Symmetrical Solutions for Edge-Loaded Annular Elastic Membranes

2009 ◽  
Vol 76 (3) ◽  
Author(s):  
Weiwei Yu ◽  
Dale G. Karr
Keyword(s):  
Exact Solution ◽  
Boundary Conditions ◽  
Excellent Agreement ◽  
Radial Stress ◽  
Axisymmetric Deformation ◽  
Membrane Theory ◽  
General Solutions ◽  
Special Cases ◽  
Elastic Membranes ◽  
Nonlinear Membrane

The Föppl–Hencky nonlinear membrane theory is employed to study the axisymmetric deformation of annular elastic membranes. The general solutions for displacements and stresses are established for arbitrary edge boundary conditions. New exact solution results are developed for central loading and edge forcing conditions. Both positive and negative radial stress solutions are found. Comparisons are made for special cases to previously known solutions with excellent agreement.

Free Vibrational Characteristics of Pretensioned Cable Roofs

1972 ◽  
Vol 94 (1) ◽  
pp. 31-37 ◽  
Author(s):  
G. N. Bathish
Keyword(s):  
Equilibrium Position ◽  
Equations Of Motion ◽  
Static Equilibrium ◽  
Transverse Load ◽  
Mode Shapes ◽  
Shear Rigidity ◽  
Membrane Theory ◽  
Special Cases ◽  
Vibrational Characteristics ◽  
Nonlinear Membrane

Cable roofs are analyzed using nonlinear membrane theory. The cable network is simulated by an equivalent thin elastic prestressed membrane without shear rigidity. The equations of motion for the vibrating membrane are formulated by considering the static equilibrium position of the membrane as the position of the membrane after it undergoes nonlinear deformation due to uniform transverse load over the projected area of the membrane. The equations of motion are then solved for natural frequencies and associated mode shapes by restricting the analysis to small amplitude vibrations about the static equilibrium position. Two special cases are considered: a flat rectangular membrane, and a membrane that has the shape of a hyperbolic paraboloid surface that is rectangular in plan. Comparisons between linear and nonlinear membrane theory solutions are presented.

scholarly journals On a Generalization of One-Dimensional Kinetics

Mathematics ◽  
2021 ◽  
Vol 9 (11) ◽  
pp. 1264
Author(s):  
Vladimir V. Uchaikin ◽  
Renat T. Sibatov ◽  
Dmitry N. Bezbatko
Keyword(s):  
Exact Solution ◽  
Asymptotic Behavior ◽  
Constant Velocity ◽  
Telegraph Equation ◽  
Material Derivative ◽  
Symmetric Random Walk ◽  
One Dimensional ◽  
Special Cases ◽  
Fractional Telegraph Equation ◽  
Asymmetric Case

One-dimensional random walks with a constant velocity between scattering are considered. The exact solution is expressed in terms of multiple convolutions of path-distributions assumed to be different for positive and negative directions of the walk axis. Several special cases are considered when the convolutions are expressed in explicit form. As a particular case, the solution of A. S. Monin for a symmetric random walk with exponential path distribution and its generalization to the asymmetric case are obtained. Solution of fractional telegraph equation with the fractional material derivative is presented. Asymptotic behavior of its solution for an asymmetric case is provided.

An inhomogeneous problem for an elastic half-strip: An exact solution

2021 ◽  
pp. 108128652199641
Author(s):  
Mikhail D Kovalenko ◽  
Irina V Menshova ◽  
Alexander P Kerzhaev ◽  
Guangming Yu
Keyword(s):  
Exact Solution ◽  
Boundary Conditions ◽  
Exact Solutions ◽  
Boundary Value Problems ◽  
Boundary Value ◽  
Theory Of Elasticity ◽  
Orthogonality Relation ◽  
Infinite Strip ◽  
Inhomogeneous Problem ◽  
Half Strip

We construct exact solutions of two inhomogeneous boundary value problems in the theory of elasticity for a half-strip with free long sides in the form of series in Papkovich–Fadle eigenfunctions: (a) the half-strip end is free and (b) the half-strip end is firmly clamped. Initially, we construct a solution of the inhomogeneous problem for an infinite strip. Subsequently, the corresponding solutions for a half-strip are added to this solution, whereby the boundary conditions at the end are satisfied. The Papkovich orthogonality relation is used to solve the inhomogeneous problem in a strip.

scholarly journals Regular approximation of singular Sturm–Liouville problems with eigenparameter dependent boundary conditions

2020 ◽  
Vol 2020 (1) ◽  
Author(s):  
Maozhu Zhang ◽  
Kun Li ◽  
Hongxiang Song
Keyword(s):  
Boundary Conditions ◽  
Operator Theory ◽  
Resolvent Convergence ◽  
Spectral Inclusion ◽  
Regular Approximation ◽  
Special Cases ◽  
Abstract Operator ◽  
Norm Resolvent Convergence ◽  
Sturm Liouville ◽  
Spectral Exactness

AbstractIn this paper we consider singular Sturm–Liouville problems with eigenparameter dependent boundary conditions and two singular endpoints. The spectrum of such problems can be approximated by those of the inherited restriction operators constructed. Via the abstract operator theory, the strongly resolvent convergence and norm resolvent convergence of a sequence of operators are obtained and it follows that the spectral inclusion of spectrum holds. Moreover, spectral exactness of spectrum holds for two special cases.

scholarly journals Impurity induced scale-free localization

2021 ◽  
Vol 4 (1) ◽  
Author(s):  
Linhu Li ◽  
Ching Hua Lee ◽  
Jiangbin Gong
Keyword(s):  
Boundary Conditions ◽  
Skin Effect ◽  
Reciprocal Lattice ◽  
Periodic Boundary Conditions ◽  
Open Boundary ◽  
Open Boundary Conditions ◽  
Translational Invariance ◽  
Scale Free ◽  
Special Cases ◽  
Simulation Results

AbstractNon-Hermitian systems have been shown to have a dramatic sensitivity to their boundary conditions. In particular, the non-Hermitian skin effect induces collective boundary localization upon turning off boundary coupling, a feature very distinct from that under periodic boundary conditions. Here we develop a full framework for non-Hermitian impurity physics in a non-reciprocal lattice, with periodic/open boundary conditions and even their interpolations being special cases across a whole range of boundary impurity strengths. We uncover steady states with scale-free localization along or even against the direction of non-reciprocity in various impurity strength regimes. Also present are Bloch-like states that survive albeit broken translational invariance. We further explore the co-existence of non-Hermitian skin effect and scale-free localization, where even qualitative aspects of the system’s spectrum can be extremely sensitive to impurity strength. Specific circuit setups are also proposed for experimentally detecting the scale-free accumulation, with simulation results confirming our main findings.

scholarly journals Coupled Systems of Sequential Caputo and Hadamard Fractional Differential Equations with Coupled Separated Boundary Conditions

Symmetry ◽  
2018 ◽  
Vol 10 (12) ◽  
pp. 701 ◽  
Author(s):  
Suphawat Asawasamrit ◽  
Sotiris Ntouyas ◽  
Jessada Tariboon ◽  
Woraphak Nithiarayaphaks
Keyword(s):  
Differential Equations ◽  
Boundary Conditions ◽  
Fractional Differential Equations ◽  
Coupled Systems ◽  
Uniqueness Of Solutions ◽  
Krasnoselskii’S Fixed Point Theorem ◽  
Hadamard Fractional Differential Equations ◽  
Special Cases ◽  
Separated Boundary Conditions ◽  
Fractional Differential

This paper studies the existence and uniqueness of solutions for a new coupled system of nonlinear sequential Caputo and Hadamard fractional differential equations with coupled separated boundary conditions, which include as special cases the well-known symmetric boundary conditions. Banach’s contraction principle, Leray–Schauder’s alternative, and Krasnoselskii’s fixed-point theorem were used to derive the desired results, which are well-illustrated with examples.

scholarly journals On Solutions of Fractional Order Boundary Value Problems with Integral Boundary Conditions in Banach Spaces

2013 ◽  
Vol 2013 ◽  
pp. 1-13 ◽  
Author(s):  
Hussein A. H. Salem ◽  
Mieczysław Cichoń
Keyword(s):  
Boundary Conditions ◽  
Boundary Value Problems ◽  
Fractional Order ◽  
Nonlinear Term ◽  
Boundary Value ◽  
Nonlocal Boundary ◽  
Integral Boundary Conditions ◽  
Point Of View ◽  
Integral Boundary ◽  
Special Cases

The object of this paper is to investigate the existence of a class of solutions for some boundary value problems of fractional order with integral boundary conditions. The considered problems are very interesting and important from an application point of view. They include two, three, multipoint, and nonlocal boundary value problems as special cases. We stress on single and multivalued problems for which the nonlinear term is assumed only to be Pettis integrable and depends on the fractional derivative of an unknown function. Some investigations on fractional Pettis integrability for functions and multifunctions are also presented. An example illustrating the main result is given.

Nonlinear TE surface waves in a ferrite slab bounded by Kerr-type metamaterials

2017 ◽  
Vol 26 (03) ◽  
pp. 1750028 ◽  
Author(s):  
Burhan Zamir ◽  
Rashid Ali
Keyword(s):  
Boundary Conditions ◽  
Surface Waves ◽  
Transverse Electric ◽  
Dispersion Relations ◽  
Double Negative ◽  
Propagation Characteristics ◽  
Special Cases ◽  
Tangential Field ◽  
Effective Wave ◽  
Ferrite Slab

In this paper, nonlinear transverse electric surface waves in a structure consisting of a ferrite slab sandwiched between a Kerr-type double-negative metamaterial (DNG-MTM) have been investigated. In addition to a DNG-MTM, two special cases with nonlinear single-negative metamaterials (SNG-MTMs) have also been discussed. The dispersion relations are obtained by applying the boundary conditions to the tangential field components of each layer. The propagation characteristics are plotted numerically for the effective wave index versus propagation frequency.

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