scholarly journals Vibrations of a Simply Supported Beam with a Fractional Viscoelastic Material Model – Supports Movement Excitation

2013 ◽  
Vol 20 (6) ◽  
pp. 1103-1112 ◽  
Author(s):  
Jan Freundlich
Keyword(s):  
Fractional Derivative ◽  
Viscoelastic Material ◽  
Material Model ◽  
Model Parameters ◽  
Beam Model ◽  
Euler Beam ◽  
Simply Supported Beam ◽  
Simply Supported ◽  
Liouville Fractional Derivative ◽  
Damping Model

The paper presents vibration analysis of a simply supported beam with a fractional order viscoelastic material model. The Bernoulli-Euler beam model is considered. The beam is excited by the supports movement. The Riemann – Liouville fractional derivative of order 0 α ⩽ 1 is applied. In the first stage, the steady-state vibrations of the beam are analyzed and therefore the Riemann – Liouville fractional derivative with lower terminal at −∞ is assumed. This assumption simplifies solution of the fractional differential equations and enables us to directly obtain amplitude-frequency characteristics of the examined system. The characteristics are obtained for various values of fractional derivative of order α and values of the Voigt material model parameters. The studies show that the selection of appropriate damping coefficients and fractional derivative order of damping model enables us to fit more accurately dynamic characteristic of the beam in comparison with using integer order derivative damping model.

Research on the Natural Frequency Solving Method of the Simply Supported Beam Bridge with Cracks

2013 ◽  
Vol 437 ◽  
pp. 51-55
Author(s):  
Ping Yi Sun ◽  
Yan Hua Wang ◽  
Han Bing Liu ◽  
Guo Jin Tan
Keyword(s):  
Natural Frequency ◽  
Natural Frequencies ◽  
Beam Model ◽  
Euler Beam ◽  
Simply Supported Beam ◽  
Simply Supported ◽  
Solution Methods ◽  
Element Approach ◽  
Experimental Values ◽  
Beam Bridge

Two kinds of natural frequency solution methods for the simply supported beam bridge with cracks are presented respectively based on the Bernoulli-Euler beam model and the finite element approach. Multiple groups of crack damages are supposed on the experimental simply supported steel I-beam, and the natural frequencies of the experimental beam are measured in all the crack cases. By comparing the calculated natural frequencies respectively obtained by the above two methods with the experimental values, the characteristics of the two kinds of natural frequency solving methods are evaluated.

Analysis of Natural Frequency of Simply Supported Beam with Vertical Elastic Constraint

2011 ◽  
Vol 141 ◽  
pp. 212-217
Author(s):  
Bo Geng ◽  
Miao Hu ◽  
Qi Chen Wang ◽  
Jin Zhou Lin ◽  
Dian Peng Li
Keyword(s):  
Vertical Direction ◽  
Least Square Method ◽  
Least Square ◽  
Beam Model ◽  
Euler Beam ◽  
Simply Supported Beam ◽  
Simply Supported ◽  
Nature Frequency ◽  
The Relationship ◽  
Elastic Constraint

Modal analysis of a simply supported beam with elastic support in vertical direction was conducted. Based on Bernoulli-Euler beam model, the first three nature frequency equations and the vibration mode function were obtained. And with different stiffness in vertical direction, the nature frequency equations were solved using numerical method, at the same time, curves of the relationship between support stiffness and nature frequency were acquired, and the corresponding functions were fitted with least square method simultaneously. Based on a typical beam structure, the accuracy of the functions was validated using finite element method, and the relative error was less than 3%.

Study on Flexibility of Intracranial Vascular Stents Based on the Finite Element Method

2018 ◽  
Vol 35 (4) ◽  
pp. 465-474 ◽  
Author(s):  
L. Liu ◽  
H. Jiang ◽  
Y. Dong ◽  
L. Quan ◽  
Y. Tong
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
Cantilever Beam ◽  
Beam Model ◽  
The Finite Element Method ◽  
Simply Supported Beam ◽  
Bending Deformation ◽  
Vascular Stents ◽  
Simply Supported ◽  
Loading Method

ABSTRACTFlexibility is a particularly important biomechanical property for intracranial vascular stents. To study the flexibility of stent, the following work was carried out by using the finite element method: Four mechanical models were adopted to simulate the bending deformation of stents, and comparative studies were conducted about the distinction between cantilever beam and simply supported beam, as well as the distinction between moment-loading method and displacement-loading method. A complete process as implanting a stent including compressing, expanding and bending was also simulated, for analyzing the effects of compressing and expanding deformation on stent flexibility. At the same time, the effects of the arrangement and the number of bridges on stent flexibility were researched. The results show that: 1. A same flexibility index was obtained from cantilever beam model and simply supported beam model; displacement-loading method is better than moment-loading for simulating the bending deformation of stents. 2. The flexibility of stent with compressing and expanding deformation is lower than that in the initial form. 3. Crossly arranging the neighboring bridges in axial direction, can effectively improve the stent flexibility and reduce the flexibility difference in various bending directions; the bridge number, has proportional non-linear correlation with the stent rigidity as well as the maximum moment required for bending the stent.

Analysis on Factors that Affect the Damping of Reinforced Concrete Beam under Hammering Method

2011 ◽  
Vol 374-377 ◽  
pp. 2130-2133
Author(s):  
Da Peng Gu ◽  
Wei Ming Yan ◽  
Yan Jiang Chen ◽  
Hai Xia Zhou
Keyword(s):  
Reinforced Concrete ◽  
Parameter Identification ◽  
Concrete Beam ◽  
Reinforced Concrete Beam ◽  
Rational Method ◽  
Beam Model ◽  
Dynamic Experiment ◽  
Simply Supported Beam ◽  
Dynamic Behaviors ◽  
Simply Supported

Abstract. Damping, as one of the most important indicators of the structure’s dynamic behaviors, depicts how energy dissipates during vibration. Using Hammering Method on Reinforced Concrete Simply Supported Beam model dynamic experiment, by analyzing the vibrating signals captured during hammering process, how the allocation of the sensors and the hammer strength affect the parameter identification can be revealed. A rational method of parameter identification can be presented as well.

Study on the Critical Plastic State of the Simply Supported Beam under Non-Linear Hardening Model

2012 ◽  
Vol 538-541 ◽  
pp. 453-457
Author(s):  
Guo Zhi Zhang ◽  
Jun Jing Fu
Keyword(s):  
Theoretical Models ◽  
Material Model ◽  
Plastic State ◽  
Element Analysis ◽  
Simply Supported Beam ◽  
Hardening Material ◽  
Simply Supported ◽  
Limit Model ◽  
The Finite Element Analysis ◽  
Curve Model

The plastic state of simply supported beam loaded by the uniformly distributed load was studied. When its material models are bilinear hardening material model and exponential hardening material model, its maximum limit model was established. Moreover, the critical curve model of the theoretical model of plastic zone was established. Furthermore, through comparing the finite element analysis results with the theoretical analysis results, the theoretical models established in the paper was verified.

Comparative Study on the Vertical Dynamic Responses of Simply Supported Beam Subjected to Two Typical Vehicle Models

2012 ◽  
Vol 178-181 ◽  
pp. 2424-2428
Author(s):  
Chun Sheng Shan ◽  
Wei Ye ◽  
Heng Li ◽  
Xiao Zhen Li
Keyword(s):  
High Speed ◽  
Damping Ratio ◽  
Dynamic Responses ◽  
Vehicle Speed ◽  
Vehicle Model ◽  
Euler Beam ◽  
Simply Supported Beam ◽  
Simply Supported ◽  
Systems Model ◽  
Mass Spring

A novel simplified vehicle model i.e. arbitrary moving mass-spring systems model, which can be simplified into moving loads model, is put forward and proved to be capable of analyzing the vertical dynamic responses of bernoulli-euler beam. Based on the matlab platform, a simply supported beam with a span of 40 m serviced in Beijing-Shanghai High-speed Railway is selected as the case study. The similarities and differences of vertical dynamic responses of the bridge based on this two vehicle models are compared. On this basis, the effects of vehicle speed and bridge damping ratio on the bridge’s dynamic magnification factor is studied. The computation results show that this new vehicle model is effective and reliable in its practical application.

scholarly journals Transient vibrations of a fractional Zener viscoelastic cantilever beam with a tip mass

Meccanica ◽  
2021 ◽  
Author(s):  
Jan Freundlich
Keyword(s):  
Fractional Derivative ◽  
Cantilever Beam ◽  
Viscoelastic Material ◽  
Material Model ◽  
Mixed System ◽  
Zener Model ◽  
Time Histories ◽  
Fractional Differential ◽  
Fractional Zener Model ◽  
Tip Mass

AbstractThe presented work concerns the kinematically excited transient vibrations of a cantilever beam with a mass element fixed to its free end. The Euler–Bernoulli beam theory and the fractional Zener model of the beam material are assumed. A fractional Caputo derivative is used to formulate a viscoelastic material law. A characteristic equation, modal frequencies, eigenfunction and orthogonality conditions are achieved for the beam considered. The equations of motion of the system are solved numerically. A numerical solution of a multi-term fractional differential equation is obtained by means of a conversion to a mixed system of ordinary and fractional differential equations, each of the order of $$0 < \gamma \le 1$$ 0 < γ ≤ 1 . The transient time histories of the beam vibrations during the passage through resonance are calculated. A comparison between the beam responses obtained with a fractional and an integer viscoelastic material model is presented. The calculations performed reveal that use of the fractional damping affects on the time histories of the system. The calculated beam responses show that for some values of the order of the fractional derivative $$\gamma$$ γ , the amplitudes occurring in the area of the second resonance are greater than those obtained in the area of the first resonance, which does not occur in the case of the integer order of the fractional derivative. Moreover, an evaluation is made of the difference between the results obtained for the calculations using the fractional Zener model and the fractional Kelvin model. It is shown that for some physical beam parameters, the calculation results obtained using both models are virtually the same for both models, which means that the the simpler, fractional Kelvin–Voigt material can be used instead of the fractional Zener material model. This simplifies the solution and decreases the time needed to make the numerical calculations.

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