Existence results and iterative method for solving the cantilever beam equation with fully nonlinear term

2017 ◽  
Vol 36 ◽  
pp. 56-68 ◽  
Author(s):  
Quang A. Dang ◽  
Thi Kim Quy Ngo
Keyword(s):  
Iterative Method ◽  
Cantilever Beam ◽  
Nonlinear Term ◽  
Existence Results ◽  
Beam Equation ◽  
Fully Nonlinear ◽  
Cantilever Beam Equation

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.

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 Positive solutions of a discrete second-order boundary value problems with fully nonlinear term

2020 ◽  
Vol 2020 (1) ◽  
Author(s):  
Liyun Jin ◽  
Hua Luo
Keyword(s):  
Positive Solutions ◽  
Fixed Point Index ◽  
Nonlinear Term ◽  
Boundary Value ◽  
Index Theory ◽  
Second Order ◽  
Fully Nonlinear ◽  
Fixed Point Index Theory ◽  
Weaker Conditions ◽  
Lower Limits

Abstract In this paper, we mainly consider a kind of discrete second-order boundary value problem with fully nonlinear term. By using the fixed-point index theory, we obtain some existence results of positive solutions of this kind of problems. Instead of the upper and lower limits condition on f, we may only impose some weaker conditions on f.

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.

Resonance and non-resonance in terms of average values. II

2001 ◽  
Vol 131 (5) ◽  
pp. 1217-1235
Author(s):  
M. N. Nkashama ◽  
S. B. Robinson
Keyword(s):  
Differential Equation ◽  
Ordinary Differential Equation ◽  
Nonlinear Term ◽  
Spectral Gap ◽  
Elliptic Boundary ◽  
Sufficient Conditions ◽  
Existence Results ◽  
Elliptic Boundary Value ◽  
Semilinear Elliptic ◽  
The Given

We prove existence results for semilinear elliptic boundary-value problems in both the resonance and non-resonance cases. What sets our results apart is that we impose sufficient conditions for solvability in terms of the (asymptotic) average values of the nonlinearities, thus allowing the nonlinear term to have significant oscillations outside the given spectral gap as long as it remains within the interval on the average in some sense. This work generalizes the results of a previous paper, which dealt exclusively with the ordinary differential equation (ODE) case and relied on ODE techniques.

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