arXiv subjects

Tobias Ameismeier

Publications and source records attributed to Tobias Ameismeier.

2 recordsLinked to original sources

arXiv2022

Convergence of Thin Vibrating Rods to a Linear Beam Equation

We show that solutions for a specifically scaled nonlinear wave equation of nonlinear elasticity converge to solutions of a linear Euler-Bernoulli beam system. We construct an approximation of the solution, using a suitable asymptotic expansion ansatz based upon solutions to the one-dimensional beam equation. Following this, we derive the existence of appropriately scaled initial data and can bound the difference between the analytical solution and the approximating sequence.

math.AP↗

arXiv2021

Large Times Existence for Thin Vibrating Rods

We consider the dynamical evolution of a thin rod described by an appropriately scaled wave equation of nonlinear elasticity. Under the assumption of well-prepared initial data and external forces, we prove that a solution exists for arbitrarily large times, if the diameter of the cross section is chosen sufficiently small. The scaling regime is such that the limiting equations are linear.

math.AP↗