Regimes of Combustion of Gasless Systems with a Melting Component in a Strong-Instability Region

2019 ◽  
Vol 92 (3) ◽  
pp. 682-686
Author(s):  
V. G. Prokof’ev ◽  
V. K. Smolyakov
Keyword(s):  
Instability Region ◽  
Strong Instability

Non-Newtonian pulsating blood flow-induced dynamic instability of visco-carotid artery within soft surrounding visco-tissue using differential cubature method

2015 ◽  
Vol 229 (16) ◽  
pp. 3002-3012 ◽  
Author(s):  
A Tabatabaie Arani ◽  
Ali Ghorbanpour Arani ◽  
Reza Kolahchi
Keyword(s):  
Blood Flow ◽  
Carotid Arteries ◽  
Shell Theory ◽  
Dynamic Instability ◽  
Current Model ◽  
Biomechanical Model ◽  
Realistic Model ◽  
Instability Region ◽  
Tissue Stiffness ◽  
Voigt Model

The high blood rate that often occurs in carotid arteries may play a role in artery failure and tortuosity which leads to blackouts, transitory ischemic attacks, and other diseases. However, dynamic analysis of carotid arteries conveying blood is lacking. The objective of this study was to present a biomechanical model for dynamic instability analysis of the embedded carotid arteries conveying pulsating blood flow. In order to present a realistic model, the carotid arteries and tissues are assumed viscoelastic using Kelvin–Voigt model. Carotid arteries are modeled as elastic cylindrical vessels based on Mindlin cylindrical shell theory (MCST). One of the main advantages of this study is considering the pulsating non-Newtonian nature of the blood flow using Carreau, Casson, and power law models. Applying energy method, Hamilton’s principle and differential cubature method (DCM), the dynamic instability region (DIR) of the visco-carotid arteries is obtained. The detailed parametric study is conducted, focusing on the combined effects of the elastic medium and non-Newtonian models on the dynamic instability of the visco-carotid arteries. It can be seen that with increasing the tissue stiffness, the natural frequency of visco-carotid arteries decreases. The current model provides a powerful tool for further experimental investigation about arterial tortuosity.

A note on strong instability of standing waves for some semilinear wave and heat equations

2017 ◽  
Vol 165 (1) ◽  
pp. 53-68
Author(s):  
T. SAANOUNI
Keyword(s):  
Ground State ◽  
Initial Value Problems ◽  
Standing Waves ◽  
Heat Equations ◽  
Initial Value ◽  
Strong Instability ◽  
Two Space Dimensions

AbstractThe initial value problems for some semilinear wave and heat equations are investigated in two space dimensions. By proving the existence of ground state, strong instability of standing waves for the associated wave and heat equations are obtained.

scholarly journals Blow-up criteria and instability of normalized standing waves for the fractional Schrödinger-Choquard equation

2020 ◽  
Vol 10 (1) ◽  
pp. 311-330 ◽  
Author(s):  
Feng Binhua ◽  
Ruipeng Chen ◽  
Jiayin Liu
Keyword(s):  
Blow Up ◽  
Standing Waves ◽  
Radial Solutions ◽  
Choquard Equation ◽  
Decomposition Theory ◽  
Profile Decomposition ◽  
Strong Instability

Abstract In this paper, we study blow-up criteria and instability of normalized standing waves for the fractional Schrödinger-Choquard equation $$\begin{array}{} \displaystyle i\partial_t\psi- (-{\it\Delta})^s \psi+(I_\alpha \ast |\psi|^{p})|\psi|^{p-2}\psi=0. \end{array}$$ By using localized virial estimates, we firstly establish general blow-up criteria for non-radial solutions in both L2-critical and L2-supercritical cases. Then, we show existence of normalized standing waves by using the profile decomposition theory in Hs. Combining these results, we study the strong instability of normalized standing waves. Our obtained results greatly improve earlier results.

Dynamic Instability Analysis and Design Charts of Curved Panels with Linearly Varying Periodic In-Plane Load

2021 ◽  
pp. 2150130
Author(s):  
G. Patel ◽  
A. N. Nayak ◽  
A. K. L. Srivastava
Keyword(s):  
Finite Element ◽  
Boundary Conditions ◽  
Dynamic Instability ◽  
Excitation Frequency ◽  
Instability Region ◽  
Concentrated Load ◽  
Simply Supported ◽  
Finite Element Software ◽  
Design Charts ◽  
Curved Panels

The present paper reports an extensive study on dynamic instability characteristics of curved panels under linearly varying in-plane periodic loading employing finite element formulation with a quadratic isoparametric eight nodded element. At first, the influences of three types of linearly varying in-plane periodic edge loads (triangular, trapezoidal and uniform loads), three types of curved panels (cylindrical, spherical and hyperbolic) and six boundary conditions on excitation frequency and instability region are investigated. Further, the effects of varied parameters, such as shallowness parameter, span to thickness ratio, aspect ratio, and Poisson’s ratio, on the dynamic instability characteristics of curved panels with clamped–clamped–clamped–clamped (CCCC) and simply supported-free-simply supported-free (SFSF) boundary conditions under triangular load are studied. It is found that the above parameters influence significantly on the excitation frequency, at which the dynamic instability initiates, and the width of dynamic instability region (DIR). In addition, a comparative study is also made to find the influences of the various in-plane periodic loads, such as uniform, triangular, parabolic, patch and concentrated load, on the dynamic instability behavior of cylindrical, spherical and hyperbolic panels. Finally, typical design charts showing DIRs in non-dimensional forms are also developed to obtain the excitation frequency and instability region of various frequently used isotropic clamped spherical panels of any dimension, any type of linearly varying in-plane load and any isotropic material directly from these charts without the use of any commercially available finite element software or any developed complex model.

scholarly journals The Cepheid Instability “Wedge“

1993 ◽  
Vol 139 ◽  
pp. 307-307
Author(s):  
Siobahn M. Morgan
Keyword(s):  
Recent Work ◽  
Observational Data ◽  
Instability Region ◽  
Mixing Length ◽  
Interesting Structure

For the most part it had been assumed that the red and the blue edges of the Cepheid Instability region were parallel. However, previous work by Pel and Lub (1978) and recent work by Fernie (1990) seems to reveal a rather interesting structure to the shape of the Cepheid Instability region. Figure 1 shows the shape defined using the data from Fernie (1990) and the observational data of Gieren (1989). It is apparent that the edges defined by the distribution of these points are not parallel.I have calculated a series of pulsation models that included varying values of the mixing length to try and produce a distribution of Cepheids as seen in Figure 1. Calculations were done using the methods outlined by Castor (1971) with a Linear Non Adiabatic pulsation code to determine the characteristics for a given model.

Pneumatic hammer instability in the aerostatic journal bearing–rotor system: A theoretical and experimental analyses

2020 ◽  
pp. 135065012090810
Author(s):  
Abdurrahim Dal ◽  
Tuncay Karaçay
Keyword(s):  
Dynamic Response ◽  
Journal Bearing ◽  
Instability Region ◽  
Rotor System ◽  
Pneumatic Hammer ◽  
Nonlinear Dynamic Response ◽  
System A ◽  
Differential Transform ◽  
Hole Configuration ◽  
Aerostatic Bearings

In this study, the pneumatic hammer instability phenomena in the aerostatic journal bearing–rotor system is analysed and discussed for different feeding hole configurations theoretically and experimentally. The influences of the configuration of the feeding holes on the nonlinear dynamics of the system are also investigated. The air flow between the surfaces is modelled with Reynold’s equation and it is numerically solved with differential transform and finite difference hybrid method. Three different aerostatic bearings are modelled and simulated to investigate the ınfluences of the configuration of the holes for different angular speeds. An experimental test rig is designed and tested for different rotor speeds to validate the obtained numerical results. The dynamic response of the system is analysed using waterfall plots, bifurcation diagrams, orbit plots, phase portrait and Poincaré map, which are drawn to determine the pneumatic hammer instability region of the modelled system. The results reveal a nonlinear dynamic response of the rotor centre. In addition, the analysis shows that the feeding hole configuration affects the rotor dynamics and the pneumatic hammer instability region.

Using Guided Balls to Auto-Balance Rotors

2002 ◽  
Vol 124 (4) ◽  
pp. 971-975 ◽  
Author(s):  
H. L. Wettergren
Keyword(s):  
Natural Frequency ◽  
Damping Ratio ◽  
Rotating Machinery ◽  
Instability Region ◽  
Instability Threshold ◽  
Asymptotically Stable ◽  
Circular Groove ◽  
Stable Position ◽  
Critical Damping

By using balancing balls constrained to move in a circular groove filled with oil, the vibration of rotating machinery can, under certain circumstances, be reduced. This paper shows that the damping from the oil reduces the instability region, i.e., the conditions when the balancing balls don’t find their equilibrium positions. However, the instability region seems to increase with increasing number of balancing balls. The critical ball damping ratio is highest just above the natural frequency and then rapidly decreases. Consequently, since the region between instability and critical damping is quite small, the ball damping should be made as small as possible without getting too close to the instability threshold. Bearing damping has a large effect on the instability region. High bearing damping will suppress the instability. The time it takes to reach the asymptotically stable position seems to increase with increasing number of balls. Keeping this time low is one of the most important things when designing a balancing ring.

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