scholarly journals Dynamic Modeling and Cutting Stability of Rotating Tapered Composite Cutter Bar considering Material Damping

2020 ◽  
Vol 2020 ◽  
pp. 1-12
Author(s):  
Yuhuan Zhang ◽  
Ren Yongsheng ◽  
Bole Ma ◽  
Jinfeng Zhang
Keyword(s):  
Constitutive Relations ◽  
Equations Of Motion ◽  
Beam Theory ◽  
Chatter Stability ◽  
Differential Motion ◽  
Chatter Suppression ◽  
Fixed Type ◽  
The Stability ◽  
The Galerkin Method ◽  
Cutting System

Traditional milling cutter bars are generally made up of metals and exhibit poor capacity of chatter suppression. This study proposes an anisotropic composites tapered cutter bar for increasing natural frequency and damping and finally achieves the goal of enhancing chatter stability. Based on Hamilton principle and Euler–Bernoulli beam theory, the partial differential motion equations of the cutting system with a 3D rotating tapered composite cutter bar are established. Next, using the Galerkin method, the equations of motion are discretized so as to derive ordinary differential equations. In the model, damping modeling of the composite cutter bar is achieved theoretically by using damping dissipation constitutive relations for viscoelastic composites. Moreover, by introducing the rotating effect of the 3D cutter bar in the 2-DOF analytical model of stability analysis first proposed for a fixed-type cutter bar, an improved prediction model is developed and used to solve the stability lobes of the cutting system in the frequency domain analytically. Furthermore, the influences of the gyroscopic effect, material, ply angle, stacking sequence, and taper ratio on chatter stability are also discussed.

AN INVESTIGATION ON THE CHARACTERISTICS OF BENDING, BUCKLING AND VIBRATION OF NANOBEAMS VIA NONLOCAL BEAM THEORY

2014 ◽  
Vol 11 (06) ◽  
pp. 1350085 ◽  
Author(s):  
SOUMIA BENGUEDIAB ◽  
ABDELWAHED SEMMAH ◽  
FOUZIA LARBI CHAHT ◽  
SOUMIA MOUAZ ◽  
ABDELOUAHED TOUNSI
Keyword(s):  
Scale Effects ◽  
Constitutive Relations ◽  
Equations Of Motion ◽  
Shear Deformation Theory ◽  
Free Vibration Analysis ◽  
Beam Theory ◽  
Small Scale ◽  
Shear Stresses ◽  
Nonlocal Timoshenko Beam Theory ◽  
Walled Carbon Nanotubes

In the present study, a nonlocal hyperbolic shear deformation theory is developed for the static flexure, buckling and free vibration analysis of nanobeams using the nonlocal differential constitutive relations of Eringen. The theory, which does not require shear correction factor, accounts for both small scale effects and hyperbolic variation of shear strains and consequently shear stresses through the thickness of the nanobeam. The equations of motion are derived from Hamilton's principle. Analytical solutions for the deflection, buckling load and natural frequency are presented for a simply supported nanobeam, and the obtained results are compared with those predicted by the nonlocal Timoshenko beam theory and Reddy beam theories. Present solutions can be used for the static and dynamic analyses of single-walled carbon nanotubes.

Free Vibration and Stability Analysis of Internally Damped Rotating Shafts With General Boundary Conditions

1998 ◽  
Vol 120 (3) ◽  
pp. 776-783 ◽  
Author(s):  
J. Melanson ◽  
J. W. Zu
Keyword(s):  
Boundary Conditions ◽  
Equations Of Motion ◽  
Normal Modes ◽  
Beam Theory ◽  
General Boundary ◽  
General Boundary Conditions ◽  
Rotating Shaft ◽  
Classical Boundary ◽  
Rotating Shafts ◽  
The Stability

Vibration analysis of an internally damped rotating shaft, modeled using Timoshenko beam theory, with general boundary conditions is performed analytically. The equations of motion including the effects of internal viscous and hysteretic damping are derived. Exact solutions for the complex natural frequencies and complex normal modes are provided for each of the six classical boundary conditions. Numerical simulations show the effect of the internal damping on the stability of the rotor system.

A NEW NONLOCAL BEAM THEORY WITH THICKNESS STRETCHING EFFECT FOR NANOBEAMS

2013 ◽  
Vol 12 (04) ◽  
pp. 1350025 ◽  
Author(s):  
ABDELOUAHED TOUNSI ◽  
SOUMIA BENGUEDIAB ◽  
MOHAMMED SID AHMED HOUARI ◽  
ABDELWAHED SEMMAH
Keyword(s):  
Shear Deformation ◽  
Constitutive Relations ◽  
Equations Of Motion ◽  
Nonlocal Parameter ◽  
Beam Theory ◽  
Dynamic Responses ◽  
Theoretical Development ◽  
Small Scale ◽  
Small Scale Effect ◽  
Nonlocal Beam

This paper presents a new nonlocal thickness-stretching sinusoidal shear deformation beam theory for the static and vibration of nanobeams. The present model incorporates the length scale parameter (nonlocal parameter) which can capture the small scale effect, and it accounts for both shear deformation and thickness stretching effects by a sinusoidal variation of all displacements through the thickness without using shear correction factor. Based on the nonlocal differential constitutive relations of Eringen, the equations of motion of the nanobeam are derived using Hamilton's principle. The effects of nonlocal parameter, aspect ratio and the thickness stretching on the static and dynamic responses of the nanobeam are discussed. The theoretical development presented herein may serve as a reference for nonlocal theories as applied to the bending and dynamic behaviors of complex-nanobeam-system such as complex carbon nanotube system.

scholarly journals Vibrations of a Beam Moving Over Supports with Clearance

1994 ◽  
Vol 1 (6) ◽  
pp. 549-557
Author(s):  
H.P. Lee
Keyword(s):  
Piecewise Linear ◽  
Equations Of Motion ◽  
Beam Theory ◽  
Euler Beam ◽  
Assumed Mode Method ◽  
Mode Method ◽  
Euler Beam Theory ◽  
The Stability ◽  
Effect Of Support ◽  
Piecewise Linear Stiffness

The transverse vibration of a beam moving over two supports with clearance is analyzed using Euler beam theory. The equations of motion are formulated based on a Lagrangian approach and the assumed mode method. The supports with clearance are modeled as frictionless supports with piecewise-linear stiffness. A feature of the present formulation is that its complexity does not increase with increased number of supports. Results of numerical simulations are presented for various prescribed motions of the beam. The effect of support clearance on the stability of the beam is investigated.

Nonconservative Stability of Gyroscopic Rotor Systems

1993 ◽  
Author(s):  
Hwang-Kuen Chen ◽  
Der-Ming Ku ◽  
Lien-Wen Chen
Keyword(s):  
Direct Method ◽  
Equations Of Motion ◽  
Beam Theory ◽  
Follower Force ◽  
The Finite Element Method ◽  
Nonconservative System ◽  
Rotor Systems ◽  
Eigenvalue Sensitivity ◽  
The Stability ◽  
Flutter Load

Abstract The stability behavior of a cantilevered shaft, rotating at a constant speed and subjected to a follower force at the free end, is studied by the finite element method. The equations of motion for such a gyroscopic system are formulated by using deformation shape functions developed from Timoshenko beam theory. The effects of translational and rotatory inertia, gyroscopic moments, bending and shear deformations are included. In order to determine the critical load of the present nonconservative system more quickly and efficiently, a simple and direct method that utilizes the eigenvalue sensitivity with respect to the follower force is introduced. The numerical results show that for the present nonconservative system, the onset of flutter instability occurs when the first and second backward whirl speeds are coincident. And also, due to the effect of the gyroscopic moments, the critical flutter load decreases as the rotational speed increases.

Modeling and Characterization of a Piezoelectric Energy Harvester Under Combined Aerodynamic and Base Excitations

2015 ◽  
Vol 137 (3) ◽  
Author(s):  
Amin Bibo ◽  
Abdessattar Abdelkefi ◽  
Mohammed F. Daqaq
Keyword(s):  
Bluff Body ◽  
Energy Harvester ◽  
Constitutive Relations ◽  
Equations Of Motion ◽  
Primary Resonance ◽  
Beam Theory ◽  
Combined Loading ◽  
Response Behavior ◽  
Piezoelectric Energy ◽  
Piezoelectric Cantilever

This paper develops and validates an aero-electromechanical model which captures the nonlinear response behavior of a piezoelectric cantilever-type energy harvester under combined galloping and base excitations. The harvester consists of a thin piezoelectric cantilever beam clamped at one end and rigidly attached to a bluff body at the other end. In addition to the vibratory base excitations, the beam is also subjected to aerodynamic forces resulting from the separation of the incoming airflow on both sides of the bluff body which gives rise to limit-cycle oscillations when the airflow velocity exceeds a critical value. A nonlinear electromechanical distributed-parameter model of the harvester under the combined excitations is derived using the energy approach and by adopting the nonlinear Euler–Bernoulli beam theory, linear constitutive relations for the piezoelectric transduction, and the quasi-steady assumption for the aerodynamic loading. The resulting partial differential equations of motion are discretized and a reduced-order model is obtained. The mathematical model is validated by conducting a series of experiments at different wind speeds and base excitation amplitudes for excitation frequencies around the primary resonance of the harvester. Results from the model and experiment are presented to characterize the response behavior under the combined loading.

Analytical Modeling of Chatter Stability in Turning and Boring Operations—Part II: Experimental Verification

2007 ◽  
Vol 129 (4) ◽  
pp. 733-739 ◽  
Author(s):  
Emre Ozlu ◽  
Erhan Budak
Keyword(s):  
Satisfactory Agreement ◽  
Experimental Verification ◽  
Analytical Modeling ◽  
Stability Limit ◽  
Experimental Results ◽  
Chatter Stability ◽  
Nose Radius ◽  
The Stability ◽  
Flexible Component ◽  
Cutting System

In this part of the paper series, chatter experiments are conducted in order to verify the proposed stability models presented in the first part (Ozlu, E., and Budak, E., 2007, ASME J. Manuf. Sci. Eng., 129(4), pp. 726–732). Turning and boring chatter experiments are conducted for the cases where the tool or the workpiece is the most flexible component of the cutting system. In addition, chatter experiments demonstrating the effect of the insert nose radius on the stability limit are presented. Satisfactory agreement is observed between the analytical predictions and the experimental results.

Dynamic Stability of a Spinning Timoshenko Beam Subjected to a Moving Mass-Spring-Damper Unit

2010 ◽  
Author(s):  
T. H. Young ◽  
M. S. Chen
Keyword(s):  
Dynamic Stability ◽  
Timoshenko Beam ◽  
Multiple Scales ◽  
Equations Of Motion ◽  
Axial Direction ◽  
Longitudinal Axis ◽  
Moving Mass ◽  
The Stability ◽  
The Galerkin Method ◽  
Mass Spring

This paper investigates the dynamic stability of a finite Timoshenko beam spinning along its longitudinal axis and subjected to a moving mass-spring-damper (MSD) unit traveling in the axial direction. The mass of the moving MSD unit makes contact with the beam all the time during traveling. Due to the moving MSD unit, the beam is acted upon by a periodic, parametric excitation. In this work, the equations of motion of the beam are first discretized by the Galerkin method. The discretized equations of motion are then partially uncoupled by the modal analysis procedure suitable for gyroscopic systems. Finally the method of multiple scales is used to obtain the stability boundaries of the beam. Numerical results show that if the displacement of the MSD unit is equal to only one of the two transverse displacements of the beam, very large unstable regions may appear at main resonances.

Dynamic Analysis of Three Parallel Beams With Electrostatic Force Interaction

2011 ◽  
Author(s):  
Pezhman A. Hassanpour ◽  
Patricia M. Nieva ◽  
Amir Khajepour
Keyword(s):  
Time Domain ◽  
Stability Condition ◽  
Initial Conditions ◽  
Electrostatic Force ◽  
Equations Of Motion ◽  
Beam Theory ◽  
Stability Margin ◽  
Modal Damping ◽  
The Stability ◽  
Euler Bernoulli Beam

In this paper, the dynamics of a micro-machined structure with three parallel cantilevers is investigated. The cantilevers are electrically charged and apply electrostatic force to each other. The governing equations of motion are derived using Euler-Bernoulli beam theory and considering structural modal damping. The stability condition of the beams for various electric charges is also studied. In addition, the equations of motion are integrated to obtain the response of the beams in time-domain for a range of initial conditions. This response is used to study the behavior of the beams at the stability margin. The end application of the structure under investigation is in the device characterization. The dynamic stability condition and time-domain responses are used to investigate the reliability of the characterization. Once translated back to physical quantities, these results can be used for improving the measurements.

scholarly journals Effect of Kerr Foundation and in-Plane Forces on Free Vibration of FGM Nanobeams with Diverse Distribution of Porosity

2020 ◽  
Vol 14 (3) ◽  
pp. 135-143
Author(s):  
Piotr Jankowski
Keyword(s):  
Porous Material ◽  
Constitutive Relations ◽  
Equations Of Motion ◽  
Strain Tensor ◽  
Beam Theory ◽  
Functionally Graded ◽  
Strain Gradient Theory ◽  
Graphical Form ◽  
Solution Technique ◽  
Gradient Theory

Abstract In the present paper, the effect of diverse distribution of functionally graded porous material and Kerr elastic foundation on natural vibrations of nanobeams subjected to in-plane forces is investigated based on the nonlocal strain gradient theory. The displacement field of the nanobeam satisfies assumptions of Reddy higher-order shear deformation beam theory. All the displacements gradients are assumed to be small, then the components of the Green-Lagrange strain tensor are linear and infinitesimal. The constitutive relations for functionally graded (FG) porous material are expressed by nonlocal and length scale parameters and power-law variation of material parameters in conjunction with cosine functions. It created possibility to investigate an effect of functionally graded materials with diverse distribution of porosity and volume of voids on mechanics of structures in nano scale. The Hamilton’s variational principle is utilized to derive governing equations of motion of the FG porous nanobeam. Analytical solution to formulated boundary value problem is obtained in closed-form by using Navier solution technique. Validation of obtained results and parametric study are presented in tabular and graphical form. Influence of axial tensile/compressive forces and three different types of porosity distribution as well as stiffness of Kerr foundation on natural frequencies of functionally graded nanobeam is comprehensively studied.

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