Flutter-Type Instability of a Beam Subjected to Coulomb Friction

2011 ◽  
Author(s):  
Yasuhiro Seo ◽  
Go Kono ◽  
Hiroshi Yabuno
Keyword(s):  
Boundary Conditions ◽  
Linear Stability ◽  
Coulomb Friction ◽  
Continuum Model ◽  
Excitation Mechanism ◽  
Governing Equations ◽  
Cosserat Theory ◽  
Floor Surface ◽  
Excited Oscillation

To analyze the excitation mechanism of self-excited oscillation in a beam which is in contact with a moving floor surface, we deal with a beam subjected to Coulomb friction and theoretically predict the occurrence of self-excited oscillation through flutter-type instability. We introduced an extensible continuum model, and derived its governing equations by special Cosserat theory, which allows for the extensibility of the beam to be considered and boundary conditions. The boundary conditions on the end of the beam are unique, because the end of the beam contacts with the moving floor surface. Then, we discretized the system, analyzed the linear stability, and indicated that the flutter-type instability in the beam is produced due to the Coulomb friction and the extension of the extensibility.

Mode Coupling-Type Instability of a Beam Subjected to Coulomb Friction

2013 ◽  
Vol 135 (6) ◽  
Author(s):  
Yasuhiro Seo ◽  
Hiroshi Yabuno ◽  
Go Kono
Keyword(s):  
Mode Coupling ◽  
Coulomb Friction ◽  
Axial Direction ◽  
Laser Printer ◽  
Beam Model ◽  
Excitation Mechanism ◽  
Cosserat Theory ◽  
Floor Surface ◽  
Excited Oscillation ◽  
Mode Coupling Instability

To analyze the excitation mechanism of self-excited oscillation in a beam that is in contact with a moving floor surface such as a cleaning blade, which is a beam mounted in a laser printer to clean the photoreceptor, we study a beam subjected to Coulomb friction and theoretically predict the occurrence of self-excited oscillation through mode-coupling instability. We present an extensible beam model, and derive its governing nonlinear equations by means of special Cosserat theory, which allows for the extensibility of the beam to be considered. The boundary conditions on the end of the beam are unique because the end of the beam makes contact with the moving floor surface. We used a discretized linearized governing equation and performed linear stability analysis. The results indicate that self-excited oscillation in the beam is produced due to both Coulomb friction and mode coupling of the bending and extension of the beam based on the extensibility in the axial direction.

scholarly journals Vibration of rotating circular cylindrical shells with distributed springs

2021 ◽  
Vol 37 ◽  
pp. 346-358
Author(s):  
Fuchun Yang ◽  
Xiaofeng Jiang ◽  
Fuxin Du
Keyword(s):  
Boundary Conditions ◽  
Galerkin Method ◽  
Shell Theory ◽  
Rotation Speed ◽  
Cylindrical Shells ◽  
Free Vibrations ◽  
Governing Equations ◽  
Natural Response ◽  
Circular Cylindrical Shells ◽  
The Galerkin Method

Abstract Free vibrations of rotating cylindrical shells with distributed springs were studied. Based on the Flügge shell theory, the governing equations of rotating cylindrical shells with distributed springs were derived under typical boundary conditions. Multicomponent modal functions were used to satisfy the distributed springs around the circumference. The natural responses were analyzed using the Galerkin method. The effects of parameters, rotation speed, stiffness, and ratios of thickness/radius and length/radius, on natural response were also examined.

scholarly journals Variational formulations of steady rotational equatorial waves

2020 ◽  
Vol 10 (1) ◽  
pp. 534-547
Author(s):  
Jifeng Chu ◽  
Joachim Escher
Keyword(s):  
Linear Stability ◽  
Stream Function ◽  
Water Waves ◽  
Variational Formulation ◽  
Energy Functional ◽  
Equatorial Waves ◽  
Second Variation ◽  
Governing Equations ◽  
The Second Variation ◽  
Variational Formulations

Abstract When the vorticity is monotone with depth, we present a variational formulation for steady periodic water waves of the equatorial flow in the f-plane approximation, and show that the governing equations for this motion can be obtained by studying variations of a suitable energy functional 𝓗 in terms of the stream function and the thermocline. We also compute the second variation of the constrained energy functional, which is related to the linear stability of steady water waves.

Application of Generalized Differential Quadrature Method to the Bending of Thick Laminated Plates with Various Boundary Conditions

2006 ◽  
Vol 5-6 ◽  
pp. 407-414 ◽  
Author(s):  
Mohammad Mohammadi Aghdam ◽  
M.R.N. Farahani ◽  
M. Dashty ◽  
S.M. Rezaei Niya
Keyword(s):  
Boundary Condition ◽  
Boundary Conditions ◽  
Simple Procedure ◽  
Shear Deformation Theory ◽  
Laminated Plates ◽  
Differential Quadrature ◽  
Governing Equations ◽  
First Order ◽  
Various Boundary Conditions ◽  
Generalized Differential

Bending analysis of thick laminated rectangular plates with various boundary conditions is presented using Generalized Differential Quadrature (GDQ) method. Based on the Reissner first order shear deformation theory, the governing equations include a system of eight first order partial differential equations in terms of unknown displacements, forces and moments. Presence of all plate variables in the governing equations provide a simple procedure to satisfy different boundary condition during application of GDQ method to obtain accurate results with relatively small number of grid points even for plates with free edges .Illustrative examples including various combinations of clamped, simply supported and free boundary condition are given to demonstrate the accuracy and convergence of the presented GDQ technique. Results are compared with other analytical and finite element predictions and show reasonably good agreement.

On the Motion of Granular Materials Due to Shear

2000 ◽  
Author(s):  
Mehrdad Massoudi ◽  
Tran X. Phuoc
Keyword(s):  
Finite Difference ◽  
Granular Materials ◽  
Continuum Model ◽  
Theory Model ◽  
Governing Equations ◽  
Flat Plates ◽  
Material Parameters ◽  
Finite Difference Technique ◽  
Linear Differential ◽  
The Continuum

Abstract In this paper we study the flow of granular materials between two horisontal flat plates where the top plate is moving with a constant speed. The constitutive relation used for the stress is based on the continuum model proposed by Rajagopal and Massoudi (1990), where the material parameters are derived using the kinetic theory model proposed by Boyle and Massoudi (1990). The governing equations are non-dimensionalized and the resulting system of non-linear differential equations is solved numerically using finite difference technique.

Investigation of heat transfer in irregular porous cavity subjected to various boundary conditions

2019 ◽  
Vol 29 (1) ◽  
pp. 418-447 ◽  
Author(s):  
Irfan Anjum Badruddin
Keyword(s):  
Heat Transfer ◽  
Boundary Conditions ◽  
Outer Boundary ◽  
Governing Equations ◽  
Content Type ◽  
Porous Cavity ◽  
Various Boundary Conditions ◽  
Heating Source ◽  
Transfer Behavior ◽  
Vertical Walls

Purpose The purpose of this paper is to investigate the heat transfer in an arbitrary cavity filled with porous medium. The geometry of the cavity is such that an isothermal heating source is placed centrally at the bottom of the cavity. The height and width of the heating source is varied to analyses its effect on the heat transfer characteristics. The investigation is carried out for three different cases of outer boundary conditions such as two outside vertical walls being maintained at cold temperature To, two vertical and top horizontal surface being heated to. To and the third case with top surface kept at To but other surfaces being adiabatic. Design/methodology/approach Finite element method is used to solve the governing equations. Findings It is observed that the cavity exhibits unique heat transfer behavior as compared to regular cavity. The cases of boundary conditions are found to affect the heat transfer rate in the porous cavity. Originality/value This is original work representing the heat transfer in irregular porous cavity with various boundary conditions. This work is neither being published nor under review in any other journal.

scholarly journals Visualization Techniques of Differentially Heated Lid-Driven Square Cavity

2020 ◽  
Vol 2020 ◽  
pp. 1-7
Author(s):  
Vekamulla Narayana
Keyword(s):  
Flow Field ◽  
Boundary Conditions ◽  
Computational Cost ◽  
Field Synergy ◽  
Governing Equations ◽  
Square Cavity ◽  
Field Synergy Principle ◽  
Visualization Techniques

In the present study, an attempt is made to explore the flow field inside the differentially heated lid-driven square cavity. The governing equations along with boundary conditions are solved numerically. The simulated results (100 ≤ Re ≤ 1000 and 0.001 ≤ Ri ≤ 10) are validated with previous results in the literature. The convection differencing schemes, namely, UPWIND, QUICK, SUPERBEE, and SFCD, are discussed and are used to simulate the flow using the MPI code. It is observed that the computational cost for all the differencing schemes get reduced tremendously when the MPI code is implemented. Plots demonstrate the influences of Re and Ri in terms of the contours of the fluid streamlines, isotherms, energy streamlines, and field synergy principle.

scholarly journals Vibration Characteristics of Piezoelectric Microbeams Based on the Modified Couple Stress Theory

2014 ◽  
Vol 2014 ◽  
pp. 1-12 ◽  
Author(s):  
R. Ansari ◽  
M. A. Ashrafi ◽  
S. Hosseinzadeh
Keyword(s):  
Boundary Conditions ◽  
Couple Stress ◽  
Natural Frequencies ◽  
Couple Stress Theory ◽  
Equations Of Motion ◽  
Modified Couple Stress Theory ◽  
Beam Model ◽  
Governing Equations ◽  
Stress Theory ◽  
Modified Couple Stress

The vibration behavior of piezoelectric microbeams is studied on the basis of the modified couple stress theory. The governing equations of motion and boundary conditions for the Euler-Bernoulli and Timoshenko beam models are derived using Hamilton’s principle. By the exact solution of the governing equations, an expression for natural frequencies of microbeams with simply supported boundary conditions is obtained. Numerical results for both beam models are presented and the effects of piezoelectricity and length scale parameter are illustrated. It is found that the influences of piezoelectricity and size effects are more prominent when the length of microbeams decreases. A comparison between two beam models also reveals that the Euler-Bernoulli beam model tends to overestimate the natural frequencies of microbeams as compared to its Timoshenko counterpart.

Meshless Integral Method for Analysis of Elastoplastic Geotechnical Materials

2010 ◽  
Author(s):  
Jianfeng Ma ◽  
Joshua David Summers ◽  
Paul F. Joseph
Keyword(s):  
Boundary Conditions ◽  
Function Approximation ◽  
Integral Method ◽  
Weak Form ◽  
Constitutive Law ◽  
Governing Equations ◽  
Natural Boundary ◽  
Pressure Sensitive ◽  
Support Domain ◽  
Natural Boundary Conditions

The meshless integral method based on regularized boundary equation [1][2] is extended to analyze elastoplastic geotechnical materials. In this formulation, the problem domain is clouded with a node set using automatic node generation. The sub-domain and the support domain related to each node are also generated automatically using algorithms developed for this purpose. The governing integral equation is obtained from the weak form of elastoplasticity over a local sub-domain and the moving least-squares approximation is employed for meshless function approximation. The geotechnical materials are described by pressure-sensitive multi-surface Drucker-Prager/Cap plasticity constitutive law with hardening. A generalized collocation method is used to impose the essential boundary conditions and natural boundary conditions are incorporated in the system governing equations. A comparison of the meshless results with the FEM results shows that the meshless integral method is accurate and robust enough to solve geotechnical materials.

Computational Study of Streamfunction-Vorticity Formulation of Incompressible Flow and Heat Transfer Problems

2011 ◽  
Vol 52-54 ◽  
pp. 511-516 ◽  
Author(s):  
Arup Kumar Borah
Keyword(s):  
Heat Transfer ◽  
Finite Element ◽  
Boundary Conditions ◽  
Incompressible Flow ◽  
Computational Study ◽  
The Other ◽  
Governing Equations ◽  
Flow And Heat Transfer ◽  
Continuity Constraint ◽  
Transfer Problems

In this paper we have studied the streamfunction-vorticity formulation can be advantageously used to analyse steady as well as unsteady incompressible flow and heat transfer problems, since it allows the elimination of pressure from the governing equations and automatically satisfies the continuity constraint. On the other hand, the specification of boundary conditions for the streamfunction-vorticity is not easy and a poor evaluation of these conditions may lead to serious difficulties in obtaining a converged solution. The main issue addressed in this paper is the specification in the boundary conditions in the context of finite element of discretization, but approach utilized can be easily extended to finite volume computations.

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