Nonlinear Structural, Inertial and Damping Effects in an Oscillating Cantilever Beam

Sayag, Michal Raviv; Dowell, Earl H.

doi:10.1007/978-3-319-74280-9_44

Nonlinear Dynamics, Volume 1

2018

DOI: 10.1007/978-3-319-74280-9_44

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Nonlinear Structural, Inertial and Damping Effects in an Oscillating Cantilever Beam

Michal Raviv Sayag

Earl H. Dowell

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2021

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Cited by 1 publication

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Theory of Solutions for an Inextensible Cantilever

Deliyianni

Webster

2021

Appl Math Optim

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Recent equations of motion for the large deflections of a cantilevered elastic beam are analyzed. In the traditional theory of beam (and plate) large deflections, nonlinear restoring forces are due to the effect of stretching on bending; for an inextensible cantilever, the enforcement of arc-length preservation leads to quasilinear stiffness effects and inertial effects that are both nonlinear and nonlocal. For this model, smooth solutions are constructed via a spectral Galerkin approach. Additional compactness is needed to pass to the limit, and this is obtained through a complex procession of higher energy estimates. Uniqueness is obtained through a non-trivial decomposition of the nonlinearity. The confounding effects of nonlinear inertia are overcome via the addition of structural (Kelvin-Voigt) damping to the equations of motion. Local well-posedness of smooth solutions is shown first in the absence of nonlinear inertial effects, and then shown with these inertial effects present, taking into account structural damping. With damping in force, global-in-time, strong well-posedness result is obtained by achieving exponential decay for small data.

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Theory of Solutions for an Inextensible Cantilever

Deliyianni

Webster

2021

Appl Math Optim

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Nonlinear Structural, Inertial and Damping Effects in an Oscillating Cantilever Beam

Cited by 1 publication

References 19 publications

Theory of Solutions for an Inextensible Cantilever

Theory of Solutions for an Inextensible Cantilever

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