A Note on the Eigenvalue Criteria for Positive Solutions of a Cantilever Beam Equation with Free End

2020 ◽  
Author(s):  
Seshadev Padhi
Keyword(s):  
Cantilever Beam ◽  
Positive Solutions ◽  
Beam Equation ◽  
Cantilever Beam Equation

An Investigation of Tip Force Characteristics of Brush Seals

2007 ◽  
Author(s):  
Mehmet Demiroglu ◽  
Mustafa Gursoy ◽  
John A. Tichy
Keyword(s):  
Cantilever Beam ◽  
Numerical Models ◽  
Operating Conditions ◽  
Beam Equation ◽  
Labyrinth Seals ◽  
Wide Range ◽  
Brush Seals ◽  
Cantilever Beam Equation ◽  
Super Alloy ◽  
Force Pressure

Thanks to their compliant nature and superior leakage performance over conventional labyrinth seals, brush seals found increasing use in turbomachinery. Utilizing high temperature super-alloy fibers and their compliance capability these seals maintain contact with the rotor for a wide range of operating conditions leaving minimal passage for parasitic leakage flow. Consequently, the contact force/pressure generated at seal rotor interface is of importance for sustained seal performance and longevity of its service life. Although some analytical and numerical models have been developed to estimate bristle tip pressures, they simply rely on linear beam equation calculations and other such assumptions for loading cases. In this paper, previously available analytical and/or numerical models for bristle tip force/pressure have been modified and enhanced. The nonlinear cantilever beam equation has been solved and results are compared to a linear cantilever beam equation solution to establish application boundaries for both methods. The results are also compared to experimental data. With the support of testing, an empirical model has been developed for tip forces under operating conditions.

scholarly journals Lower and upper solutions method to the fully elastic cantilever beam equation with support

2021 ◽  
Vol 2021 (1) ◽  
Author(s):  
Mei Wei ◽  
Yongxiang Li ◽  
Gang Li
Keyword(s):  
Cantilever Beam ◽  
Function Method ◽  
Continuous Functions ◽  
Existence Results ◽  
Monotone Iterative Technique ◽  
Beam Equation ◽  
Iterative Technique ◽  
Monotone Iterative ◽  
Cantilever Beam Equation ◽  
Supporting Device

AbstractThe aim of this paper is to consider a fully cantilever beam equation with one end fixed and the other connected to a resilient supporting device, that is, $$ \textstyle\begin{cases} u^{(4)}(t)=f(t,u(t),u'(t),u''(t),u'''(t)), \quad t\in [0,1], \\ u(0)=u'(0)=0, \\ u''(1)=0,\qquad u'''(1)=g(u(1)), \end{cases} $$ { u ( 4 ) ( t ) = f ( t , u ( t ) , u ′ ( t ) , u ″ ( t ) , u ‴ ( t ) ) , t ∈ [ 0 , 1 ] , u ( 0 ) = u ′ ( 0 ) = 0 , u ″ ( 1 ) = 0 , u ‴ ( 1 ) = g ( u ( 1 ) ) , where $f:[0,1]\times \mathbb{R}^{4}\rightarrow \mathbb{R}$ f : [ 0 , 1 ] × R 4 → R , $g: \mathbb{R}\rightarrow \mathbb{R}$ g : R → R are continuous functions. Under the assumption of monotonicity, two existence results for solutions are acquired with the monotone iterative technique and the auxiliary truncated function method.

scholarly journals Application of ADM Using Laplace Transform to Approximate Solutions of Nonlinear Deformation for Cantilever Beam

2016 ◽  
Vol 2016 ◽  
pp. 1-5
Author(s):  
Ratchata Theinchai ◽  
Siriwan Chankan ◽  
Weera Yukunthorn
Keyword(s):  
Laplace Transform ◽  
Cantilever Beam ◽  
Adomian Decomposition Method ◽  
Small Deformation ◽  
Approximate Solutions ◽  
Beam Equation ◽  
Bernoulli Beam ◽  
Initial Value ◽  
Adomian Decomposition ◽  
Euler Bernoulli Beam

We investigate semianalytical solutions of Euler-Bernoulli beam equation by using Laplace transform and Adomian decomposition method (LADM). The deformation of a uniform flexible cantilever beam is formulated to initial value problems. We separate the problems into 2 cases: integer order for small deformation and fractional order for large deformation. The numerical results show the approximated solutions of deflection curve, moment diagram, and shear diagram of the presented method.

scholarly journals Existence of Positive Solutions of a Discrete Elastic Beam Equation

2010 ◽  
Vol 2010 ◽  
pp. 1-15 ◽  
Author(s):  
Ruyun Ma ◽  
Jiemei Li ◽  
Chenghua Gao
Keyword(s):  
Positive Solutions ◽  
Fourth Order ◽  
Nonlinear Boundary ◽  
Global Bifurcation ◽  
Elastic Beam ◽  
Beam Equation ◽  
Nonlinear Boundary Value Problems ◽  
Order Difference ◽  
Bifurcation Theorem ◽  
Existence Of Positive Solutions

LetTbe an integer withT≥5and letT2={2,3,…,T}. We consider the existence of positive solutions of the nonlinear boundary value problems of fourth-order difference equationsΔ4u(t−2)−ra(t)f(u(t))=0,t∈T2,u(1)=u(T+1)=Δ2u(0)=Δ2u(T)=0, whereris a constant,a:T2→(0,∞),  and  f:[0,∞)→[0,∞)is continuous. Our approaches are based on the Krein-Rutman theorem and the global bifurcation theorem.

Sign in / Sign up

Export Citation Format

Share Document