Nonlinear Dynamics of Breathing Cracked Jeffcott Rotor Under Axial Excitation

2014 ◽  
Author(s):  
J. Zhao ◽  
H. A. DeSmidt ◽  
W. Yao
Keyword(s):  
Damage Detection ◽  
Coupling Effect ◽  
Longitudinal Vibration ◽  
Axial Loading ◽  
Crack Model ◽  
Open Area ◽  
Time Step ◽  
Crack Open ◽  
Axial Excitation ◽  
Jeffcott Rotor

The rotor may operate at various working conditions in practice and the crack breathing behavior at different rotating speeds is essential for damage detection and health monitoring of rotor system. In this paper, the coupling of lateral and longitudinal vibration is investigated by building a Jeffcott rotor model with imbalance. By using D’Alambert Principle, four degree-of-freedom equation of motion is derived in fixed coordinate system and the crack model is built based on the fracture mechanics. Zero SIF method is used to determine the crack open area by computing the SIF of opening mode for every point in crack area. The stiffness matrix is updated every time step by integrating compliant coefficients over instantly calculated crack open area. In addition, the breathing behavior of the crack under axial excitation is studied in terms of several eccentricity phases and rotation speeds, which provide effective guidance for damage detection in such scenarios. The paper also explores the coupling effect of external axial loading on the vibration response and its effectiveness for damage detection.

Nonlinear Breathing Behavior Study of Transverse Crack on a Jeffcott Rotor Under Torsional Excitation

2014 ◽  
Author(s):  
J. Zhao ◽  
H. A. DeSmidt ◽  
W. Yao
Keyword(s):  
Damage Detection ◽  
Stiffness Matrix ◽  
Strain Energy Release ◽  
Vibration Response ◽  
Crack Model ◽  
Open Area ◽  
Lagrange Principle ◽  
Time Step ◽  
Crack Open ◽  
Jeffcott Rotor

In this paper, Jeffcott rotor model is employed to explore the vibration response of breathing cracked system with unbalance mass. Based on the energy method and Lagrange principle, 6 degree-of-freedom equation of motion is derived in fixed coordinate system. The crack model is established using strain energy release theory of facture mechanics. The stiffness matrix induced by the crack is changing with the variation of crack open area. Zero stress intensity factor (SIF) method is used to determine the crack closure line by computing the SIF for opening mode. By integrating compliant coefficients over newly determined crack open area, the stiffness matrix is updated and vibration response is solved for every time step by Gear’s method. In addition, the breathing behavior of the crack is studied for multiple eccentricity phases and rotation speeds in order to provide effective guidance for damage detection. The paper explores the effect of external torsional loading on the crack breathing behavior. Finally, the coupling of lateral and torsional vibration is investigated to be used as an indicator of damage detection and health monitoring.

Roll-Yaw Coupling Effect of Jeffcott Rotor With Breathing Crack

2015 ◽  
Author(s):  
J. Zhao ◽  
H. A. DeSmidt ◽  
M. Peng ◽  
W. Yao
Keyword(s):  
Coupling Effect ◽  
Rotor System ◽  
Crack Model ◽  
Breathing Crack ◽  
Cracked Rotor ◽  
Lagrange Principle ◽  
Jeffcott Rotor ◽  
Vibration Responses ◽  
Cracked Rotor System ◽  
Rotor Model

A new rotor model is developed in this paper to explore the dynamic coupling effect of roll-yaw motion. The rotor model employs a 6 degree-of-freedom Jeffcott rotor with a breathing crack. Based on the energy method and Lagrange principle, equation of motion is derived in yawing coordinate system with consideration of unbalance mass. The breathing crack model is established by Zero Stress Intensity Factor (SIF) method based on the crack released strain energy concept in fracture mechanics. SIF method is used to determine the crack closure line by computing SIF for opening mode. The vibration responses of the cracked rotor system are solved by Gear’s method. The coupling effect of yawing and rolling motion is studied in this paper to investigate vibration response of cracked rotor system. With the yawing motion, the dynamics of the rotor-bearing system is changed by additional stiffness and force terms. The parametric study is conducted to analyze the effect of yawing rate and acceleration on the crack breathing behavior. Finally, the vibration responses of the nominal and damaged rotor systems are analyzed to find out the indication for the damage detection and health monitoring.

Experimental Investigation of Non-Linear Coupled Vibrations in Elastic Columns Excited at High Frequencies

1971 ◽  
Vol 13 (3) ◽  
pp. 224-226 ◽  
Author(s):  
H. Ramsey ◽  
D. Johnson ◽  
C. R. Hazell
Keyword(s):  
Longitudinal Vibration ◽  
Rectangular Cross Section ◽  
Axial Loading ◽  
Vibration Modes ◽  
Coupled Modes ◽  
Flexural Mode ◽  
High Frequencies ◽  
Longitudinal Modes ◽  
Axial Excitation ◽  
Slender Column

Contributions intended for publication as Research Notes should be limited in length to 1000 words and two illustrations, and should be addressed to the Editor of Proceedings at the Institution Headquarters in London. Coupling of flexual and longitudinal vibration modes has been observed experimentally in a slender column of rectangular cross-section subjected to periodic axial loading at frequencies up to 10 kHz; the fundamental longitudinal frequency of the specimen is 8·7 kHz. Resonance in the coupled flexural–longitudinal modes was observed when the frequency of axial excitation was 1, ½, and ⅓ times the fundamental longitudinal frequency. Strain levels at resonance in the coupled modes were comparable to strain levels in the purely flexural modes which were excited when the frequency of axial excitation corresponded to a flexural mode.

Parametric Study on Dynamics of Breathing Cracked Rotor via Laser Scanner

2015 ◽  
Author(s):  
J. Zhao ◽  
H. A. DeSmidt ◽  
M. Peng ◽  
W. Yao
Keyword(s):  
Stress Intensity Factor ◽  
Stress Intensity ◽  
Intensity Factor ◽  
Parametric Study ◽  
Laser Scanner ◽  
Crack Model ◽  
Transverse Cracks ◽  
Time Step ◽  
Crack Open ◽  
Opening Mode

The study is based on the finite element model which was developed to investigate the nonlinear breathing behavior of transverse cracks in terms of crack location and rotation speed. The crack model is built using the released strain energy concept in fracture mechanics. Zero Stress Intensity Factor (SIF) method is employed to determine the crack closure line at each time step by calculating the stress intensity factor of opening mode for prescribed resolutions in crack area. The crack is considered open at the points where the stress intensity factor for opening mode is larger than zero. The stiffness matrix is updated at every time step by integrating compliant coefficients over instantly calculated crack open area. With the updated stiffness and force matrices, the vibration response at next time step is solved by Newmark integration method. To investigate the effectiveness of laser scanner, parametric study is conducted to analyze the vibration responses collected by the laser scanner with different scanning functions and frequencies. With this model, the displacement or velocity along the shaft can be extracted to form time based data sets for different scanning function or scanning frequency to explore its usefulness for damage identification.

scholarly journals Semi-Analytical Solution for Free Vibration Differential Equations of Curved Girders

2017 ◽  
Vol 63 (1) ◽  
pp. 115-132
Author(s):  
Y. Song ◽  
X. Chai
Keyword(s):  
Analytical Solution ◽  
Differential Equations ◽  
Free Vibration ◽  
Coupling Effect ◽  
Longitudinal Vibration ◽  
Synthesis Method ◽  
Variable Separation ◽  
Element Analysis ◽  
Plane Vibration ◽  
Curved Girders

Abstract In this paper, a semi-analytical solution for free vibration differential equations of curved girders is proposed based on their mathematical properties and vibration characteristics. The solutions of in-plane vibration differential equations are classified into two cases: one only considers variable separation of non-longitudinal vibration, while the other is a synthesis method addressing both longitudinal and non-longitudinal vibration using Rayleigh’s modal assumption and variable separation method. A similar approach is employed for the out of- plane vibration, but further mathematical operations are conducted to incorporate the coupling effect of bending and twisting. In this case study, the natural frequencies of a curved girder under different boundary conditions are obtained using the two proposed methods, respectively. The results are compared with those from the finite element analysis (FEA) and results show good convergence.

scholarly journals Probabilistic Damage Detection and Identification of Coupled Structural Parameters using Bayesian Model Updating with Added Mass

2021 ◽  
Author(s):  
jice zeng ◽  
Young Hoon Kim
Keyword(s):  
Convergence Rate ◽  
Damage Detection ◽  
Bayesian Model ◽  
Model Updating ◽  
Coupling Effect ◽  
Structural Parameters ◽  
Added Mass ◽  
Distribution Functions ◽  
Single Chain ◽  
Characteristic Equations

Damage detection inevitably involves uncertainties originated from measurement noise and modeling error. It may cause incorrect damage detection results if not appropriately treating uncertainties. To this end, vibration-based Bayesian model updating (VBMU) is developed to utilize vibration responses or modal parameters to identify structural parameters (e.g., mass and stiffness) as probability distribution functions (PDF) and uncertainties. However, traditional VBMU often assumes that mass is well known and invariant because simultaneous identification of mass and stiffness may yield an unidentifiable problem due to the coupling effect of the mass and stiffness. In addition, the posterior PDF in VBMU is usually approximated by single-chain based Markov Chain Monte Carlo (MCMC), leading to a low convergence rate and limited capability for complex structures. This paper proposed a novel VBMU to address the coupling effect and identify mass and stiffness by adding known mass. Two vibration data sets are acquired from original and modified systems with added mass, giving the new characteristic equations. Then, the posterior PDF is reformulated by measured data and predicted counterparts from new characteristic equations. For efficiently approximating the posterior PDF, Differential Evolutionary Adaptive Metropolis (DREAM) Algorithm are adopted to draw samples by running multiple Markov chains parallelly to enhance convergence rate and sufficiently explore possible solutions. Finally, a numerical example with a ten-story shear building and a laboratory-scale three-story frame structure are utilized to demonstrate the efficacy of the proposed VBMU framework. The results show that the proposed method can successfully identify both mass and stiffness, and their uncertainties. Reliable probabilistic damage detection can also be achieved.

Theoretical Study on Space Coupling Free Vibration Analysis of Self-Anchored Cable-Stayed Suspension Bridge

2014 ◽  
Vol 501-504 ◽  
pp. 1107-1111
Author(s):  
Miao Feng
Keyword(s):  
Free Vibration ◽  
Strain Energy ◽  
Coupling Effect ◽  
Longitudinal Vibration ◽  
Free Vibration Analysis ◽  
Flexural Vibration ◽  
Suspension Bridge ◽  
Large Displacement ◽  
Generalized Variational Principle ◽  
Suspension Bridges

Based on Large-displacement Non-linear Elastic Generalized Variational Principle, coupling effect of axial and flexural action, shearing strain energy, torsional strain energy of stiffening girder were considered, the large-displacement incomplete generalized potential energy functional of space coupling free vibration of a three-span self-anchored cable-stayed suspension bridge was presented. By constraint variation, fundamental differential equations of vertical flexural vibration, lateral flexural vibration, longitudinal vibration and torisional vibration were formulated, also presented the equations for the main tower with respect to longitudinal and lateral vibration. The linear free vibration differential equation was obtained when the nonlinear items were discarded. This approach provides theoretical basis for analysis of natural vibration character of self-anchored cable-stayed suspension bridges.

Contribution to Bridge Damage Analysis

2014 ◽  
Vol 704 ◽  
pp. 435-441 ◽  
Author(s):  
Mohammed Lamine Moussaoui ◽  
Abderrahmane Kibboua ◽  
Mohamed Chabaat
Keyword(s):  
Finite Element ◽  
Reinforced Concrete ◽  
Damage Detection ◽  
Sparse Matrix ◽  
System Of Equations ◽  
Shape Functions ◽  
Time Step ◽  
Analytical Geometry ◽  
Matrix Algorithms ◽  
Bridge Damage

Structural damage detection has become an important research area since several works [2] were focused on the crack zones detection in order to foresee the appropriate solutions. The present research aims to carry out the reinforced concrete bridge damage detection with the finite element mathematical model updating method (MMUM). Unknown degrees of freedom dof are expanded from measured ones. The partitioned system of equations has provided a large sub-system of equations which can be solved efficiently by handling sparse matrix algorithms at each time step of the finite time centered space FTCS discretization. A new and efficient method for the calculation of the constant strain tetrahedron shape functions has been developed [1,3,4,5,6]. The topological and analytical geometry of the tetrahedron and its useful formulae enabled us to develop its shape functions and its corresponding finite element matrices. The global finite element matrices and sparse matrix computations have been achieved with a calculus source code. The reinforced concrete mixture has been modeled with the mixture laws [16] which led to its material properties matrix as an orthotropic case with 9 constants and 2 planes of symmetry from the generalizedHooke’slaw [1]. It is noticed that the material is made of steel, cement, gravels, sand and impurities. The data computations have been implemented with optimized cpu time and data storage using vectorial programming of efficient algorithms [11,12]. The sparse matrix algorithms used in this study are: solution of symmetric systems of equations UTDUd=R, multiplication, addition, transposition, permutation of rows and columns, and ordering of the matrices representations. All the sparse matrices are given in row-wise sparse format.

Analysis on Mechanics and Reliability of Drill String during Deep Drilling

2011 ◽  
Vol 94-96 ◽  
pp. 1519-1522
Author(s):  
Shang Yu Yang ◽  
Xiu Juan Yang ◽  
Xiang Zhen Yan
Keyword(s):  
Yield Strength ◽  
Transverse Vibration ◽  
Longitudinal Vibration ◽  
Axial Loading ◽  
Drill String ◽  
Drilling Process ◽  
External Diameter ◽  
Force Analysis ◽  
Finite Element Software ◽  
Very High

The deep drill string is subjected to many kinds of loading under the condition of vibration and precession, such as tension, compression, bending and torsion, while the temperature and press are very high. Under this circumstance, the shallow drill string is more likely to failure. Based on the force analysis of the drill string, the drilling process of the deep drill string is simulated using finite element software. The stress distribution and displacement of the drill string is obtained under the interaction of drilling pressure, torque and temperature. At the same time, the effect of transverse vibration, longitudinal vibration and torsional vibration, on the stress and displacement of the drill string, is compared. The change law of the natural frequency of transverse vibration varying with the length of drill string, rotational speed and the hole size is discussed. Connected with concrete examples, the reliability and sensitivity of some influencing factors such as external diameter, wall thickness, the minimum yield strength, temperature, elastic modulus, Poisson’s ratio, axial loading and torque is obtained. The main factors that influence the reliability of the drill string are the yield strength and torque. The reliability of the drill string increases as the increase of yield strength, and decreases as the increase of the torque.

Tunable Energy Harvesting From Ambient Vibrations

2010 ◽  
Author(s):  
Mohamed Rhimi ◽  
Nizar Lajnef
Keyword(s):  
Energy Harvesting ◽  
Lead Zirconate Titanate ◽  
Coupling Effect ◽  
Energy Levels ◽  
Axial Loading ◽  
Lead Zirconate ◽  
Energy Scavenging ◽  
Ambient Vibrations ◽  
Civil Structures ◽  
Piezoelectric Energy

Most civil structures have a low vibration response frequency range, generally one to two orders of magnitude lower than the operating frequency spectrum of most piezoelectric energy scavenging devices, which is dictated by the device’s design and the used materials. This considerably limits the levels of harvestable power under ambient vibrations. In this paper, the improvement of the energy harvesting characteristics of a bimorph cantilever lead zirconate titanate (PZT) piezoelectric beam through the application of initial pre-stress loading conditions is studied. A generalized model that can take into account all the vibration modes of the beam as well as the back coupling effect is derived using the Hamiltonian principle. The model describes the effect of the pre-stress parameters on the harvestable energy levels. Results showing the variations of the natural frequency, amplitude, and efficiency of the piezoelectric device with varying preload are presented. Vibration recordings from a bridge under ambient loading are used to show variations of the harvested power with different pre-stress conditions. Increases of up to 250% in the output power levels are shown possible through the application of 8N of compressive axial loading for a system with a 15g vibrating mass. Experimental verification of the model is also performed. The time and frequency domain responses of a piezoelectric bimorph are measured and compared to theoretical results.

Sign in / Sign up

Export Citation Format

Share Document