Integral solutions to transient nonlinear heat (mass) diffusion with a power-law diffusivity: a semi-infinite medium with fixed boundary conditions

2015 ◽  
Vol 52 (3) ◽  
pp. 635-655 ◽  
Author(s):  
Jordan Hristov
Keyword(s):  
Boundary Conditions ◽  
Power Law ◽  
Mass Diffusion ◽  
Infinite Medium ◽  
Fixed Boundary ◽  
Integral Solutions

scholarly journals Semi-derivative integral method (SDIM) to transient heat conduction: Time-dependent (power-law) temperature boundary conditions

2021 ◽  
pp. 143-143
Author(s):  
Jordan Hristov
Keyword(s):  
Heat Conduction ◽  
Boundary Conditions ◽  
Power Law ◽  
Integral Method ◽  
Transient Heat Conduction ◽  
Infinite Medium ◽  
Time Dependent ◽  
Conduction Time ◽  
Parabolic Profile ◽  
Temperature Boundary

Transient heat conduction in semi-infinite medium with a power-law time-dependent boundary conditions has been solved by an integral-balance integral method applying to a semi-derivative approach. Two versions of the integral-balance method have been applied: Goodman?s method with a generalized parabolic profile and Zien?s method with exponential (original and modified) profile.

Vibration analysis of a thin functionally graded plate having an out of plane material inhomogeneity resting on Winkler–Pasternak foundation under different combinations of boundary conditions

2018 ◽  
Vol 233 (8) ◽  
pp. 2636-2662 ◽  
Author(s):  
Piyush Pratap Singh ◽  
Mohammad Sikandar Azam ◽  
Vinayak Ranjan
Keyword(s):  
Boundary Conditions ◽  
Power Law ◽  
Functionally Graded Material ◽  
Functionally Graded ◽  
Pasternak Foundation ◽  
Functionally Graded Plate ◽  
Material Inhomogeneity ◽  
Power Law Exponent ◽  
Out Of Plane ◽  
Graded Material

In the present research article, classical plate theory has been adopted to analyze functionally graded material plate, having out of plane material inhomogeneity, resting on Winkler–Pasternak foundation under different combinations of boundary conditions. The material properties of the functionally graded material plate vary according to power law in the thickness direction. Rayleigh–Ritz method in conjugation with polynomial displacement functions has been used to develop a computationally efficient mathematical model to study free vibration characteristics of the plate. Convergence of frequency parameters (nondimensional natural frequencies) has been attained by increasing the number of polynomials of displacement function. The frequency parameters of the functionally graded material plate obtained by proposed method are compared with the open literature to validate the present model. Firstly, the present model is used to calculate first six natural frequencies of the functionally graded plate under all possible combinations of boundary conditions for the constant value of stiffness of Winkler and Pasternak foundation moduli. Further, the effects of density, aspect ratio, power law exponent, Young’s modulus on frequency parameters of the functionally graded plate resting on Winkler–Pasternak foundation under specific boundary conditions viz. CCCC (all edges clamped), SSSS (all edges simply supported), CFFF (cantilever), SCSF (simply supported-clamped-free) are studied extensively. Furthermore, effect of stiffness of elastic foundation moduli (kp and kw) on frequency parameters are analyzed. It has been observed that effects of aspect ratios, boundary conditions, Young’s modulus and density on frequency parameters are significant at lower value of the power law exponent. It has also been noted from present investigation that Pasternak foundation modulus has greater effect on frequency parameters as compared to the Winkler foundation modulus. Most of the results presented in this paper are novel and may be used for the validation purpose by researchers. Three dimensional mode shapes for the functionally graded plate resting on elastic foundation have also been presented in this article.

Investigation of the Complex Two Degrees of Freedom Systems for Force Limited Vibration

2004 ◽  
Author(s):  
Andre Cote ◽  
Ramin Sedaghati ◽  
Yvan Soucy
Keyword(s):  
Free Boundary ◽  
Boundary Conditions ◽  
Degrees Of Freedom ◽  
Simple Approach ◽  
Conservative Estimate ◽  
Two Degrees Of Freedom ◽  
Jet Propulsion ◽  
Fixed Boundary ◽  
Free Boundary Conditions ◽  
Force Data

Force Limited Vibration (FLV) Testing developed at Jet Propulsion Laboratory offers many opportunities to decrease the overtesting problem associated with traditional vibration testing. Among the force limited vibration methods, the complex two degrees of freedom system (TDFS) appears to be the most complete and versatile model which gives reasonably conservative force limits, and does not require extrapolation of interface force data for similar mounting structures and test articles. However there are some limitations to the complex TDFS model. The model is well adapted for nicely separated modes but issues regarding the closely space modes have not been fully addressed in the literature. Also, the complex TDFS model is based on free boundary conditions for the mounting structure, which appear to be natural for many cases such as spacecraft mounted on a launch vehicle. However this is not necessarily true for some other cases such as an electronic component mounted on a spacecraft antenna, which requires fixed boundary conditions. The main objective of this paper is to give greater insights into the complex TDFS method and propose methodologies to overcome its limitations. It is shown that a simple approach can be used to assure conservative estimate of the force limits in situations regarding closely spaced modes. It is also demonstrated that although the complex TDFS method is not perfectly adapted to fixed boundary conditions of the mounting structure, given certain precautions, it still provides good estimates of the force limits.

Analysis and Design of Fixed–Fixed Bistable Arch-Profiles Using a Bilateral Relationship

2019 ◽  
Vol 11 (3) ◽  
Author(s):  
Safvan Palathingal ◽  
G. K. Ananthasuresh
Keyword(s):  
Boundary Conditions ◽  
Closed Form ◽  
Sufficient Conditions ◽  
Necessary And Sufficient Conditions ◽  
Single Variable ◽  
Fixed Boundary ◽  
Analysis And Design ◽  
Bilateral Relationship ◽  
Variable Equation ◽  
Necessary And Sufficient

Arch-profiles of bistable arches, in their two force-free equilibrium states, are related to each other. This bilateral relationship is derived for arches with fixed–fixed boundary conditions in two forms: a nonlinear single-variable equation for analysis and a closed-form analytical expression for design. Some symmetrical features of shape as well as necessary and sufficient conditions for bistability are presented as corollaries. Analysis and design of arch-profiles using the bilateral relationship are illustrated through examples.

scholarly journals SrTiO3—Glimpses of an Inexhaustible Source of Novel Solid State Phenomena

2020 ◽  
Vol 5 (4) ◽  
pp. 58
Author(s):  
Wolfgang Kleemann ◽  
Jan Dec ◽  
Alexander Tkach ◽  
Paula M. Vilarinho
Keyword(s):  
Solid Solution ◽  
Solid State ◽  
Boundary Conditions ◽  
Power Law ◽  
Mesoscopic Physics ◽  
Third Order ◽  
Spin Cluster ◽  
Various Boundary Conditions ◽  
Glass Forming ◽  
Quantum Paraelectric

The purpose of this selective review is primarily to demonstrate the large versatility of the insulating quantum paraelectric perovskite SrTiO3 explained in “Introduction” part, and “Routes of SrTiO3 toward ferroelectricity and other collective states” part. Apart from ferroelectricity under various boundary conditions, it exhibits regular electronic and superconductivity via doping or external fields and is capable of displaying diverse coupled states. “Magnetoelectric multiglass (Sr,Mn)TiO3” part, deals with mesoscopic physics of the solid solution SrTiO3:Mn2+. It is at the origin of both polar and spin cluster glass forming and is altogether a novel multiferroic system. Independent transitions at different glass temperatures, power law dynamic criticality, divergent third-order susceptibilities, and higher order magneto-electric interactions are convincing fingerprints.

Sign in / Sign up

Export Citation Format

Share Document