A Continuous Model for Forced Vibration Analysis of a Cracked Beam

2005 ◽  
Author(s):  
M. Behzad ◽  
A. Meghdari ◽  
A. Ebrahimi
Keyword(s):  
Natural Frequency ◽  
Vibration Analysis ◽  
Crack Depth ◽  
Continuous Model ◽  
Forced Response ◽  
Galerkin Projection ◽  
Cracked Beam ◽  
Bending Vibration ◽  
Crack Depth Ratio ◽  
Forced Vibration Analysis

In this paper the equation of motion and corresponding boundary conditions has been developed for forced bending vibration analysis of a beam with an open edge crack. A uniform Euler-Bernoulli beam and the Hamilton principle have been used in this research. The natural frequencies and the forced response of this beam have been obtained using the new developed model in conjunction with the Galerkin projection method. The crack has been modeled as a continuous disturbance function in displacement filed which could be obtained from fracture mechanics. The results show that the first natural frequency will reduce when the crack depth ratio increases. Also the rate of this reduction depends on the position of the crack. In addition it can be seen that the FRF amplitude for a cracked beam is more than a similar uncracked beam before the first natural frequency. But just after the first natural frequency the amplitude of vibration of a healthy beam is more than a cracked beam. There is an excellent agreement between the theoretical results and those obtained by the finite element method.

scholarly journals Stiffness Estimation of Cracked Beams Based on Nonlinear Stress Distributions Near the Crack

2018 ◽  
Vol 2018 ◽  
pp. 1-12 ◽  
Author(s):  
Chunyu Fu ◽  
Yuyang Wang ◽  
Dawei Tong
Keyword(s):  
Crack Depth ◽  
Internal Force ◽  
Stress Distributions ◽  
Cracked Beam ◽  
Section Shape ◽  
Nonlinear Stress ◽  
Crack Depth Ratio ◽  
Element Technique ◽  
Force Equilibrium ◽  
Cracked Beams

The crack presence causes nonlinear stress distributions along the sections of a beam, which change the neutral axis of the sections and further affect the beam stiffness. Thus, this paper presents a method for the stiffness estimation of cracked beams based on the stress distributions. First, regions whose stresses are affected by the crack are analyzed, and according to the distance to the crack, different nonlinear stress distributions are modeled for the effect regions. The inertia moments of section are evaluated by substituting these stress distributions into the internal force equilibrium of section. Then the finite-element technique is adopted to estimate the stiffness of the cracked beam. The estimated stiffness is used to predict the displacements of simply supported beams with a crack, and the results show that both static and vibrational displacements are accurately predicted, which indicates that the estimated stiffness is precise enough. Besides, as the section shape of beam is not limited in the process of modeling the stress distributions, the method could be applicable not only to the stiffness estimation of cracked beams with a rectangular section, but also to that of the beams with a T-shaped section if the crack depth ratio is not larger than 0.7.

Damage Analysis of One-Dimensional Euler–Bernoulli Cracked Beam with Traveling Wave Method

2017 ◽  
Vol 09 (04) ◽  
pp. 1750048 ◽  
Author(s):  
Ya-Qiong Tang ◽  
Tuan-Jie Li ◽  
Qiong-Yao Yan
Keyword(s):  
Traveling Wave ◽  
Power Flow ◽  
Continuous Model ◽  
Analytic Solutions ◽  
Wave Method ◽  
Cracked Beam ◽  
Bending Vibration ◽  
One Dimensional ◽  
Flow Response ◽  
Traveling Wave Method

Based on the elastic fracture mechanics, we establish a continuous model of one-dimensional Euler–Bernoulli cracked beam using the traveling wave method, and analyze the damage characteristics of cracked beam through the changes of deflection and power flow response. First, the control equation of bending vibration of healthy beam is deduced by traveling wave method. Then, the reflection and transmission matrices of waves at force point, constraint point, crack point are derived. The analytic solutions of deflection and power flow are expressed explicitly as the function of crack location and size. The effects of crack width and depth on deflection and power flow response of cracked beam are revealed. Finally, the numerical example illustrates the effectiveness of the proposed method.

Forced vibration analysis for dynamic coupling of finite-element spring-reduced suspension system

2008 ◽  
Vol 222 (3) ◽  
pp. 349-356 ◽  
Author(s):  
Jaeyoung Kang
Keyword(s):  
Forced Vibration ◽  
Vibration Analysis ◽  
Load Transfer ◽  
Contact Stiffness ◽  
Coupled System ◽  
Suspension System ◽  
Frequency Variation ◽  
Coil Spring ◽  
Bending Vibration ◽  
Forced Vibration Analysis

The current paper studies the dynamic behaviour of a coil spring in a vehicle suspension system. A portion of the coil spring is contacted with the top and bottom spring pads. The contact interface is modelled as a set of linear spring elements on the contact nodes of the coil spring. The eigensensitivity analysis is conducted to investigate the frequency variation of the stiffness-coupled system with respect to the contact stiffness variation. In the forced vibration analysis, the transfer function through the coil spring is obtained. The contribution of the coil spring modes to the load transfer is calculated by the modal contribution factor. It is shown that some of the longitudinal and bending vibration modes participate on the load transfer.

scholarly journals Free and Forced Vibration Analysis of H-type and Hybrid Vertical-Axis Wind Turbines

Energies ◽  
2020 ◽  
Vol 13 (24) ◽  
pp. 6747
Author(s):  
Minhui Tong ◽  
Weidong Zhu ◽  
Xiang Zhao ◽  
Meilin Yu ◽  
Kan Liu ◽  
...  
Keyword(s):  
Energy Harvesting ◽  
Wind Energy ◽  
Natural Frequency ◽  
Forced Vibration ◽  
Vibration Analysis ◽  
Cfd Simulation ◽  
Vertical Axis ◽  
Aerodynamic Loads ◽  
Vertical Axis Wind Turbines ◽  
Forced Vibration Analysis

Vertical-axis wind turbines (VAWTs) are compact and efficient and have become increasingly popular for wind energy harvesting. This paper mainly focuses on free and forced vibration analysis of two different types of VAWTs, i.e., an H-type VAWT and a new hybrid VAWT. The H-type VAWT has a lower cost, while the hybrid VAWT has a better self-starting capability at a low wind velocity. Both of them can be used for wind energy harvesting. By using the assumed modes method, the two VAWTs are simplified by a single degree-of-freedom (SDOF) model. By utilizing the method of structural mechanics, a multi-degree-of-freedom (MDOF) model is developed for the two VAWTs and the turbines in them are reasonably simplified. Natural frequency analyses for the SDOF and MDOF models of the two VAWTs are conducted. A beam element model (BEM) of the two VAWTs is created to calculate their natural frequencies and mode shapes and to verify natural frequency results from the SDOF and MDOF models. By using the BEM of the two VAWTs, their amplitude-frequency responses are obtained from harmonic response analysis. To analyze forced vibrations of the two VAWTs, aerodynamic loads on the two VAWTs are obtained from computational fluid dynamics (CFD) simulation. By using solid element models of the two VAWTs, forced transient responses of the two VAWTs are calculated by using the aerodynamic loads from CFD simulation. Steady-state forced response amplitudes of the 1 m-mast hybrid VAWT are 23.8% and 20.5% smaller in X- and Y-directions than those of the 1 m-mast H-type VAWT, respectively. Frequency contents of the aerodynamic loads from CFD simulation are calculated, which confirm that they are periodic, and the power efficiency of the H-type VAWT is about 2.6% higher that of the hybrid VAWT.

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