the basic equations are derived and then solved in order to determine the maximum static and dynamic deflections, dynamic factors, and critical velocity of composite cylinders reinforced with CNTs. After checking the reliability of the proposed formulation and the accuracy of the results in accordance with the available literature, a systematic study is aimed at checking the sensitivity of the dynamic response to the geometry, velocity, type of distribution, and volume fraction of CNTs.

Dynamic deflection of concrete plate in semi-rigid supports and various damping condition

There are numerous researches about the dynamic behaviour of concrete plate. Most of them are done with the assumptions of simply supported supports along its edge. This study will calculate the dynamic deflection of isotropic concrete plate in semi-rigid support condition along the edges. The damping ratio will be varied to analyse how much it affects the dynamic deflection. The free vibration solution will be done with Modified Bolotin Method to solve the transcendental equations. The load subjected to plate, as the forced vibration, is the dynamic moving load considered as vehicle’s load on the road, moving along the mid-side of the plate with constant velocity. The result shows that damping ratio can reduce the dynamic deflection up to 48% at lower velocity (around 20-50 km/h); up to 30% at mid velocity (around 60-180 km/h); and up to 8% at upper velocity (around 190-200 km/h). Critical velocity is also analysed in this study. The critical velocity of this system is on 112 km/h which will conduct the maximum dynamic deflection on the plate. This result can be used as a basic for designing the plate efficiently yet safety for the users.

Forced vibration analysis of concrete slabs reinforced by agglomerated SiO2 nanoparticles based on numerical methods

Abstract In this research, forced vibration analysis of a concrete slab reinforced by SiO2 nanoparticles is investigated. The Mori-Tanaka low is used for obtaining the material properties of nano-composite structure and considering agglomeration effects. By means of third order shear deformation theory or Reddy theory, the total potential energy of system is calculated. Also, using Hamilton’s principle, the coupled motion equations are obtained. Based on the harmonic differential quadrature method (HDQM), finite element method (FEM) and Newmark method, the frequency response of system is calculated. The effects of volume percent and agglomeration of SiO2 nanoparticles, boundary conditions and geometrical parameters of structure are shown on the frequency response of system. Results show that with growing the volume percent of SiO2 nanoparticles up to 0.37, the linear frequency of the structure is increased and the maximum dynamic deflection is decreased.

Vibration Theoretical Analysis of Elastically Connected Multiple Beam System under the Moving Oscillator

To investigate the vibration analysis of elastically connected multiple beam system (ECMB) under the moving oscillator, finite sine‐Fourier transform has been applied to the dynamic partial differential equations of ECMB with respect to space coordinates. Then, the numerical integration has been used to solve the equations. Finally, the expression for vibration analysis of ECMB under the moving oscillator has been derived based on finite sine‐Fourier inverse transform. Using the method developed in this study and ANSYS numerical method, the vibration analysis of a four‐layer beam system under moving oscillator with different speeds has been calculated. The results show that the calculated results from the method developed in this study are in good agreement with the ANSYS numerical calculation results, and the differences between the two calculation results are all less than 2%, which verified the correctness of the method developed in this study. The method developed in this study has been applied to the beam‐rail system on a railway line in China. The effect of the train speed and interlayer stiffness on the vibration of beam‐rail system has been investigated. The results show that the maximum dynamic deflection of the rail under the train load is always near the midspan, while the maximum dynamic deflections of the track plate, base plate, and bridge occur after the train travel through the midspan. The interlayer stiffness has a larger impact on the vibration of the rail and the track plate and little impact on the vibration of the base plate and the bridge.

Thermo-resonance analysis of an excited graphene sheet using a new approach

Forced vibration of graphene nanoplate based on a refined plate theory in conjunction with higher-order nonlocal strain gradient theory in the thermal environment has been investigated. Regarding the higher-order nonlocal strain gradient theory, both stress nonlocality and size-dependent effects are taken into account, so the equilibrium equations which are governing on the graphene sheet have been formulated by the theory. The extracted equations will be solved by a closed-form approach by which maximum dynamic deflection has been obtained while all the edges are considered as simple boundaries. To approve the results of the plate theory, several available well-known references have been compared. Finally, after determining the accuracy of the equations, different parameters have been examined for showing the behavior of the nanoplate exposed to a transverse dynamic harmonic load.

Electromagnetic forced vibrations of composite nanoplates using nonlocal strain gradient theory

This article is intended to analyze forced vibrations of a piezoelectric-piezomagnetic ceramic nanoplate by a new refined shear deformation plate theory in conjunction with higher-order nonlocal strain gradient theory. As both stress nonlocality and strain gradient size-dependent effects are taken into account using the higher-order nonlocal strain gradient theory, the governing equations of the composite nanoplate are formulated. When the nanoplate is subjected to a transverse harmonic loading and all the edges are considered as simple boundaries, the governing equations can be solved with a closed-form solution, from which the maximum dynamic deflections are obtained. To validate the results of the new proposed plate theory, the comparisons between ours and the well-known papers in the literature are presented. The influences of different nonlocal parameters and material properties on the nanoplate’s dynamic responses are also studied.

Calibration Method for Dynamic Deflection Measurement of Bridges by Photogrammetry

Heavy vehicular traffic and aggressive environmental conditions can cause unexpected bridge deterioration, thus, periodic inspections to identify and assess possible defects are required. One indicator is the amount of vertical deflection that occurs during loading. Some different types of transducers can be used to measure the deflection. One of them is the photogrammetry. It is a typical noncontact measurement method. Unfortunately, it is difficult to calibrate this type of instruments. The key point is the evaluation of the dynamic deflection measurement capability. A dynamic calibration system of bridge photogrammetric measurement system was composed of the motorized linear stage, LED target and computer. The Fréchet distance was used as a model to evaluate the dynamic deflection measurement capability of bridge deflection photogrammetry. The photogrammetric bridge deflection measuring instruments are products of BIOET, which are used to carry out the measurement experiment. The results show that this system can calibrate the dynamic deflection measurement error of photogrammetric bridge deflection measuring instruments. Fréchet distance can reflect the relationship between the curves. This evaluation method is more accurate than the current evaluation method based on the error of indication of maximum dynamic deflection.

Damped forced vibration analysis of single-walled carbon nanotubes resting on viscoelastic foundation in thermal environment using nonlocal strain gradient theory

In this paper, the damped forced vibration of single-walled carbon nanotubes (SWCNTs) is analyzed using a new shear deformation beam theory. The SWCNTs are modeled as a flexible beam on the viscoelastic foundation embedded in the thermal environment and subjected to a transverse dynamic load. The equilibrium equations are formulated by the new shear deformation beam theory which is accompanied with higher-order nonlocal strain gradient theory where the influences of both stress nonlocality and strain gradient size-dependent effects are taken into account. In this new shear deformation beam theory, there is no need to use any shear correction factor and also the number of unknown variables is the only one that is similar to the Euler-Bernoulli beam hypothesis. The governing equations are solved by utilizing an analytical approach by which the maximum dynamic deflection has been obtained with simple boundary conditions. To validate the results of the new proposed beam theory, the results in terms of natural frequencies are compared with the results from an available well-known reference. The effects of nonlocal parameter, half-wave length, damper, temperature and material variations on the dynamic vibration of the nanotubes, are discussed in detail.

Seismic response of functionally graded-carbon nanotubes-reinforced submerged viscoelastic cylindrical shell in hygrothermal environment

The current work suggests mathematical model for the seismic response of submerged cylindrical shells subjected to hygrothermal load. The structural damping effects are considered based on Kelvin-Voigt model. The cylindrical shell is reinforced by functionally graded (FG)-carbon nanotubes (CNTs) and carbon fibers where the Halpin-Tsai model is used for calculating the effective material properties of the structure. The acoustic wave equation is utilized for the effect of the fluid around the structure. The problem is framed combining shell motion equations with the acoustic wave equation where the fluid-loaded terms are considered with Hankel function of second kind. The equations of motion are derived based on Reddy shear deformation theory (RSDT) in conjunction with energy method and Hamilton's principle. The dynamic deflection of the structure is obtained using differential quadrature method (DQM) and Newmark approach. The effects of fluid, boundary condition, thermal load, moisture changes, structural damping parameter, length to thickness ratio of shell, CNTs volume percent and distribution type are shown on the dynamic deflection of the structure. The results show that with increasing the CNTs volume percent, the dynamic deflection decreases. In addition, the FG-X type (FGX) distribution of CNTs for the submerged cylindrical shell is the best choice among the FG-O type (FGO), FG-V type (FGV) and uniform distributions. Furthermore, the maximum dynamic deflection of the structure increases where the structure is in the hygrothermal environment.

Dynamic analysis of concrete beams reinforced with Tio 2 nano particles under earthquake load

This research studies the dynamic analysis of a concrete column reinforced with titanium dioxide (TiO2) nanoparticles under earthquake load. The effect of nanoparticles accumulation in a region of concrete column is examined using Mori-Tanaka model. The structure is simulated mathematically based on the theory of sinusoidal shear deformation theory (SSDT). By calculating strain-displacement and stress-strain relations, the system energies include potential energy, kinetic energy, and external works are derived. Then, using the Hamilton\'s principle, the governing equations for the structure are extracted. Using these equations, the response of the concrete column under earthquake load is investigated using the numerical methods of differential quadrature (DQ) and Newark. The purpose of this study is to study the effects of percentage of nanoparticles, nanoparticles agglomeration, geometric parameters and boundary conditions on the dynamic response of the structure. The results indicate that by increasing the volume percent of TiO2 nanoparticles, the maximum dynamic deflection of the structure decreases.

Parametric study of dynamic response of sandwich plate under moving loads

Constrained layer damper is widely used in engineering applications to suppress the severe vibration of structural systems, especially for the cases with moving loads, such as sandwich beam or sandwich plate. The response analysis and parametric analysis of these sandwich structures under moving loads have not still understood comprehensively. To do this, a hybrid approach based on extended Rayleigh-Ritz solution together with penalty method and differential quadrature method is presented to predict the dynamic responses of sandwich plate with isotropic face plate and a viscoelastic core subjected to moving loads. Both the energy terms related to the sandwich plate and the energy terms introduced by boundary conditions are derived based on the first order shear deformation theory (FSDT) and expressed using the Rayleigh-Ritz solutions, and then the governing equation of motion of sandwich plate is obtained through Lagrange equation, which can model a sandwich plate with various boundary conditions. Different with classical Rayleigh-Ritz solutions, the admissible functions adopted here is a set of combination of simple polynomials and trigonometric functions, which just satisfy a totally unconstrained boundary condition, and penalty method is applied to handle constraints. Then the variations of the natural frequency, associated modal loss factor and vibration response with the parameters (such as thicknesses of constrained layer and damping layer, elastic modulus of constrained layer material, and shear modulus and loss factor of damping layer material) of sandwich plate are studied. Moreover, the variations of maximum dynamic deflections with different boundary conditions as well as moving speeds are investigated.

Assessing Absolute Maximum Vibration Amplitude of a Rectangular Plate Subjected to a Moving Mass

Dynamic behavior of bridges under moving loads is a challenging engineering problem, which has attracted a great interest in a myriad of papers and books in structural dynamics field. In case of a slab-type bridge, a plate influenced by a traversing mass can reflect the full two-dimensional mechanical behavior of the supporting structure. This paper investigates absolute maximum response amplitude of a plate-type structure subject to a moving mass. To this end, the absolute maximum dynamic deflection of a rectangular plate under a moving mass is sought at all interior points of it, while the existing literature is restricted to capturing maximum values at the plate center point. Unlike the conventional methods that seek maximum dynamic response at the center point of the plate, extracting absolute maximum response—which does not necessarily take place at the center point—is an onerous task and computationally demanding. According to the findings of the current paper, accurate values of the plate maximum vibration amplitude significantly differ from those maximum responses obtained at the plate center point.