Engineering applications and analysis of vibratory motion fourth order fluid film over the time dependent heated flat plate

2017 ◽  
Author(s):  
Muhammad Ismail Mohmand ◽  
Mustafa Bin Mamat ◽  
Qayyum Shah
Keyword(s):  
Flat Plate ◽  
Fourth Order ◽  
Time Dependent ◽  
Fluid Film ◽  
Engineering Applications ◽  
Vibratory Motion

scholarly journals Vibratory motion of fourth order fluid film over a unsteady heated flat

2017 ◽  
Author(s):  
Muhammad Ismail Mohmand ◽  
Mustafa Bin Mamat ◽  
Qayyum Shah ◽  
Taza Gul
Keyword(s):  
Fourth Order ◽  
Fluid Film ◽  
Vibratory Motion

Nonlinear Phenomena in Axially Moving Beams with Speed-Dependent Tension and Tension-Dependent Speed

2021 ◽  
Vol 31 (03) ◽  
pp. 2150037
Author(s):  
Ling Chen ◽  
You-Qi Tang ◽  
Shuang Liu ◽  
Yuan Zhou ◽  
Xing-Guang Liu
Keyword(s):  
Differential Equations ◽  
Fourth Order ◽  
Fourier Transforms ◽  
Time Dependent ◽  
Nonlinear Phenomena ◽  
Maximum Lyapunov Exponent ◽  
Material Derivative ◽  
Domains Of Attraction ◽  
Moving Beam ◽  
Galerkin Truncation

This paper investigates some nonlinear dynamical behaviors about domains of attraction, bifurcations, and chaos in an axially accelerating viscoelastic beam under a time-dependent tension and a time-dependent speed. The axial speed and the axial tension are coupled to each other on the basis of a harmonic variation over constant initial values. The transverse motion of the moving beam is governed by nonlinear integro-partial-differential equations with the rheological model of the Kelvin–Voigt energy dissipation mechanism, in which the material derivative is applied to the viscoelastic constitutive relation. The fourth-order Galerkin truncation is employed to transform the governing equation to a set of nonlinear ordinary differential equations. The nonlinear phenomena of the system are numerically determined by applying the fourth-order Runge–Kutta algorithm. The tristable and bistable domains of attraction on the stable steady state solution with a three-to-one internal resonance are analyzed emphatically by means of the fourth-order Galerkin truncation and the differential quadrature method, respectively. The system parameters on the bifurcation diagrams and the maximum Lyapunov exponent diagram are demonstrated by some numerical results of the displacement and speed of the moving beam. Furthermore, chaotic motion is identified in the forms of time histories, phase-plane portraits, fast Fourier transforms, and Poincaré sections.

Transient Heat Transfer for Turbulent Flow Over a Flat Plate of Appreciable Thermal Capacity and Containing Time-Dependent Heat Source

1967 ◽  
Vol 89 (4) ◽  
pp. 362-370 ◽  
Author(s):  
M. Soliman ◽  
H. A. Johnson
Keyword(s):  
Heat Transfer ◽  
Turbulent Flow ◽  
Flat Plate ◽  
Reynolds Numbers ◽  
Thermal Capacity ◽  
High Flow ◽  
Time Dependent ◽  
Approximate Analysis ◽  
Heat Generation Rate ◽  
Theory And Experiments

An approximate analysis and experimental data are presented for the transient mean wall temperature of a flat plate of appreciable thermal capacity, heated by a step in the heat generation rate and cooled on both sides by a steady, incompressible turbulent flow with a Prandtl number of unity. Theory and experiments are in agreement over a range of Reynolds numbers 5 × 105 ≤ ReL ≤ 2 × 106. The experimental mean heat transfer coefficient is observed to go through a dip to a minimum before reaching the steady state. This dip is found to be due to the conjunction of a large wall thermal capacity and a sufficiently high flow velocity.

A Study of Thermohydrodynamic Squeeze Films

1974 ◽  
Vol 96 (2) ◽  
pp. 198-205 ◽  
Author(s):  
S. M. Rohde ◽  
H. A. Ezzat
Keyword(s):  
Heat Conduction Equation ◽  
Reynolds Equation ◽  
Energy Equation ◽  
Time Dependent ◽  
Fluid Film ◽  
Squeeze Film ◽  
3 Dimensional ◽  
Temperature Distributions ◽  
Film Parameter ◽  
The Mathematical Model

This paper presents an analysis of the thermohydrodynamic performance of squeeze films. The mathematical model consists of a 3-dimensional Reynolds equation, a 3-dimensional time dependent energy equation, and a 3-dimensional time dependent heat conduction equation. The system of equations is solved numerically. Fluid film pressure and temperature distributions and the temperature distribution in the solids are presented. Fluid film velocity profiles as a function of time are also shown. The load-time characteristics for different operative conditions are studied. It is shown that a thermohydrodynamic squeeze-film parameter can give rise to a phenomenon which radically changes the fluid film performance.

Stress Intensity Factor Coefficients for Circumferential ID Surface Flaws in Cylinders for Appendix A of ASME Section XI

2013 ◽  
Author(s):  
Russell C. Cipolla ◽  
Darrell R. Lee
Keyword(s):  
Stress Intensity Factor ◽  
Stress Intensity ◽  
Intensity Factor ◽  
Flat Plate ◽  
Closed Form ◽  
Fourth Order ◽  
Surface Crack ◽  
Crack Size ◽  
Plate Geometry

The stress intensity factor (KI) equations for a surface crack in ASME Section XI, Appendix A are based on non-dimensional coefficients (Gi) that allow for the calculation of stress intensity factors for a cubic varying stress field. Currently, the coefficients are in tabular format for the case of a surface crack in a flat plate geometry. The tabular form makes the computation of KI tedious when determination of KI for various crack sizes is required and a flat plate geometry is conservative when applied to a cylindrical geometry. In this paper, closed-form equations are developed based on tabular data from API 579 (2007 Edition) [1] for circumferential cracks on the ID surface of cylinders. The equations presented, represent a complete set of Ri/t, a/t, and a/l ratios and include those presented in the 2012 PVP paper [8]. The closed-form equations provide G0 and G1 coefficients while G2 through G4 are obtained using a weight function representation for the KI solutions for a surface crack. These equations permit the calculation of the Gi coefficients without the need to perform tabular interpolation. The equations are complete up to a fourth order polynomial representation of applied stress, so that the procedures in Appendix A have been expanded. The fourth-order representation for stress will allow for more accurate fitting of highly non-linear stress distributions, such as those depicting high thermal gradients and weld residual stress fields. The equations developed in this paper will be added to the Appendix A procedures in the next major revision to ASME Section XI. With the inclusion of equations to represent Gi, the procedures of Appendix A for the determination of KI can be performed more efficiently without the conservatism of using flat plate solutions. This is especially useful when performing flaw growth evaluations where repetitive calculations are required in the computations of crack size versus time. The equations are relatively simple in format so that the KI computations can be performed by either spreadsheet analysis or by simple computer programming. The format of the equations is generic in that KI solutions for other geometries can be added to Appendix A relatively easily.

Closed Form Solutions for Stress Intensity Factor Coefficients for Circumferential ID Surface Flaws in Cylinders in ASME Section XI Appendix A

2012 ◽  
Author(s):  
Russell C. Cipolla ◽  
Darrell R. Lee
Keyword(s):  
Stress Intensity Factor ◽  
Stress Intensity ◽  
Intensity Factor ◽  
Flat Plate ◽  
Closed Form ◽  
Fourth Order ◽  
Surface Crack ◽  
Crack Size ◽  
Plate Geometry

The stress intensity factor (KI) equations for a surface crack in ASME Section XI, Appendix A are based on non-dimensional coefficients (Gi) that allow for the calculation of stress intensity factors for a cubic varying stress field. Currently, the coefficients are in tabular format for the case of a surface crack in a flat plate geometry. The tabular form makes the computation of KI tedious when determination of KI for various crack sizes is pursued and a flat plate geometry is conservative when applied to a cylindrical geometry. In this paper, closed-form equations are developed based on tabular data from API 579 (2007 Edition) [1] for circumferential cracks on the ID surface of cylinders. The closed-form equations provide G0 and G1 coefficients while G2 through G4 are obtained using a weight function representation for the KI solutions for a surface crack. These equations permit the calculation of the Gi coefficients without the need to perform tabular interpolation. The equations are complete up to a fourth order polynomial representation of applied stress, so that the procedures in Appendix A have been expanded. The fourth-order representation for stress will allow for more accurate fitting of highly non-linear stress distributions, such as those depicting high thermal gradients and weld residual stress fields. It is expected that the equations developed in this paper will be added to the Appendix A procedures. With the inclusion of equations to represent Gi, the procedures of Appendix A for the determination of KI can be performed more efficiently without the conservatism of using flat plate solutions. This is especially useful in performing flaw growth calculations where repetitive calculations are required in the computations of crack size versus time. The equations are relatively simple in format so that the KI computations can be performed by either spreadsheet analysis or by simple computer programming. The format of the equations is generic in that KI solutions for other geometries can be added to Appendix A relatively easily.

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