Accurate compact solution of fluid-filled FG cylindrical shell inducting fluid term: Frequency analysis

2021 ◽  
pp. 109963622199389
Author(s):  
Muzamal Hussain ◽  
Muhammad N Naeem
Keyword(s):  
Cylindrical Shell ◽  
Partial Differential Equations ◽  
Differential Equations ◽  
Integral Form ◽  
Energy Functional ◽  
Acoustic Wave Equation ◽  
Partial Differential ◽  
Motion Equations ◽  
Constituent Material ◽  
Shell Motion

Shell motion equations are framed with first order shell theory of Love. Vibration investigation of fluid-filled three layered cylindrical shells is studied here. It is also exhibited that the effect of frequencies is investigated by varying the different layers with constituent material. The coupled and uncoupled frequencies changes with these layers according to the material formation of fluid-filled FG-CSs. A cylindrical shell is immersed in a fluid which is a non-viscous one. These equations are partial differential equations which are usually solved by approximate technique. Robust and efficient techniques are favored to get precise results. Use of acoustic wave equation is done to incorporate the sound pressure produced in a fluid. Hankel’s functions of second kind designate the fluid influence. Mathematically the integral form of the Lagrange energy functional is converted into a set of three partial differential equations.

Computations of Higher Class Solutions of Partial Differential Equations

2001 ◽  
Author(s):  
K. S. Surana ◽  
M. A. Bona
Keyword(s):  
Partial Differential Equations ◽  
Differential Equations ◽  
Convergence Rates ◽  
Integral Form ◽  
Mathematical Framework ◽  
Partial Differential ◽  
Computational Framework ◽  
Fundamental Point ◽  
Adaptive Processes ◽  
Fixed Order

Abstract This paper presents a new computational strategy, computational framework and mathematical framework for numerical computations of higher class solutions of differential and partial differential equations. The approach presented here utilizes ‘strong forms’ of the governing differential equations (GDE’s) and least squares approach in constructing the integral form. The conventional, or currently used, approaches seek the convergence of a solution in a fixed (order) space by h, p or hp-adaptive processes. The fundamental point of departure in the proposed approach is that we seek convergence of the computed solution by changing the orders of the spaces of the basis functions. With this approach convergence rates much higher than those from h,p–processes are achievable and the progressively computed solutions converge to the ‘strong’ i.e. ‘theoretical’ solutions of the GDE’s. Many other benefits of this approach are discussed and demonstrated. Stationary and time-dependant convection-diffusion and Burgers equations are used as model problems.

scholarly journals Introduction: Big data and partial differential equations

2017 ◽  
Vol 28 (6) ◽  
pp. 877-885 ◽  
Author(s):  
YVES VAN GENNIP ◽  
CAROLA-BIBIANE SCHÖNLIEB
Keyword(s):  
Partial Differential Equations ◽  
Differential Equations ◽  
Large Scale ◽  
Data Science ◽  
Applied Mathematics ◽  
Mathematical Finance ◽  
Energy Functional ◽  
Continuous Change ◽  
Opinion Formation ◽  
Partial Differential

Partial differential equations (PDEs) are expressions involving an unknown function in many independent variables and their partial derivatives up to a certain order. Since PDEs express continuous change, they have long been used to formulate a myriad of dynamical physical and biological phenomena: heat flow, optics, electrostatics and -dynamics, elasticity, fluid flow and many more. Many of these PDEs can be derived in a variational way, i.e. via minimization of an ‘energy’ functional. In this globalised and technologically advanced age, PDEs are also extensively used for modelling social situations (e.g. models for opinion formation, mathematical finance, crowd motion) and tasks in engineering (such as models for semiconductors, networks, and signal and image processing tasks). In particular, in recent years, there has been increasing interest from applied analysts in applying the models and techniques from variational methods and PDEs to tackle problems in data science. This issue of the European Journal of Applied Mathematics highlights some recent developments in this young and growing area. It gives a taste of endeavours in this realm in two exemplary contributions on PDEs on graphs [1, 2] and one on probabilistic domain decomposition for numerically solving large-scale PDEs [3].

scholarly journals Kaitan Antara Ruang Sobolev dan Ruang Lebesgue

2017 ◽  
Vol 6 (1) ◽  
pp. 21
Author(s):  
Pipit Pratiwi Rahayu
Keyword(s):  
Partial Differential Equations ◽  
Sobolev Space ◽  
Differential Equations ◽  
Function Space ◽  
Lebesgue Space ◽  
Applied Mathematics ◽  
Integral Form ◽  
Partial Differential ◽  
Function Element

Measureable function space and its norm with integral form has been known, one of which is Lebegsue Space and Sobolev Space. In applied Mathematics like in finding solution of partial differential equations, that two spaces is soo usefulness. Sobolev space is subset of Lebesgue space, its mean if we have a function that element of Sobolev Space then its element of Lebesgue space. But the converse of this condition is not applicable. In this research, we will give an example to shows that there is a function element of Lebesgue space but not element of Sobolev space

Nonlinear Vibration of Functionally Graded Material Cylindrical Shell Based on Reddy’s Third-Order Plates and Shells Theory

2012 ◽  
Vol 625 ◽  
pp. 18-24 ◽  
Author(s):  
Lu Dong ◽  
Yu Xin Hao ◽  
Jian Hua Wang ◽  
Li Yang
Keyword(s):  
Cylindrical Shell ◽  
Partial Differential Equations ◽  
Differential Equations ◽  
Nonlinear Vibration ◽  
Functionally Graded Material ◽  
Functionally Graded ◽  
Third Order ◽  
Partial Differential ◽  
Graded Material ◽  
Plates And Shells

In this paper, an analysis on nonlinear dynamics of a simply supported functionally graded material (FGM) cylindrical shell subjected to the different excitation in thermal environment. Material properties of cylindrical shell are assumed to be temperature-dependent. Based on the Reddy’s third-order plates and shells theory[1], the nonlinear governing partial differential equations of motion for the FGM cylindrical shell are derived by using Hamilton’s principle. Galerkin’s method is utilized to transform the partial differential equations into a two-degree-of-freedom nonlinear system including the quadratic and cubic nonlinear terms under combined parametric and external excitation. The effects played by different excitation and system initial conditions on the nonlinear vibration of the cylindrical shell are studied. In addition, the Runge–Kutta method is used to find out the nonlinear dynamic responses of the FGM cylindrical shell.

Finite Difference, Finite Element and Boundary Element Formulae as a Language of Applied Physics

1991 ◽  
Vol 02 (01) ◽  
pp. 383-386
Author(s):  
JIŘÍ KAFKA ◽  
NGUYEN VAN NHAC
Keyword(s):  
Differential Equation ◽  
Partial Differential Equation ◽  
Finite Element ◽  
Partial Differential Equations ◽  
Finite Difference ◽  
Differential Equations ◽  
Integral Form ◽  
The Other ◽  
Applied Physics ◽  
Partial Differential

When deducing the finite difference formulae, one has to discretize partial differential equations. On the other hand, those equations have been previously derived having started from laws of physics in their integral form. So, a question arises, why not avoid the approach to the limit (necessary to deduce the partial differential equation) and why not deduce the finite difference formulae directly on the base of laws of physics in their integral form.

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