Stability analysis of an exponentially tapered, pre-twisted asymmetric sandwich beam on a variable Pasternak foundation with viscoelastic supports under temperature gradient

2020 ◽  
Vol 42 (3) ◽  
Author(s):  
D. K. Nayak ◽  
A. Dubey ◽  
C. R. Nayak ◽  
P. R. Dash
Keyword(s):  
Stability Analysis ◽  
Temperature Gradient ◽  
Sandwich Beam ◽  
Pasternak Foundation

Stability of an exponentially tapered asymmetric sandwich beam placing on a variable Pasternak Foundation with variable temperature gradient

2020 ◽  
pp. 095745652097237
Author(s):  
Madhusmita Pradhan ◽  
Pusparaj Dash ◽  
Dipesh Kumar Nayak
Keyword(s):  
Mathematical Modeling ◽  
Temperature Gradient ◽  
Variable Temperature ◽  
Complete Solution ◽  
Equations Of Motion ◽  
Sandwich Beam ◽  
Pasternak Foundation ◽  
Buckling Loads ◽  
The Stability ◽  
Hill’S Equations

The stability investigation of an exponentially tapered sandwich beam, asymmetric in nature placed upon a Pasternak foundation with variable behavior acted upon by a periodic longitudinal load with variable temperature grade with clamped-pinned condition provided at the ends is analyzed in this article. By using Hamilton’s energy method, a complete solution for the mathematical modeling of the system is obtained. The equations of motion along with the related boundary conditions are obtained in non-dimensional form. A group of Hill’s equations are found by generalized Galerkin’s method. Different parameters have significant influence on both the static buckling loads as well as the zones of instability. These effects of these parameters are examined and are presented in a graphical manner. The outcomes resulted due to uniform and variable temperature grade are compared.

scholarly journals Stability Analysis of a Tapered Symmetric Sandwich Beam Resting on a Variable Pasternak Foundation

2019 ◽  
Vol 24 (2) ◽  
pp. 228-240 ◽  
Author(s):  
Madhusmita Pradhan ◽  
P. R. Dash ◽  
Mrunal Kanti Mishra ◽  
Prasanta Kumar Pradhan
Keyword(s):  
Stability Analysis ◽  
Parametric Instability ◽  
Core Loss ◽  
Sandwich Beam ◽  
Weight Ratio ◽  
High Strength ◽  
Computational Method ◽  
Space Vehicles ◽  
Density Parameter ◽  
Pasternak Foundation

The static and dynamic stability analysis of a three-layered, tapered and symmetric sandwich beam resting on a variable Pasternak foundation and undergoing a periodic axial load has been carried out for two different boundary conditions by using a computational method. The governing equation of motion has been derived by using Hamilton’s principle along with generalized Galerkin’s method. The effects of elastic foundation parameter, core-loss factor, the ratio of length of the beam to the thickness of the elastic layer, the ratio of thickness of shear-layer of Pasternak foundation to the length of the beam, different modulus ratios, taper parameter, core thickness parameter, core-density parameter and geometric parameter on the non-dimensional static buckling load and on the regions of parametric instability are studied. This type of study will help the designers to achieve a system with high strength to weight ratio and better stability which are the desirable parameters for many modern engineering applications, such as in the attitude stability of spinning satellites, stability of helicopter components, stability of space vehicles etc.

Stability analysis for the onset of thermoacoustic oscillations in a gas-filled looped tube

2014 ◽  
Vol 741 ◽  
pp. 585-618 ◽  
Author(s):  
H. Hyodo ◽  
N. Sugimoto
Keyword(s):  
Wave Equation ◽  
Stability Analysis ◽  
Temperature Gradient ◽  
Energy Flux ◽  
Diffusion Layer ◽  
Wave Mode ◽  
Frequency Equation ◽  
Acoustic Energy ◽  
Tube Length ◽  
Thermoacoustic Oscillations

AbstractThis paper develops a stability analysis for the onset of thermoacoustic oscillations in a gas-filled looped tube with a stack inserted, subject to a temperature gradient. Analysis is carried out based on approximate theories for a thermoviscous diffusion layer derived from the thermoacoustic-wave equation taking account of the temperature dependence of the viscosity and the heat conductivity. Assuming that the stack consists of many pores axially and that the thickness of the diffusion layer is much thicker than the pore radius, the diffusion wave equation with higher-order terms included is applied for the gas in the pores of the stack. For the gas outside of the pores, the theory of a thin diffusion layer is applied. In a section called the buffer tube over which the temperature relaxes from that at the hot end of the stack to room temperature, the effects of the temperature gradient are taken into account. With plausible temperature distributions specified on the walls of the stack and the buffer tube, the solutions to the equations in both theories are obtained and a frequency equation is finally derived analytically by matching the conditions at the junctions between the various sections. Seeking a real solution to the frequency equation, marginal conditions of instability are obtained numerically not only for the one-wave mode but also for the two-wave mode, where the tube length corresponds to one wavelength and two wavelengths, respectively. It is revealed that the marginal conditions depend not only on the thickness of the diffusion layer but also on the porosity of the stack. Although the toroidal geometry allows waves to be propagated in both senses along the tube, it is found that the wave propagating in the sense from the cold to the hot end through the stack is always greater, so that a travelling wave in this sense emerges as a whole. The spatial and temporal variations of excess pressure and mean axial velocity averaged over the cross-section of a flow passage are displayed for the two modes of oscillations at the marginal state. The spatial distribution of mean acoustic energy flux (acoustic intensity) over one period is also shown. It is unveiled that the energy flux is generated only in the stack, and it decays slowly in the other sections by lossy effects due to a boundary layer. Mechanisms for the generation of the acoustic energy flux are also discussed.

scholarly journals Rayleigh-Benard convection in a viscoelastic fluid-filled high-porosity medium with nonuniform basic temperature gradient

2001 ◽  
Vol 25 (9) ◽  
pp. 609-619 ◽  
Author(s):  
Pradeep G. Siddheshwar ◽  
C. V. Sri Krishna
Keyword(s):  
Stability Analysis ◽  
Temperature Gradient ◽  
Viscoelastic Fluid ◽  
High Porosity ◽  
Rigid Boundary ◽  
Viscoelastic Problem ◽  
Bénard Convection ◽  
Benard Convection ◽  
Rayleigh Benard Convection ◽  
Rayleigh Benard

The qualitative effect of nonuniform temperature gradient on the linear stability analysis of the Rayleigh-Benard convection problem in a Boussinesquian, viscoelastic fluid-filled, high-porosity medium is studied numerically using the single-term Galerkin technique. The eigenvalue is obtained for free-free, free-rigid, and rigid-rigid boundary combinations with isothermal temperature conditions. Thermodynamics and also the present stability analysis dictates the strain retardation time to be less than the stress relaxation time for convection to set in as oscillatory motions in a high-porosity medium. Furthermore, the analysis predicts the critical eigenvalue for the viscoelastic problem to be less than that of the corresponding Newtonian fluid problem.

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