scholarly journals Chatter and Stability Analysis of the Slender Composite Boring Bar with Constrained Damping Layer

2020 ◽  
Vol 10 (13) ◽  
pp. 4537
Author(s):  
Jinfeng Zhang ◽  
Hao Wang ◽  
Yongsheng Ren ◽  
Chao Feng ◽  
Chunjin Zhang
Keyword(s):  
Stability Analysis ◽  
Dynamic Stiffness ◽  
Beam Theory ◽  
Base Layer ◽  
Boring Bar ◽  
Rotating Speed ◽  
Stability Lobe ◽  
Analysis Theory ◽  
Constrained Damping ◽  
Euler Bernoulli Beam

This study investigates the chattering stability of the composite boring bar with a constrained damping layer during the deep-hole boring process in depth. Based on the Euler-Bernoulli beam theory, the regenerative chattering linear kinetic model of the composite boring bar with a constrained damping layer was established, and the computational formulas of the rotating speed of the spindle and the corresponding limit cutting depth were derived. By analyzing the chattering stability, the cutting stability lobe curves of the composite boring bar with a constrained damping layer were plotted so as to reveal the effects of the materials of both base layer and constrained layer, the ply angle, the damping composite structure (free or constrained damping structure) and the thickness of various layers on the chattering stability of the boring bar. Through the analysis of dynamic stiffness, the chatter stability analysis theory of a composite boring bar with a constrained damping layer is verified.

Free Vibration Analysis of Frames Using the Transfer Dynamic Stiffness Matrix Method

2008 ◽  
Vol 130 (2) ◽  
Author(s):  
Tsung-Hsien Tu ◽  
Jen-Fang Yu ◽  
Hsin-Chung Lien ◽  
Go-Long Tsai ◽  
B. P. Wang
Keyword(s):  
Free Vibration ◽  
Stiffness Matrix ◽  
Dynamic Stiffness ◽  
Free Vibration Analysis ◽  
Beam Theory ◽  
System Matrix ◽  
Dynamic Stiffness Matrix ◽  
3D Space ◽  
Euler Bernoulli Beam ◽  
Good Agreement

A method for free vibration of 3D space frame structures employing transfer dynamic stiffness matrix (TDSM) method based on Euler–Bernoulli beam theory is developed in this paper. The exact TDSM of each member is assembled to obtain the system matrix that is frequency dependent. All free vibration eigensolutions including coincident roots for the characteristic equation can be obtained to any desired accuracy using the algorithm developed by Wittrick and Williams (1971, “A General Algorithm for Computing Natural Frequencies of Elastic Structures,” Q. J. Mech. Appl. Math., 24, pp. 263–284). Exact eigenfunction of structures can then be computed using the dynamic shape function and the corresponding eigenvector. The results showed good agreement with those computed by finite element method.

scholarly journals Stability Analysis of a Periodic Fluid-Conveying Heterogeneous Nanotube System

2020 ◽  
Vol 33 (6) ◽  
pp. 756-769
Author(s):  
Jiayin Dai ◽  
Yongshou Liu ◽  
Guojun Tong
Keyword(s):  
Dynamic Stiffness ◽  
Beam Theory ◽  
Longitudinal Direction ◽  
Length Ratio ◽  
Governing Equations ◽  
Periodic Distribution ◽  
The Stability ◽  
Material Length ◽  
Euler Bernoulli Beam ◽  
Selection Of

AbstractIn this paper, the stability of a periodic heterogeneous nanotube conveying fluid is investigated. The governing equations of the nanotube system are derived based on the nonlocal Euler–Bernoulli beam theory. The dynamic stiffness method is employed to analyze the natural frequencies and critical flow velocities of the heteronanotube. The results and discussions are presented from three aspects which reveal the influences of period number, material length ratio and boundary conditions. In particular, we make comparisons between the heterogeneous nanotubes with periodic structure and the homogeneous ones with the same integral values of material properties along the longitudinal direction to isolate the influences of periodic distribution. According to the simulation results, we can conclude that with a proper selection of period number in terms of length ratio, the stability of the constructed nanotube can be improved.

scholarly journals Dynamic Finite Element (DFE) Formulation of Functionally Graded Beams

2021 ◽  
Author(s):  
Aaron Gee
Keyword(s):  
Finite Element ◽  
Dynamic Stiffness ◽  
Beam Theory ◽  
Functionally Graded ◽  
Future Research ◽  
Test Cases ◽  
Dynamic Finite Element ◽  
Fem Method ◽  
Graded Material ◽  
Euler Bernoulli Beam

The Dynamic Finite Element (DFE) theory is applied to calculate the natural frequencies of Functionally Graded Material (FGM) beams. The formulation derived is based on Euler-Bernoulli beam theory and material grading is assumed to follow a power law variation through the thickness of the beam. Results from DFE are numerically validated against methods such as Classical Finite Element Method (FEM) and the Dynamic Stiffness Method (DSM), as well as other data found in literature. Commercial software was used to further validate the proposed DFE formulation. The test cases showed that DFE results displayed excellent agreement to published results. When compared to the FEM method, DFE showed higher accuracy while requiring fewer elements to converge to the solution. Finally some general comments are made on possible future research paths for DFE method on FGM beams.

scholarly journals Dynamic Finite Element (DFE) Formulation of Functionally Graded Beams

2021 ◽  
Author(s):  
Aaron Gee
Keyword(s):  
Finite Element ◽  
Dynamic Stiffness ◽  
Beam Theory ◽  
Functionally Graded ◽  
Future Research ◽  
Test Cases ◽  
Dynamic Finite Element ◽  
Fem Method ◽  
Graded Material ◽  
Euler Bernoulli Beam

The Dynamic Finite Element (DFE) theory is applied to calculate the natural frequencies of Functionally Graded Material (FGM) beams. The formulation derived is based on Euler-Bernoulli beam theory and material grading is assumed to follow a power law variation through the thickness of the beam. Results from DFE are numerically validated against methods such as Classical Finite Element Method (FEM) and the Dynamic Stiffness Method (DSM), as well as other data found in literature. Commercial software was used to further validate the proposed DFE formulation. The test cases showed that DFE results displayed excellent agreement to published results. When compared to the FEM method, DFE showed higher accuracy while requiring fewer elements to converge to the solution. Finally some general comments are made on possible future research paths for DFE method on FGM beams.

Prediction of Regeneration Chatter Stability of Composite Boring Bar

2019 ◽  
Vol 295 ◽  
pp. 73-83
Author(s):  
Yong Sheng Ren ◽  
Ji Shuang Tian ◽  
Yu Huan Zhang ◽  
Jing Min Ma
Keyword(s):  
Dynamic Stiffness ◽  
Stability Boundary ◽  
Structural Damping ◽  
Chatter Stability ◽  
Cutting Depth ◽  
Boring Bar ◽  
Critical Cutting Depth ◽  
Time Domain Response ◽  
Euler Bernoulli Beam ◽  
Chatter Stability Prediction

The deep holes cutting process by metal boring bar is usually limited due to the development of chatter vibration. This is because metal boring bar has not only low bending stiffness but also low structural damping. A chatter stability prediction of composite boring bar under regenerative cutting force is presented. Based on the theory of Euler-Bernoulli beam, the regenerative chatter dynamic model of composite boring bar is proposed, and the solution formula of the limited cutting depth and corresponding spindle speed is given. The dynamic stability lobes of the composite boring bar are obtained by numerical calculation. The results indicate that composite boring bar exhibits efficient chatter stability than metal boring bar. Chatter stability is closely related to fiber ply angle. It is demonstrated that when ply angle is 0o, carbon/ epoxy reaches its critical cutting depth, and for graphite/ epoxy boring bar about 25o of ply angle gives its critical cutting depth, It is also demonstrated that stability boundary decreases as the ratio length and diameter increases. Finally, the prediction results of stability are compared with those from the dynamic stiffness and time-domain response, agreement is found.

scholarly journals The effect of two-parameter of Pasternak foundations on the dynamics and stability of multi-span pipe conveying fluids

2020 ◽  
Vol 12 (11) ◽  
pp. 168781402097453
Author(s):  
Nan Wu ◽  
Yuzhen Zhao ◽  
Qing Guo ◽  
Yongshou Liu
Keyword(s):  
Dynamic Stiffness ◽  
Beam Theory ◽  
Shear Stiffness ◽  
Elastic Stiffness ◽  
Pipe Conveying Fluid ◽  
Pasternak Foundation ◽  
Control Equation ◽  
Two Parameters ◽  
Euler Bernoulli Beam ◽  
Conveying Fluid

In this paper, the dynamics and stability of multi-span pipe conveying fluid embedded in Pasternak foundation is studied. Based on Euler-Bernoulli beam theory, the dynamics of multi-span pipe conveying fluid embedded in two parameters Pasternak foundation is analyzed. The dynamic stiffness method (DSM) is used to solve the control equation. A seven span pipe is calculated. The affection of two parameters of Pasternak foundation is mainly studied. Along with increasing the elastic stiffness K and shear stiffness G, the frequency is also increasing.

Vibration Analysis of the Flexible Connecting Rod With the Breathing Crack in a Slider-Crank Mechanism

2013 ◽  
Vol 135 (6) ◽  
Author(s):  
Yan-Shin Shih ◽  
Chen-Yuan Chung
Keyword(s):  
Governing Equation ◽  
Moving Boundary ◽  
Beam Theory ◽  
Crack Model ◽  
Breathing Crack ◽  
Connecting Rod ◽  
Bernoulli Beam ◽  
The Galerkin Method ◽  
Euler Bernoulli Beam ◽  
Crank Mechanism

This paper investigates the dynamic response of the cracked and flexible connecting rod in a slider-crank mechanism. Using Euler–Bernoulli beam theory to model the connecting rod without a crack, the governing equation and boundary conditions of the rod's transverse vibration are derived through Hamilton's principle. The moving boundary constraint of the joint between the connecting rod and the slider is considered. After transforming variables and applying the Galerkin method, the governing equation without a crack is reduced to a time-dependent differential equation. After this, the stiffness without a crack is replaced by the stiffness with a crack in the equation. Then, the Runge–Kutta numerical method is applied to solve the transient amplitude of the cracked connecting rod. In addition, the breathing crack model is applied to discuss the behavior of vibration. The influence of cracks with different crack depths on natural frequencies and amplitudes is also discussed. The results of the proposed method agree with the experimental and numerical results available in the literature.

Chaotic vibrations of carbon nanotubes subjected to a traversing force considering nonlocal elasticity theory

2021 ◽  
pp. 239779142110633
Author(s):  
Reza Ebrahimi
Keyword(s):  
Nonlocal Parameter ◽  
Power Spectra ◽  
Beam Theory ◽  
Nonlocal Elasticity Theory ◽  
Effective Control ◽  
Maximum Lyapunov Exponent ◽  
Harmonic Force ◽  
Spectra Analysis ◽  
Chaotic Vibrations ◽  
Euler Bernoulli Beam

The existence of chaos in the lateral vibration of the carbon nanotube (CNT) can contribute to source of instability and inaccuracy within the nano mechanical systems. So, chaotic vibrations of a simply supported CNT which is subjected to a traversing harmonic force are studied in this paper. The model of the system is formulated by using nonlocal Euler–Bernoulli beam theory. The equation of motion is solved using the Rung–Kutta method. The effects of the nonlocal parameter, velocity and amplitude of the traversing harmonic force on the nonlinear dynamic response of the system are analyzed by the bifurcation diagrams, phase plane portrait, power spectra analysis, Poincaré map and the maximum Lyapunov exponent. The results indicate that the nonlocal parameter, velocity and amplitude of the traversing harmonic force have considerable effects on the bifurcation behavior and can be used as effective control parameters for avoiding chaos.

Fatigue Life Prediction of Drill-String Subjected to Random Loadings

2014 ◽  
Author(s):  
Jiahao Zheng ◽  
Hongyuan Qiu ◽  
Jianming Yang ◽  
Stephen Butt
Keyword(s):  
Fatigue Life ◽  
Time History ◽  
Beam Theory ◽  
Drill String ◽  
Finite Element Models ◽  
Bernoulli Beam ◽  
Stress Cycles ◽  
Rainflow Counting ◽  
Euler Bernoulli Beam ◽  
Random Nature

Based on linear damage accumulation law, this paper investigates the fatigue problem of drill-strings in time domain. Rainflow algorithms are developed to count the stress cycles. The stress within the drill-string is calculated with finite element models which is developed using Euler-Bernoulli beam theory. Both deterministic and random excitations to the drill-string system are taken into account. With this model, the stress time history in random nature at any location of the drill-string can be obtained by solving the random dynamic model of the drill-string. Then the random time history is analyzed using rainflow counting method. The fatigue life of the drill-string under both deterministic and random excitations can therefore be predicted.

Experimental and Theoretical Study of a Dual-Beam Piezoelectric Energy Harvester With Misaligned Magnets

2018 ◽  
Author(s):  
Wei-Jiun Su ◽  
Hsuan-Chen Lu
Keyword(s):  
Energy Harvester ◽  
Theoretical Study ◽  
Beam Theory ◽  
Main Beam ◽  
Bernoulli Beam ◽  
Potential Wells ◽  
Piezoelectric Energy ◽  
Dual Beam ◽  
Frequency Sweeps ◽  
Euler Bernoulli Beam

In this study, a dual-beam piezoelectric energy harvester is proposed. This harvester consists of a main beam and an auxiliary beam with a pair of magnets attached to couple their motions. The potential energy of the system is modeled to understand the influence of the potential wells on the dynamics of the harvester. It is noted that the alignment of the magnets significantly influences the potential wells. A theoretical model of the harvester is developed based on the Euler-Bernoulli beam theory. Frequency sweeps are conducted experimentally and numerically to study the dynamics of the harvester. It is shown that the dual-beam harvester can exhibit hardening effect with different configurations of magnet alignments in frequency sweeps. The performance of the harvester can be improved with proper placement of the magnets.

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