scholarly journals Inertia and Couple-Stress Effects in a Curvilinear Thrust Hydrostatic Bearing

2017 ◽  
Vol 22 (3) ◽  
pp. 759-767 ◽  
Author(s):  
A. Walicka ◽  
P. Jurczak ◽  
J. Falicki
Keyword(s):  
Couple Stress ◽  
Equations Of Motion ◽  
Inertia Effects ◽  
Numerical Examples ◽  
Thrust Bearings ◽  
Hydrostatic Bearing ◽  
Stress Effects ◽  
Pressure Distributions ◽  
Radial Thrust ◽  
Inertia Forces

AbstractThe flow of a couple-stress lubricant in a clearance of a curvilinear thrust hydrostatic bearing with impermeable walls is considered. The flow in the bearing clearance is considered with inertia forces. The equations of motion are solved by an averaged inertia method. As a result, the formulae for pressure distributions without and with inertia effects were obtained. Radial thrust bearings and spherical bearings are discussed as numerical examples. It is shown that inertia effects influence the bearing performance considerably.

Vibration Analysis of High Speed Stepped Thrust Gas Film Bearings With Inertia Effects

1997 ◽  
Author(s):  
Masayuki Ochiai ◽  
Hiromu Hashimoto
Keyword(s):  
Vibration Analysis ◽  
High Speed ◽  
Reynolds Equation ◽  
Dynamic Pressure ◽  
Mechanical Energy ◽  
Inertia Effects ◽  
Pressure Distributions ◽  
Load Carrying ◽  
Inertia Forces ◽  
Generalized Reynolds Equation

Abstract Stepped thrust gas film bearings are widely used for high speed rotating machinery because of their simple structure, relatively high load carrying capacity and stability. In such bearings, the gas film inertia forces may play an important role under high speed conditions. In this paper, the vibration analysis of high speed, stepped thrust gas film bearings considering the inertia effects is described. In the numerical analysis, the static and dynamic pressure distributions in pocket and land regions are evaluated from the generalized Reynolds equation considering the centrifugal force. The pressure values at the step are calculated by considering the conservation of mechanical energy and the continuity of gas film flow in pocket and land regions. Moreover, the dynamic response of bearings subjected to impulsive and sinusoidal excitations are analyzed for different values of film thickness ratios. From the numerical results, the effects of gas film inertia on the vibration characteristics of bearings are clarified.

Thermal and Inertia Effects in Turulent-Flow Thrust Bearings

1980 ◽  
Vol 22 (1) ◽  
pp. 43-45 ◽  
Author(s):  
Z. S. Safar
Keyword(s):  
Carrying Capacity ◽  
Thermal Effects ◽  
Analytical Study ◽  
Load Carrying Capacity ◽  
Inertia Effects ◽  
Thrust Bearings ◽  
Load Carrying ◽  
Laminar And Turbulent Flow ◽  
Energy Equations ◽  
Inertia Forces

This paper presents a semi-analytical study of the influence of inertia terms on the thermohydrodynamic analysis of infinitely-wide thrust bearings operating under conditions of laminar and turbulent flow. The momentum and energy equations are not seriously affected by the presence of inertia forces. Results show that the inclusion of inertia terms causes an increase in the fluid film pressure and load-carrying capacity. Thermal effects exert a pronounced influence on bearing performance.

Size-dependent free vibration analysis of a three-layered exponentially graded nano-/micro-plate with piezomagnetic face sheets resting on Pasternak’s foundation via MCST

2017 ◽  
Vol 22 (1) ◽  
pp. 55-86 ◽  
Author(s):  
Mohammad Arefi ◽  
Masoud Kiani ◽  
Ashraf M Zenkour
Keyword(s):  
Couple Stress ◽  
Couple Stress Theory ◽  
Equations Of Motion ◽  
Free Vibration Analysis ◽  
Modified Couple Stress Theory ◽  
Stress Theory ◽  
Modified Couple Stress ◽  
Material Length Scale ◽  
Material Length ◽  
Exponentially Graded

The present work is devoted to the free vibration analysis of elastic three-layered nano-/micro-plate with exponentially graded core and piezomagnetic face-sheets using the modified couple stress theory. To capture size-dependency for a nano-/micro-sized rectangular plate, the couple stress theory is used as a non-classical continuum theory. The rectangular elastic three-layered nano-/micro-plate is resting on Pasternak’s foundation. The present model contains one material length scale parameter and can capture the size effect. Material properties of the core are supposed to vary along the thickness direction based on the exponential function. The governing equations of motion are derived from Hamilton’s principle based on the modified couple stress theory and first-order shear deformation theory. The analytical solution is presented to solve seven governing equations of motion using Navier’s solution. Eventually the natural frequency is scrutinized for different side length ratio, thickness ratio, inhomogeneity parameter, material length scale, and parameters of foundation numerically.

Free nonlinear vibration analysis of nano-truncated conical shells based on modified strain gradient theory

2021 ◽  
pp. 146442072110419
Author(s):  
Alireza Sheykhi ◽  
Shahrokh Hosseini-Hashemi ◽  
Adel Maghsoudpour ◽  
Shahram E Haghighi
Keyword(s):  
Boundary Conditions ◽  
Strain Gradient ◽  
Couple Stress ◽  
Equations Of Motion ◽  
Differential Quadrature ◽  
Strain Gradient Theory ◽  
Gradient Theory ◽  
Modified Strain Gradient Theory ◽  
Conical Shells ◽  
Modified Couple Stress

In this study, the nonlinear free vibrations behaviour of nano-truncated conical shells was analysed, using the first-order shear deformable shell model. The analysis took into account the structure size through modified strain gradient theory, and differential quadrature and Fréchet derivative methods in von Kármán-Donnell-type approach to kinematic nonlinearity. The governing equations were obtained, utilizing Hamilton's principle. Partial differential equations plus the non-classical and classical boundary conditions were used to obtain the shells’ equations of motion. Discretizing the boundary conditions and equations of motion were performed based on a generalized differential quadrature analogy. The eigenvalue system was considered based on the harmonic balance technique. The Galerkin and Fréchet derivative approaches were used to determine the nonlinear free vibration behaviour of the carbon nano-cone, which was modelled in the simply- and clamped-supported boundary conditions. Comparisons were made between the findings from the new model versus the couple and classical stress theories, indicating that the classical and modified couple stress theories are distinct representations of modified strain gradient theory. The results also revealed that the degree of hardening of nano-truncated conical shells in the modified strain gradient theory is less than that of modified couple stress and classical theories. This led to a rise in the non-dimensional amplitude and frequency ratios. This study investigated the effect of size on free nonlinear vibrations of nano-truncated conical shells for various apex angles and lengths. Finally, we evaluated and compared our findings versus those reported by previous studies, which confirmed the precision and accuracy of our results.

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