Coupled Longitudinal and Bending Vibrations of a Cracked Shaft

1988 ◽  
Vol 110 (1) ◽  
pp. 1-8 ◽  
Author(s):  
C. A. Papadopoulos ◽  
A. D. Dimarogonas
Keyword(s):  
Longitudinal Vibration ◽  
Slenderness Ratio ◽  
Crack Depth ◽  
Crack Identification ◽  
Open Crack ◽  
Vibration Modes ◽  
Bending Vibrations ◽  
Local Flexibility ◽  
Cracked Shaft ◽  
Identification Tool

This paper describes the coupling of bending and longitudinal vibration of a stationary cracked shaft with an open crack. The crack is modeled by way of a 2×2 local flexibility matrix with coupling terms. The elements of this matrix are obtained analytically. One of the elements compares well with experimental data of other investigators. The free vibration of the shaft, and the influence of the crack on the vibrational behavior of the shaft is studied. The relation of the eigenvalues of the system and the crack depth as functions of the slenderness ratio are presented. The forced vibration of the shaft is also studied and the coupling of the vibration modes is verified analytically and experimentally. The applicability of the method as a crack identification tool is demonstrated.

Detection of Cracks in Stationary Rotors via the Modal Frequency Changes Induced by a Roving Disc

2014 ◽  
Author(s):  
Z. N. Haji ◽  
S. O. Oyadiji
Keyword(s):  
Natural Frequencies ◽  
Crack Depth ◽  
Mode Shapes ◽  
Crack Identification ◽  
Open Crack ◽  
Suggested Approach ◽  
Rotor Systems ◽  
Crack Location ◽  
High Crack ◽  
Frequency Changes

In this study, a crack identification approach based on a finite element cracked model is presented to identify the location and depth ratios of a crack in rotor systems. A Bernoulli-Euler rotor carrying an auxiliary roving disc has been used to model the cracked rotor, in which the effect of a transverse open crack is modelled as a time-varying stiffness matrix. In order to predict the crack location in the rotor-disc-bearing system, the suggested approach utilises the variation of the normalized natural frequency curves versus the non-dimensional location of a roving disc which traverses along the rotor span. The merit of the suggested approach is to identify the location and sizes of a crack in a rotor by determining only the natural frequencies of the stationary rotor system. The first four natural frequencies are employed for the identification and localisation of a crack in the stationary rotor. Furthermore, this approach is not only efficient and practicable for high crack depth ratios but also for small crack depth ratios and for a crack close to or at the node of mode shapes, where natural frequencies are unaffected.

Coupled Vibration of Cracked Shafts

1992 ◽  
Vol 114 (4) ◽  
pp. 461-467 ◽  
Author(s):  
C. A. Papadopoulos ◽  
A. D. Dimarogonas
Keyword(s):  
Circular Cross Section ◽  
Vibration Modes ◽  
Coupled Vibration ◽  
Frequency Range ◽  
Bending Vibrations ◽  
Flexibility Matrix ◽  
Local Flexibility ◽  
Modes Of Vibration ◽  
Small Cracks ◽  
Cracked Shafts

The coupling of vibration modes of vibration of a clamped-free circular cross-section Timoshenko beam with a transverse crack is investigated in this paper. A 6 × 6 local flexibility matrix is used to simulate the crack. The nondiagonal terms of this matrix cause coupling between the longitudinal, torsional, and bending vibrations. Coupling is apparent in all spectra obtained with a harmonic sweeping excitation throughout the frequency range. The method is very sensitive even for small cracks.

scholarly journals Design and Performance Evaluation of a Single-Phase Driven Ultrasonic Motor Using Bending-Bending Vibrations

Micromachines ◽  
2021 ◽  
Vol 12 (8) ◽  
pp. 853
Author(s):  
Dongmei Xu ◽  
Wenzhong Yang ◽  
Xuhui Zhang ◽  
Simiao Yu
Keyword(s):  
Single Phase ◽  
Oblique Line ◽  
Ultrasonic Motor ◽  
Vibration Modes ◽  
Bending Vibrations ◽  
Bending Vibration ◽  
Output Performance ◽  
Resonance Frequencies ◽  
And Performance ◽  
Line Trajectory

An ultrasonic motor as a kind of smart material drive actuator has potential in robots, aerocraft, medical operations, etc. The size of the ultrasonic motor and complex circuit limits the further application of ultrasonic motors. In this paper, a single-phase driven ultrasonic motor using Bending-Bending vibrations is proposed, which has advantages in structure miniaturization and circuit simplification. Hybrid bending vibration modes were used, which were excited by only single-phase voltage. The working principle based on an oblique line trajectory is illustrated. The working bending vibration modes and resonance frequencies of the bending vibration modes were calculated by the finite element method to verify the feasibility of the proposed ultrasonic motor. Additionally, the output performance was evaluated by experiment. This paper provides a single-phase driven ultrasonic motor using Bending-Bending vibrations, which has advantages in structure miniaturization and circuit simplification.

scholarly journals MATHEMATICAL MODELLING OF VIBRATIONS OF NON-UNIFORM RING-SHAPED ULTRASONIC WAVEGUIDES

2021 ◽  
Vol 3 (56) ◽  
pp. 90-96
Author(s):  
Dmitry A. STEPANENKO ◽  
◽  
Ksenija A. BUNCHUK ◽  
Keyword(s):  
Harmonic Balance ◽  
Harmonic Balance Method ◽  
Central Line ◽  
Balance Method ◽  
Vibration Modes ◽  
Constant Sign ◽  
Algebraic Equations ◽  
Bending Vibrations ◽  
Singular Matrices ◽  
Uniform Ring

The article describes technique for modelling of ultrasonic vibrations amplifiers, which are implemented in the form of non-uniform ring-shaped waveguides, based on application of harmonic balance method. Bending vibrations of the waveguide are described by means of non-uniform integral and differential equations equivalent to Euler–Bernoulli equations in order to simplify calculation of amplitude-frequency characteristics of vibrations, particularly, to exclude the need of working with singular matrices. Using harmonic balance method, equations of vibrations are reduced to overdetermined non-uniform linear system of algebraic equations, which least-squares solution is determined by means of pseudo-inverse matrix. On the basis of analysis of numerical example possibility of existence of variable-sign and constant-sign vibration modes of the waveguide is shown and it is determined that for realization of amplifying function it is necessary to use waveguide at constant-sign vibration mode. The constant-sign vibration modes are combinations of bending defor-mation and extensional deformation of central line of the waveguide and they are detected due to accounting extensibility of the central line in equations of vibrations. Validity of the obtained results is confirmed by comparing them to the results of modelling by means of finite element method.

Refined Theory of Damped Axisymmetric Vibrations of Double-Layered Cylindrical Shells

1979 ◽  
Vol 21 (1) ◽  
pp. 33-37 ◽  
Author(s):  
Ŝ. Markuŝ
Keyword(s):  
Outer Layer ◽  
Loss Factor ◽  
Longitudinal Vibration ◽  
Cylindrical Shells ◽  
Strong Dependence ◽  
Normal Modes ◽  
Present Theory ◽  
Damping Capacity ◽  
Refined Theory ◽  
Vibration Modes

The governing differential equations of vibrations of double-layered cylindrical shells are derived from classical thinshell theory. The outer layer of the shell is assumed to be viscoelastic, possessing high damping capacity to control vibrations (loss factor, β = 0.3). Decoupled torsional and coupled radial-longitudinal vibration modes are analysed by the method of ‘damped normal modes’. The present theory refines Kagawa and Krokstad's former analysis (1)‡. The results obtained point to a strong dependence of mechanical losses upon the thickness-to-radius ratio, h1/ R, even in the case of axisymmetric modes. This phenomenon was not recognized in Kagawa-Krokstad's approach.

Effect of a breathing crack on the damping changes in nonlinear vibrations of a cracked beam: Experimental and theoretical investigations

2020 ◽  
pp. 107754632096031
Author(s):  
Masoud Kharazan ◽  
Saied Irani ◽  
Mohammad Ali Noorian ◽  
Mohammad Reza Salimi
Keyword(s):  
Nonlinear Vibrations ◽  
Crack Depth ◽  
Beam Theory ◽  
Experimental Tests ◽  
Damping Coefficient ◽  
Crack Identification ◽  
Breathing Crack ◽  
Cracked Beam ◽  
Identification Method ◽  
Nonlinear Crack

The attempts to identify damping changes in a cracked beam can improve the accuracy of the nonlinear crack identification method. For the purpose of this aim, a parametric nonlinear equation of motion is obtained using the Euler–Bernoulli beam theory and parametric nonlinear breathing crack assumptions. Several experiments were conducted to identify the effect of breathing cracks on changing the damping value in nonlinear vibrations of a cracked beam. Experimental tests have revealed that increasing the crack depth and the level of excitation enlarges the damping coefficient in a vibrating beam. For this reason, the effects of the excitation force and crack depth on the structural damping coefficient are investigated. The obtained results indicated that considering the nonlinear response of a cracked beam and measuring the value of the damping changes can significantly improve the accuracy of the nonlinear crack identification method.

In-Plane Vibration and Crack Detection of a Rotating Shaft-Disk Containing a Transverse Crack

1998 ◽  
Vol 120 (2) ◽  
pp. 551-556 ◽  
Author(s):  
Ming-Chuan Wu ◽  
Shyh-Chin Huang
Keyword(s):  
Crack Detection ◽  
Transverse Crack ◽  
Rotation Speed ◽  
Crack Depth ◽  
Multiple Scale ◽  
Crack Identification ◽  
Response Curves ◽  
Rotating Shaft ◽  
Crack Location ◽  
Depth Rotation

Dynamic response and stability of a rotating shaft-disk containing a transverse crack is investigated. FFT analysis of response amplitudes showed that the 2Ω component (Ω: rotation speed) was excited by crack breathing and could serve as a good index for crack identification. Intensive numerical studies of crack location, crack depth, rotation speed, and sensing position on response amplitudes displayed a feasible technique for the identification of crack depth and crack location. It is achieved by intersecting the two equi-amplitude response curves of two separated sensing probes. Finally, the instability of the system caused by a crack is examined via Floquet theory and the multiple scale method. The stability diagrams, illustrated as functions of crack depth, rotation speed, and damping, are shown and discussed.

Detection and Quantitative Assessment of Damages in Beam Structures Using Frequency and Stiffness Changes

2013 ◽  
Vol 569-570 ◽  
pp. 1013-1020 ◽  
Author(s):  
Gilbert Rainer Gillich ◽  
Zeno Iosif Praisach
Keyword(s):  
Natural Frequency ◽  
Mode Shape ◽  
Quantitative Assessment ◽  
Vibration Modes ◽  
Stored Energy ◽  
Bending Vibrations ◽  
Bending Vibration ◽  
Mathematical Relation ◽  
3D Elements ◽  
Frequency Changes

This paper is concerned with vibration based non-destructive evaluation of structures, with a focus on quantitative assessment of damage. In previous works, a reliable method to locate open cracks in beams has been proposed and tested using both data from numerical simulations and laboratory experiments. It bases on the fact the natural frequency of a bending vibrations mode attend different changes, depending on the loss of stored energy for the slice on which the damage is located. As bigger the mode shape curvature value on that location, so bigger the loss of stored energy and consequently the natural frequency decrease in that mode. Analyzing the natural frequency changes for a larger series of vibration modes, it’s possible to precisely locate damages. The authors succeed to find a single mathematical relation describing the frequency changes for all bending vibration modes, involving one term defining damage’s location and one defining its depth. While the first term changes for different modes, being defined by the mode shape curvature, the second maintain its value for all modes, being affected just by damage depth. This finding permits decoupling the location issue with that of quantitative assessment of damage. Latest researches, presented in this paper, succeed by finding the relation between the second term of the relation and some mechanical characteristics of the beam, i.e. extending the proposed method by including evaluation of damage severity. The approach is illustrated on a cantilever beam, modeled with 3D elements.

Design of Ultrasonic Vibrator for Conformal Coating Spray in LED Packaging

2009 ◽  
Vol 79-82 ◽  
pp. 715-718
Author(s):  
Byeong Ho Son ◽  
Seung Bok Choi ◽  
Quoc Hung Nguyen ◽  
Seung Min Hong ◽  
Soo Jin Lee ◽  
...  
Keyword(s):  
Longitudinal Vibration ◽  
Flow Characteristics ◽  
Film Surface ◽  
Wave Theory ◽  
Operating Conditions ◽  
Vibration Modes ◽  
Element Analysis ◽  
Surface Theory ◽  
Conformal Coating ◽  
Fluid Flow Characteristics

This paper presents the design of ultrasonic vibrator utilizing a piezoelectric actuator. After describing a geometric configuration of the proposed atomizer, an analytical model of the ultrasonic atomizer is formulated by considering liquid film surface theory and wave theory. The dynamic analysis is then undertaken using a finite element analysis to determine principal longitudinal vibration modes. An optimization is performed by taking the amplitude of the tip displacement as an objective function. The fluid flow characteristics of the proposed atomizer is also analyzed under operating conditions through commercial software FLUENT.

Stability assessment of slopes with cracks using limit analysis

2013 ◽  
Vol 50 (10) ◽  
pp. 1011-1021 ◽  
Author(s):  
Radoslaw L. Michalowski
Keyword(s):  
Limit Analysis ◽  
Pore Water Pressure ◽  
Water Pressure ◽  
Crack Depth ◽  
Optimization Procedure ◽  
Collapse Mechanism ◽  
Open Crack ◽  
Stability Assessment ◽  
Critical Height ◽  
Maximum Crack

Cracks are a common occurrence in soil slopes, and a method is described for including the presence of cracks in stability assessment based on the kinematic approach of limit analysis. While many cracks may be present in a slope, the failure mechanism typically involves one crack, whose location has the most adverse influence on stability. A translational mechanism, typical of rock slope failures, is demonstrated to illustrate the method, followed by a rotation collapse analysis that is more appropriate for soils. Pre-existing (open) cracks are considered, as well as the cracks that form as part of the slope collapse mechanism. The maximum crack depth is determined by stability of the vertical crack boundary. This maximum crack depth may be reduced significantly by seepage forces in the slope. The most adverse location of the crack is determined from an optimization procedure where the minimum of the slope critical height is sought. The presence of water is included in the analysis, and stability charts are developed. The influence of the presence of cracks on stability of gentle slopes was not found to be significant, but the effect on the outcome of the analysis increases with an increase in inclination angle and the presence of pore-water pressure. The difference in the critical height of a 60° slope with an open crack and without one can be as much as 50%.

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