Dynamic Response of Fractionally Damped Viscoelastic Plates Subjected to a Moving Point Load

2020 ◽  
Vol 142 (4) ◽  
Author(s):  
Rajendra Kumar Praharaj ◽  
Nabanita Datta ◽  
Mohammed Rabius Sunny
Keyword(s):  
Dynamic Response ◽  
Fractional Derivative ◽  
Dynamic Behavior ◽  
Moving Load ◽  
Viscoelastic Model ◽  
Point Load ◽  
Dynamic Amplification Factor ◽  
Modal Summation ◽  
Liouville Fractional Derivative ◽  
Dynamic Amplification

Abstract The dynamic response of fractionally damped viscoelastic plates subjected to a moving point load is investigated. In order to capture the viscoelastic dynamic behavior more accurately, the material is modeled using the fractionally damped Kelvin–Voigt model (rather than the integer-type viscoelastic model). The Riemann–Liouville fractional derivative of order 0 < α ≤ 1 is applied. Galerkin's method and Newton–Raphson technique are used to evaluate the natural frequencies and corresponding damping coefficients. The structure is subject to a moving point load, traveling at different speeds. The modal summation technique is applied to generate the dynamic response of the plate. The influence of the order of the fractional derivative on the free and transient vibrations is studied for different velocities of the moving load. The results are compared with those using the classical integer-type Kelvin–Voigt viscoelastic model. The results show that an increase in the order of the fractional derivative causes a significant decrease in the maximum dynamic amplification factor, especially in the “dynamic zone” of the normalized sweep time. The dynamic behavior of the plate is verified with ansys.

scholarly journals Dynamic Behavior of a Bidirectional Functionally Graded Sandwich Beam under Nonuniform Motion of a Moving Load

2020 ◽  
Vol 2020 ◽  
pp. 1-15 ◽  
Author(s):  
Dinh Kien Nguyen ◽  
An Ninh Thi Vu ◽  
Ngoc Anh Thi Le ◽  
Vu Nam Pham
Keyword(s):  
Dynamic Response ◽  
Dynamic Behavior ◽  
Moving Load ◽  
Sandwich Beam ◽  
Point Load ◽  
Functionally Graded ◽  
Beam Model ◽  
Material Distribution ◽  
Aspect Ratios ◽  
Nonuniform Motion

A bidirectional functionally graded Sandwich (BFGSW) beam model made from three distinct materials is proposed and its dynamic behavior due to nonuniform motion of a moving point load is investigated for the first time. The beam consists of three layers, a homogeneous core, and two functionally graded face sheets with material properties varying in both the thickness and longitudinal directions by power gradation laws. Based on the first-order shear deformation beam theory, a finite beam element is derived and employed in computing dynamic response of the beam. The element which used the shear correction factor is simple with the stiffness and mass matrices evaluated analytically. The numerical result reveals that the material distribution plays an important role in the dynamic response of the beam, and the beam can be designed to meet the desired dynamic magnification factor by appropriately choosing the material grading indexes. A parametric study is carried out to highlight the effects of the material distribution, the beam layer thickness and aspect ratios, and the moving load speed on the dynamic characteristics. The influence of acceleration and deceleration of the moving load on the dynamic behavior of the beam is also examined and highlighted.

scholarly journals Damped dynamic response of strengthened beams by composite coats under moving force by FEM

2018 ◽  
Vol 106 (2) ◽  
pp. 206
Author(s):  
Abdennacer Chemami ◽  
Youcef Khadri ◽  
Sabiha Tekili ◽  
El Mostafa Daya ◽  
Ali Daouadji ◽  
...  
Keyword(s):  
Dynamic Response ◽  
Numerical Study ◽  
Moving Load ◽  
Damping Ratio ◽  
Time Integration ◽  
Superposition Method ◽  
Dynamic Amplification Factor ◽  
Aluminum Composite ◽  
Strengthened Beam ◽  
Dynamic Amplification

This paper presents a numerical study of the free and damped forced vibration of simply-supported beams with composite coats subjected to a moving load by use of finite elements method. Three types of beam configurations, aluminum, composite and strengthened beam are investigated. The equation of motion of the beam is solved using the modal superposition method and integrated by applying the Newmark time integration procedure. Good agreements were achieved between the FEM and analytical solutions. The damped dynamic response, critical velocities and the dynamic amplification factor of the beam are calculated for different parameters such as the thickness ratio, the fiber orientation of the coat and damping ratio.

scholarly journals Effect of temperature and porosities on dynamic response of functionally graded beams carrying a moving load

2017 ◽  
Vol 20 (K2) ◽  
pp. 24-33
Author(s):  
Tuyen Van Bui
Keyword(s):  
Dynamic Response ◽  
Temperature Rise ◽  
Material Properties ◽  
Amplification Factor ◽  
Moving Load ◽  
Functionally Graded ◽  
Effect Of Temperature ◽  
Element Formulation ◽  
Dynamic Amplification Factor ◽  
Dynamic Amplification

The effect of temperature and porosities on the dynamic response of functionally graded beams carrying a moving load is investigated. Uniform and nonlinear temperature distributions in the beam thickness are considered. The material properties are assumed to be temperature dependent and they are graded in the thickness direction by a power-law distribution. A modified rule of mixture, taking the porosities into consideration, is adopted to evaluate the effective material properties. Based on Euler-Bernoulli beam theory, equations of motion are derived and they are solved by a finite element formulation in combination with the Newmark method. Numerical results show that the dynamic amplification factor increases by the increase of the temperature rise and the porosity volume fraction. The increase of the dynamic amplification factor by the temperature rise is more significant by the uniform temperature rise and for the beam associated with a higher grading index.

scholarly journals Dynamic Behavior of Tied-Arch Bridges under the Action of Moving Loads

2016 ◽  
Vol 2016 ◽  
pp. 1-17 ◽  
Author(s):  
Paolo Lonetti ◽  
Arturo Pascuzzo ◽  
Alessandro Davanzo
Keyword(s):  
Dynamic Behavior ◽  
Structural Characteristics ◽  
Moving Load ◽  
Sensitivity Analyses ◽  
Impact Factors ◽  
Moving Loads ◽  
Centripetal Acceleration ◽  
Design Variables ◽  
Dynamic Amplification ◽  
Arch Bridges

The dynamic behavior of tied-arch bridges under the action of moving load is investigated. The main aim of the paper is to quantify, numerically, dynamic amplification factors of typical kinematic and stress design variables by means of a parametric study developed in terms of the structural characteristics of the bridge and moving loads. The basic formulation is developed by using a finite element approach, in which refined schematization is adopted to analyze the interaction between the bridge structure and moving loads. Moreover, in order to evaluate, numerically, the influence of coupling effects between bridge deformations and moving loads, the analysis focuses attention on usually neglected nonstandard terms in the inertial forces concerning both centripetal acceleration and Coriolis acceleration. Sensitivity analyses are proposed in terms of dynamic impact factors, in which the effects produced by the external mass of the moving system on the dynamic bridge behavior are evaluated.

Dynamic response of bridges under travelling loads

1993 ◽  
Vol 20 (2) ◽  
pp. 287-298 ◽  
Author(s):  
J. L. Humar ◽  
A. M. Kashif
Keyword(s):  
Dynamic Response ◽  
Rational Design ◽  
Weight Ratio ◽  
Experimental Investigations ◽  
Speed Ratio ◽  
Force Model ◽  
Beam Model ◽  
Dynamic Amplification Factor ◽  
Design Procedures ◽  
Dynamic Amplification

In spite of a number of analytical and experimental investigations on the dynamic response of bridges to moving vehicle loads, the controlling parameters that govern the response have not been clearly identified. This has, in turn, inhibited the development of rational design procedures. Based on an analytical investigation of the response of a simplified beam model traversed by a moving mass, the present study identifies the governing parameters. The results clearly show why attempts to correlate the response to a single parameter, either the span length or the fundamental frequency, are unsuccessful. Simple design procedures are developed based on relationships between the speed ratio, the weight ratio, and the dynamic amplification factors; and a set of design curves are provided. Key words: dynamic response of bridges, vehicle–bridge interaction, moving force model, moving sprung mass model, dynamic amplification factor.

Dynamic response of Euler–Bernoulli beam resting on fractionally damped viscoelastic foundation subjected to a moving point load

2020 ◽  
Vol 234 (24) ◽  
pp. 4801-4812 ◽  
Author(s):  
Rajendra K Praharaj ◽  
Nabanita Datta
Keyword(s):  
Dynamic Response ◽  
Fractional Derivative ◽  
Fractional Order ◽  
Point Load ◽  
Order Derivative ◽  
Viscoelastic Foundation ◽  
Bernoulli Beam ◽  
Integer Order ◽  
Foundation Model ◽  
Euler Bernoulli Beam

The dynamic behaviour of an Euler–Bernoulli beam resting on the fractionally damped viscoelastic foundation subjected to a moving point load is investigated. The fractional-order derivative-based Kelvin–Voigt model describes the rheological properties of the viscoelastic foundation. The Riemann–Liouville fractional derivative model is applied for a fractional derivative order. The modal superposition method and Triangular strip matrix approach are applied to solve the fractional differential equation of motion. The dependence of the modal convergence on the system parameters is studied. The influences of (a) the fractional order of derivative, (b) the speed of the moving point load and (c) the foundation parameters on the dynamic response of the system are studied and conclusions are drawn. The damping of the beam-foundation system increases with increasing the order of derivative, leading to a decrease in the dynamic amplification factor. The results are compared with those using the classical integer-order derivative-based foundation model. The classical foundation model over-predicts the damping and under-predicts the dynamic deflections and stresses. The results of the classical (integer-order) foundation model are verified with literature.

Dynamic Response of High Steep Rock Slopes Based on Wenchuan Near-Field Seismic Motion Characteristics

2010 ◽  
Vol 168-170 ◽  
pp. 1090-1097
Author(s):  
Shi Guo Xiao ◽  
Wen Kai Feng
Keyword(s):  
Numerical Analysis ◽  
Dynamic Response ◽  
Amplification Factor ◽  
Near Field ◽  
Seismic Load ◽  
Rock Slopes ◽  
Dynamic Amplification Factor ◽  
Seismic Motion ◽  
Dynamic Amplification ◽  
Motion Characteristics

Near-field seismic motion characteristics are analyzed in accordance with records of the 2008 Ms8.0 Wenchuan Earthquake measured at Wolong Station, upon which the determination of seismic load is introduced. Dynamic response features, such as acceleration, displacement and stress, of high steep rock slopes on the banks of Zipingpu Reservoir at a variety of locations resulting from horizontal seismic force are analyzed with a numerical analysis routine. The dynamic amplification factor on the slope top is determined, leading to a characterization of the mode of failure of the high steep slope. Analyses show that the dynamic amplification factor at the top of the slopes is about 1.34; however, dynamic response deformation features and stress state at different positions on the slope vary. Earthquake damage of the high steep rock slopes consists mainly of partial avalanche of the rock mass at the top of the slopes by joint cutting. Field investigations after the earthquake have partially confirmed the numerical analysis results presented in this paper.

Dynamic Response of Multi-bay Frames Subjected to Successive Moving Forces

2019 ◽  
Vol 19 (04) ◽  
pp. 1950042
Author(s):  
Salih Demirtas ◽  
Hasan Ozturk ◽  
Mustafa Sabuncu
Keyword(s):  
Finite Element ◽  
Dynamic Response ◽  
Moving Load ◽  
Single Point ◽  
Vertical Direction ◽  
Point Load ◽  
Dynamic Responses ◽  
Moving Loads ◽  
Element Analysis ◽  
Constant Interval

This paper investigates the dynamic responses of multi-bay frames with identical bay lengths subjected to a transverse single moving load and successive moving loads with a constant interval at a constant speed. The effects of the bay length and the speed of the moving load on the response of the multi-bay frame subjected to a single point load are investigated numerically by the finite element method. A computer code is developed by using MATLAB to perform the finite element analysis. The Newmark method is employed to solve for the dynamic responses of the multi-bay frame. With this, the dynamic response of the frame subjected to successive moving loads with a constant interval is investigated. Also, the resonance and cancellation speeds are determined by using the 3D relationship of speed parameter-force span length to beam length ratio-dynamic magnification factor and the associated contour lines. The maximum impact factor of a 1-bay frame and multi-bay frames under single moving load are determined at the specific speed parameters. Those values are independent of elastic modulus, area moment of inertia, beam/column lengths of the frame and also the number of bays forming the frame. It is also found that the first resonance response in the vertical direction of the frame is related to the second mode of vibration.

Dynamic Behaviour of Minimum Platforms Under Random Seas

2003 ◽  
Author(s):  
Micaela Pilotto ◽  
Beverley F. Ronalds
Keyword(s):  
Dynamic Response ◽  
Dynamic Behaviour ◽  
Amplification Factor ◽  
Finite Element Models ◽  
Dynamic Amplification Factor ◽  
Maximum Value ◽  
Random Seas ◽  
Exponential Stretching ◽  
Structural Configurations ◽  
Dynamic Amplification

This paper describes the dynamic response of minimum facilities with different structural configurations which are subjected to random seas. The finite element models are kept simple with the aim of focusing on the physics of the phenomena involved. The response is studied in terms of the dynamic amplification factor (DAF), representing the ratio between the dynamic and the static response. Two different formulations of the DAF under random seas are compared. The first is defined in terms of standard deviation (DAF1), the second in terms of the most probable maximum value (DAF2). Ringing is observed to be a relevant feature of the dynamic response and to affect primarily the braced monopod configurations. Ringing is detected using DAF2. The paper also addresses the importance of the kinematic representation above the still water level. Different methods of stretching the velocity field in the wave zone (delta, Wheeler and exponential stretching) are shown to have a significant impact on the dynamic response of the platforms.

scholarly journals Dynamic Response and Robustness Evaluation of Cable-Supported Arch Bridges Subjected to Cable Breaking

2021 ◽  
Vol 2021 ◽  
pp. 1-14
Author(s):  
Guotao Shao ◽  
Hui Jin ◽  
Ruinian Jiang ◽  
Yue Xu
Keyword(s):  
Dynamic Response ◽  
Evaluation Method ◽  
Progressive Collapse ◽  
Bending Moment ◽  
Simulation Method ◽  
Dynamic Amplification Factor ◽  
Cable System ◽  
Evaluation Indexes ◽  
Dynamic Amplification ◽  
Arch Bridges

Cable-supported arch bridges have had many cable break accidents, which led to dramatic deck damage and even progressive collapse. To investigate the dynamic response and robustness of cable-supported arch bridges subjected to cable breaking, numerical simulation methods were developed, compared, and analyzed, and an effective and accurate simulation method was presented. Then, the cable fracture of a prototype bridge was simulated, and the dynamic response of the cable system, deck, and arch rib was illustrated. Finally, the robustness evaluation indexes of the cable system, deck, and arch rib were constructed, and their robustness was evaluated. The results show that the dynamic response of the adjacent cables is proportional to the length of the broken cable, while the dynamic response of the deck is inversely proportional to the length of the broken cable. The dynamic amplification factor of the cable tension and deck displacement is within 2.0, while that of the arch rib bending moment exceeds 2.0. The break of a single cable will not trigger progressive collapse. When subjected to cable breaking, the deck system has the least robustness. The proposed cable break simulation procedure and the robustness evaluation method are applicable to both existing and new cable-supported bridges.

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