Large-Amplitude Periodic Oscillations in Suspension Bridges: Some New Connections with Nonlinear Analysis

Abstract

This paper surveys an area of nonlinear functional analysis and its applications. The main application is to the existence and multiplicity of periodic solutions of a possible mathematical models of nonlinearly supported bending beams, and their possible application to nonlinear behavior as observed in large-amplitude flexings in suspension bridges. A second area, periodic flexings in a floating beam, also nonlinearly supported, is covered a t the end of the paper.

The Fucík spectrum for nonlocal BVP with Sturm–Liouville boundary condition

“…The interest in these type of problems grew also in connection with the theory of suspension bridges (see e.g. [2]). From the mathematical point of view the Fučík equation became a source of numerous investigations generalizing and refining the results by Fučík.…”

Infinitely many nontrivial solutions for a class of biharmonic equations via variant fountain theorems

“…In [4], Lazer and Mckenna considered the biharmonic problem: where u + = max{u, 0} and d ∈ R. They pointed out that this type of nonlinearity furnishes a model to study traveling waves in suspension bridges. In [5], the authors got 2k − 1 solutions when N = 1 and d > λ k (λ k − c) (λ k is the sequence of the eigenvalues of −∆ in H 1 0 (Ω)) via the global bifurcation method.…”

Rational-Harmonic Balancing Approach to Nonlinear Phenomena Governed by Pendulum-Like Differential Equations

“…As Lima [22] pointed out, these 0932-0784 / 09 / 1200-0819 $ 06.00 c 2009 Verlag der Zeitschrift für Naturforschung, Tübingen · http://znaturforsch.com nonlinear equations arise in many fields of science and technology, such as acoustic vibrations [2], oscillations in small molecules [21], oscillations of buildings during earthquakes [25], post-buckling in cantilever columns [26], optically torqued nanorods [27], Josephson superconductivity junctions [21,28], elliptic filters for electronic devices [21], analysis of smectic C liquid crystals [29], gravitational lensing in general relativity [30], advanced models in field theory [31], and others.…”