scholarly journals Nonlinear Stability Analysis of a Spinning Top with an Interior Liquid-Filled Cavity

2020 ◽  
Author(s):  
Giovanni Paolo Galdi ◽  
Giusy Mazzone
Keyword(s):  
Nonlinear Stability ◽  
Center Of Mass ◽  
Coupled System ◽  
Vertical Axis ◽  
Navier Stokes ◽  
Physical Parameters ◽  
Nonlinear Stability Analysis ◽  
Spinning Top ◽  
Axis Passing

Consider the  motion of the the coupled system, $\mathscr S$, constituted by a (non-necessarily symmetric) top, $\mathscr B$, with an interior cavity, $\mathscr C$, completely filled up with a Navier-Stokes  liquid, $\mathscr L$. A particular steady-state motion $\bar{\sf s}$ (say) of $\mathscr S$, is when $\mathscr L$ is at rest with respect to $\mathscr B$, and $\mathscr S$, as a whole rigid body, spins with a constant angular velocity $\bar{\V\omega}$ around a vertical axis passing through its center of mass $G$ in its highest position ({\em upright spinning top}). We then provide a completely characterization of the nonlinear stability of $\bar{\sf s}$ by showing, roughly speaking, that $\bar{\sf s}$ is stable if and only if $|\bar{\V\omega}|$ is sufficiently large, all other physical parameters being fixed. Moreover we show that, unlike the case when $\mathscr C$ is empty, under the above stability conditions, the top will eventually return to the unperturbed upright configuration.

scholarly journals Optimal Stability Thresholds in Rotating Fully Anisotropic Porous Medium with LTNE

2021 ◽  
Author(s):  
Florinda Capone ◽  
Maurizio Gentile ◽  
Jacopo A. Gianfrani
Keyword(s):  
Porous Layer ◽  
Nonlinear Stability ◽  
Steady Motion ◽  
Vertical Axis ◽  
Linear Instability ◽  
List Type ◽  
Nonlinear Stability Analysis ◽  
Onset Of Convection ◽  
Anisotropic Porous Medium ◽  
Necessary And Sufficient

Abstract The onset of thermal convection in an anisotropic horizontal porous layer heated from below and rotating about vertical axis, under local thermal non-equilibrium hypothesis is studied. Linear and nonlinear stability analysis of the conduction solution is performed. Coincidence between the linear instability and the global nonlinear stability thresholds with respect to the L2—norm is proved. Article Highlights A necessary and sufficient condition for the onset of convection in a rotating anisotropic porous layer has been obtained. It has been proved that convection can occur only through a steady motion. A detailed proof is reported thoroughly. Numerical analysis shows that permeability promotes convection, while thermal conductivities and rotation stabilize conduction.

Nonlinear Stability Analysis for FGM Shallow Conical Shells Subjected to Thermal and Mechanical United Loads

2012 ◽  
Vol 476-478 ◽  
pp. 2515-2522
Author(s):  
Jia Chu Xu ◽  
Chao Deng ◽  
Hao Wang
Keyword(s):  
Nonlinear Stability ◽  
Shallow Shell ◽  
Large Deflection ◽  
Physical Parameters ◽  
Thermal Loads ◽  
Nonlinear Stability Analysis ◽  
Conical Shells ◽  
Power Rate ◽  
Deflection Theory ◽  
Large Deflection Theory

Based on the Von Karman large deflection theory of shallow shell, the problem of nonlinear stability of symmetrically FGM shallow conical shells under the action of mechanical and thermal loads is investigated. The nonlinear governing equation under the united action of mechanical and thermal loads of FGM shallow conical shells whose physical parameters change with the power rate is derived and solved by the modified iteration method. The nonlinear characteristic relation of load, deflection and temperature is obtained. The extremum buckling principle is employed to determine the critical buckling load. The influences of gradient constants, geometric parameters and temperature differences on buckling are discussed as well.

Methods of centre manifold and multiple scales in the theory of weakly nonlinear stability for fluid motions

1991 ◽  
Vol 434 (1892) ◽  
pp. 719-733 ◽  
Keyword(s):  
Nonlinear Stability ◽  
Stokes Equations ◽  
Multiple Scales ◽  
Navier Stokes ◽  
Nonlinear Stability Analysis ◽  
Centre Manifold ◽  
Navier Stokes Equations ◽  
Weakly Nonlinear ◽  
Seventh Order ◽  
The Relationship

The equivalence between the method of centre manifold and the method of multiple scales was examined when they are applied to the weakly nonlinear stability analysis for fluid motions. The relationship between the Landau equations of the seventh order, which were reduced from the Navier-Stokes equations by applying these two methods, is clarified. How we should define the disturbance amplitude to obtain the complete equivalence between them is discussed.

scholarly journals Nonlinear stability of two-layer shallow water flows with a free surface

2020 ◽  
Vol 476 (2236) ◽  
pp. 20190594
Author(s):  
Francisco de Melo Viríssimo ◽  
Paul A. Milewski
Keyword(s):  
Free Surface ◽  
Initial Data ◽  
Nonlinear Stability ◽  
Mathematical Proof ◽  
Passive Layer ◽  
Physical Parameters ◽  
Immiscible Fluid ◽  
Dimensional System ◽  
The Cauchy Problem ◽  
The Difference

The problem of two layers of immiscible fluid, bordered above by an unbounded layer of passive fluid and below by a flat bed, is formulated and discussed. The resulting equations are given by a first-order, four-dimensional system of PDEs of mixed-type. The relevant physical parameters in the problem are presented and used to write the equations in a non-dimensional form. The conservation laws for the problem, which are known to be only six, are explicitly written and discussed in both non-Boussinesq and Boussinesq cases. Both dynamics and nonlinear stability of the Cauchy problem are discussed, with focus on the case where the upper unbounded passive layer has zero density, also called the free surface case. We prove that the stability of a solution depends only on two ‘baroclinic’ parameters (the shear and the difference of layer thickness, the former being the most important one) and give a precise criterion for the system to be well-posed. It is also numerically shown that the system is nonlinearly unstable, as hyperbolic initial data evolves into the elliptic region before the formation of shocks. We also discuss the use of simple waves as a tool to bound solutions and preventing a hyperbolic initial data to become elliptic and use this idea to give a mathematical proof for the nonlinear instability.

scholarly journals Acoustic Characterization of Some Steel Industry Waste Materials

2021 ◽  
Vol 11 (13) ◽  
pp. 5924
Author(s):  
Elisa Levi ◽  
Simona Sgarbi ◽  
Edoardo Alessio Piana
Keyword(s):  
Thermal Characteristic ◽  
Environmental Benefits ◽  
Acoustic Properties ◽  
Physical Parameters ◽  
Industry Waste ◽  
Acoustic Characterization ◽  
Minimization Procedure ◽  
The Difference ◽  
By Products

From a circular economy perspective, the acoustic characterization of steelwork by-products is a topic worth investigating, especially because little or no literature can be found on this subject. The possibility to reuse and add value to a large amount of this kind of waste material can lead to significant economic and environmental benefits. Once properly analyzed and optimized, these by-products can become a valuable alternative to conventional materials for noise control applications. The main acoustic properties of these materials can be investigated by means of a four-microphone impedance tube. Through an inverse technique, it is then possible to derive some non-acoustic properties of interest, useful to physically characterize the structure of the materials. The inverse method adopted in this paper is founded on the Johnson–Champoux–Allard model and uses a standard minimization procedure based on the difference between the sound absorption coefficients obtained experimentally and predicted by the Johnson–Champoux–Allard model. The results obtained are consistent with other literature data for similar materials. The knowledge of the physical parameters retrieved applying this technique (porosity, airflow resistivity, tortuosity, viscous and thermal characteristic length) is fundamental for the acoustic optimization of the porous materials in the case of future applications.

scholarly journals Nonlinear stability analysis of rotor-bearing systems

PAMM ◽  
2009 ◽  
Vol 9 (1) ◽  
pp. 279-280 ◽  
Author(s):  
Aydin Boyaci ◽  
Wolfgang Seemann ◽  
Carsten Proppe
Keyword(s):  
Stability Analysis ◽  
Nonlinear Stability ◽  
Nonlinear Stability Analysis ◽  
Rotor Bearing
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