Vibrations of a geometrically nonlinear viscoelastic shallow shell with concentrated masses

On a dynamic contact problem for a geometrically nonlinear viscoelastic shell

We deal with an initial-boundary value problem describing the perpendicular vibrations of a viscoelastic Kármán-Donnell shell with a rigid inner obstacle. A weak formulation of a problem is in a form of a hyperbolic variational inequality. We solve this problem using the penalization method

Nonlinear Vibrations of Timoshenko Beams Carrying a Concentrated Mass

Transverse vibrations of Timoshenko type beams carrying a concentrated mass have been investigated. Both ends of this mass-beam system have simply supports. Hamilton Principle has been used in order to derive equation of motion . For this coupled differential equations, approximately solutions have been searched by means of Method of Multiple Scales(a perturbation method). These solutions consi...

A Uniqueness Theorem for a Classical Nonlinear Shallow Shell Model

The main goal of this paper is to establish the uniqueness of solutions of finite energy for a classical dynamic nonlinear thin shallow shell model with clamped boundary conditions. The static representation of the model is an extension of a Koiler shallow shell model. Until now, this has been an open problem in the literature. The primary difficulty is due to a lack of regularity in the nonlin...

Optimal Design of Geometrically Nonlinear Structures Under a Stability Constraint

This paper suggests an optimization-based methodology for the design of minimum weight structures with kinematic nonlinear behavior. Attention is focused on three-dimensional reticulated structures idealized with beam elements under proportional static loadings. The algorithm used for optimization is based on a classical optimality criterion approach using an active-set strategy for extreme lim...

The Post-processed Galerkin Method Applied to Nonlinear Shell Vibrations