Vibration Analysis of Simply Supported Beams Traversed by Uniformly Distributed Two-Layer Spring-Mass System

2014 ◽  
Vol 919-921 ◽  
pp. 1164-1168
Author(s):  
Yu Yang ◽  
Yan Wang ◽  
Yun Fang Yang
Keyword(s):  
Governing Equation ◽  
Vibration Analysis ◽  
Vertical Vibration ◽  
Dynamic Responses ◽  
Mass Ratio ◽  
Mass System ◽  
Simply Supported ◽  
Integral Methods ◽  
Linear Interpolating ◽  
Numerical Integral

Vertical vibration of identical simply supported bridges traversed by a train with uniformly distributed mass is investigated in this paper. The train with passengers onboard is simplified as a uniformly distributed two-layer spring-mass system as well as the bridges are simplified as consecutive simply supported Euler-Bernoulli beams. To analyze dynamic responses of the train and the bridges, the dynamic governing equation of the system is obtained and solved by a specific linear interpolating method and numerical integral methods. The result graphs indicate that dynamic responses of both beam and train carriage increase along with the mass ratio of bogie to car.

THEORETICAL OF DYNAMIC LOADING AGAINST WATER-FILLED SIMPLY SUPPORTED PIPES

2015 ◽  
Vol 75 (11) ◽  
Author(s):  
Roslina Mohammad ◽  
Astuty Amrin ◽  
Sallehuddin Muhamad
Keyword(s):  
Dynamic Behavior ◽  
Dynamic Loading ◽  
Transient Response ◽  
Governing Equation ◽  
Dynamic Models ◽  
Dynamic Responses ◽  
Perturbation Approach ◽  
Flowing Water ◽  
Euler Beam ◽  
Simply Supported

The primary aim of this study had been to investigate the effects of water-filled flow on the transient response of a simply supported pipe subjected to dynamically applied loading. The importance of this study is manifested in numerous applications, such as oil and gas transportations, where dynamic loading can be the result of an accident. The classical Bernoulli-Euler beam theory was adopted to describe the dynamic behavior of an elastic pipe and a new governing equation of a long pipe transporting gas or liquid was derived. This governing equation incorporated the effects of inertia, centrifugal, and Coriolis forces due to the flowing water. This equation can be normalized to demonstrate that only two non-dimensional parameters governed the static and the dynamic responses of the system incorporating a pipe and flowing water. The transient response of this system was investigated based on a standard perturbation approach. Moreover, it had been demonstrated that the previous dynamic models, which largely ignored the internal flow effects and interactions between the flow and the structure, normally produced a large error and are inapplicable to the analysis of many practical situations. One interesting effect identified was that at certain flow ratio, the system became dynamically unstable and any, even very small, external perturbation led to a growing unstable dynamic behavior. Such behavior, which is called pipe whip, is well-known to everyone who waters a garden using a flexible long hose.

Influence of Moving Vehicles on Vertical Vibration of Simply Supported Bridge

2013 ◽  
Vol 405-408 ◽  
pp. 1578-1586
Author(s):  
Yan Han ◽  
Xiao Dong Wang ◽  
Chao Qun Li
Keyword(s):  
Great Influence ◽  
Vertical Vibration ◽  
Dynamic Responses ◽  
Mass Action ◽  
Impact Factors ◽  
Inertia Force ◽  
Analysis Model ◽  
Euler Beam ◽  
Beam Dynamic ◽  
Simply Supported

Euler beam dynamic analysis model under moving loads and wheels plus spring-damper-sprung mass action were established respectively. The simply-supported beam motion control equations were derived and the corresponding simulation analysis procedures were worked out. The vertical dynamic responses of simply-supported bridge under typical vehicles at different speeds were studied systematically. Impact factors calculated from the two analysis model were compared with the values of the current bridge specifications. It is shown that vehicle inertia force has little effect on the vertical deflection and vertical vibration acceleration of the bridge, the vehicle impact effect on bridge gradually go up with the passing speed increasing, vehicle weight has great influence on the vertical vibration of the bridge. The problem of passing overloaded vehicles must be considered seriously in bridge design and use.

Analytical Solution for Vertical Dynamic Response of Railway Simply Supported Beam Bridge under Bidirectional Moving Loads

2012 ◽  
Vol 594-597 ◽  
pp. 1552-1556
Author(s):  
Wei Ye ◽  
Xiao Zhen Li ◽  
Hong Duan ◽  
Chun Sheng Shan ◽  
Xiao Han Liu
Keyword(s):  
High Speed ◽  
Vertical Vibration ◽  
Simulation Software ◽  
Dynamic Responses ◽  
Moving Loads ◽  
Simply Supported Beam ◽  
Double Line ◽  
Simply Supported ◽  
Numerical Result ◽  
Beam Bridge

In this thesis, the dynamic responses of simply supported beam bridge in a double-line railway under bidirectional moving loads are mainly studied. To study the characteristics of Euler- Bernoulli beam, a train is simplified as a series of concentrated forces with fixed wheelbase.Structural dynamics is used to deduce the analytical expressions of vertical vibration of simply supported beam under bidirectional moving loads. By simulation software MATLAB, the numerical result of the dynamic responses of simply supported beam bridge could be obtained. Then the 48 meters simply supported beam bridge in a high-speed railway is analyzed, the dynamic responses of simply supported beam of bidirectional moving loads with different interarrival times are discussed.Finally, some general laws for the design of double-line railway bridge are gained.

Vibration Analysis of a Flexibly Connected Double Span Beam Traversed by Uniformly Distributed Moving Load

2011 ◽  
Vol 71-78 ◽  
pp. 375-378
Author(s):  
Yu Yang ◽  
Yun Fang Yang ◽  
Qi Mao Cai
Keyword(s):  
Vibration Analysis ◽  
High Speed ◽  
Moving Load ◽  
Transportation Systems ◽  
Vertical Vibration ◽  
Dynamic Responses ◽  
Superposition Method ◽  
Mode Superposition Method ◽  
Distributed Load ◽  
Duhamel Integral

Considering the engineering background of high speed transportation systems such as maglev, vertical vibration of a flexibly connected double span beam is studied. The beam can be taken as two Euler-Bernoulli beams flexibly connected by an elastic joint and the model of it bearing moving distributed load with constant speed is then established. Duhamel integral as well as mode superposition method is applied to solve the dynamic responses of the beam. Numerical analysis base on different parameters such as the length of the train, the span of the beam and the velocity of the train are compared. The following conclusions are made:(1) the left span and right span’s dynamic responses is different so that each span should be analyzed separately; (2)the dynamic response of the beam is tied up with the factors such as the frequency of the beam, the moving frequency of the load and the relative bending stiffness of the joint.

scholarly journals Research on the Dynamic Responses of Simply Supported Horizontal Pipes Conveying Gas-Liquid Two-Phase Slug Flow

Processes ◽  
2021 ◽  
Vol 9 (1) ◽  
pp. 83
Author(s):  
Gang Liu ◽  
Zongrui Hao ◽  
Yueshe Wang ◽  
Wanlong Ren
Keyword(s):  
Slug Flow ◽  
Peak Frequency ◽  
Dynamic Responses ◽  
Piping System ◽  
Transverse Displacement ◽  
Vibration Acceleration ◽  
Two Phase ◽  
Horizontal Pipes ◽  
Simply Supported ◽  
Superficial Gas Velocity

The dynamic responses of simply supported horizontal pipes conveying gas-liquid two-phase slug flow are explored. The intermittent characteristics of slug flow parameters are mainly considered to analyze the dynamic model of the piping system. The results show that the variations of the midpoint transverse displacement could vary from periodic-like motion to a kind of motion whose amplitude increases as time goes on if increasing the superficial gas velocity. Meanwhile, the dynamic responses have certain relations with the vibration acceleration. By analyzing the parameters in the power spectrum densities of vibration acceleration such as the number of predominant frequencies and the amplitude of each peak frequency, the dynamic behaviors of the piping system like periodicity could be calculated expediently.

scholarly journals Analysis study the used of Tuned Mass Damper (TMD) on an existing train bridge due to high speed train with moving mass load approach

2019 ◽  
Vol 258 ◽  
pp. 05005 ◽  
Author(s):  
Wivia Octarena Nugroho ◽  
Dina Rubiana Widarda ◽  
Oryza Herdha Dwyana
Keyword(s):  
High Speed ◽  
Tuned Mass Damper ◽  
Dynamic Responses ◽  
Mass Ratio ◽  
High Speed Train ◽  
Maximum Deformation ◽  
Mass Load ◽  
Mass Damper ◽  
Existing Bridges ◽  
Comfort Criteria

As the need of the train speed increased, the existing bridges need to be evaluated, especially in dynamic responses, which are deformation and acceleration. In this study, Cisomang Bridge is modeled and analyzed due to the high-speed train SJ X2 in varying speeds, 50 km/h, 100 km/h, 150 km/h, and 200 km/h. The used of tuned mass damper also will be varied on its setting and placing. The tuned mass dampers setting be varied based on the first or second natural frequency and the placing of tuned mass damper be varied based on maximum deformation of the first or second mode. Moreover, the tuned mass damper ratio will be varied 1% and 1.6%. For all speed variations, dynamic responses of structure without TMD still fulfil the Indonesian Government Criterion based on PM 60 - 2012 but do not meet requirement of comfort criteria based on DIN-Fachbericht 101. Furthermore, only for the speed train 50km/h dynamic responses of structure fulfil safety criteria based on Eurocode EN 1990:2002, whereas the other speed variations do not meet that requirement. In the use of TMD 1% mass ratio, the structure fulfils the safety criteria for all speed variations. In the use of TMD 1.6% mass ratio, all the structure fulfils the safety and comfort criteria except 100 km/h speed which only fulfils the safety criteria.

Dynamic Response of the Spectral Element Model by Using the FFT

2007 ◽  
Vol 345-346 ◽  
pp. 845-848
Author(s):  
Joo Yong Cho ◽  
Han Suk Go ◽  
Usik Lee
Keyword(s):  
Fourier Transforms ◽  
Initial Conditions ◽  
Element Model ◽  
Spectral Element ◽  
Dynamic Responses ◽  
Analysis Method ◽  
Euler Beam ◽  
Exact Analytical Solutions ◽  
Simply Supported ◽  
Spectral Analysis Method

In this paper, a fast Fourier transforms (FFT)-based spectral analysis method (SAM) is proposed for the dynamic analysis of spectral element models subjected to the non-zero initial conditions. To evaluate the proposed SAM, the spectral element model for the simply supported Bernoulli-Euler beam is considered as an example problem. The accuracy of the proposed SAM is evaluated by comparing the dynamic responses obtained by SAM with the exact analytical solutions.

A semi-analytical three-dimensional free vibration analysis of functionally graded curved panels integrated with piezoelectric layers

2014 ◽  
Vol 21 (4) ◽  
pp. 571-587 ◽  
Author(s):  
Hamid Reza Saeidi Marzangoo ◽  
Mostafa Jalal
Keyword(s):  
Boundary Conditions ◽  
Vibration Analysis ◽  
Natural Frequencies ◽  
Differential Quadrature Method ◽  
Three Dimensional ◽  
Free Vibration Analysis ◽  
Functionally Graded ◽  
Simply Supported ◽  
Piezoelectric Layers ◽  
Curved Panels

AbstractFree vibration analysis of functionally graded (FG) curved panels integrated with piezoelectric layers under various boundary conditions is studied. A panel with two opposite edges is simply supported, and arbitrary boundary conditions at the other edges are considered. Two different models of material property variations based on the power law distribution in terms of the volume fractions of the constituents and the exponential law distribution of the material properties through the thickness are considered. Based on the three-dimensional theory of elasticity, an approach combining the state space method and the differential quadrature method (DQM) is used. For the simply supported boundary conditions, closed-form solution is given by making use of the Fourier series expansion, and applying the differential quadrature method to the state space formulations along the axial direction, new state equations about state variables at discrete points are obtained for the other cases such as clamped or free-end conditions. Natural frequencies of the hybrid curved panels are presented by solving the eigenfrequency equation, which can be obtained by using edges boundary conditions in this state equation. The results obtained for only FGM shell is verified by comparing the natural frequencies with the results obtained in the literature.

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