Parametric vibrations of a damaged orthotropic geometrical shell stiffened with an inhomogeneous rod and rings on viscoelastic medium

TL;DR

This paper investigates the parametric vibrations of a damaged orthotropic shell reinforced with an inhomogeneous rod and rings, considering contact with a viscoelastic medium, and derives the frequency equation for such a complex system.

Contribution

It introduces a novel analysis of vibrational behavior of damaged orthotropic shells with reinforcement and viscoelastic contact, using hereditary damage theory and variational principles.

Findings

Derived the frequency equation considering damage and reinforcement effects.

Analyzed the influence of viscoelastic medium on shell vibrations.

Proposed practical applications in bridge foundation design.

Abstract

The structural element considered in the presented article consists, according to the geometric structure, of a coating and reinforcement elements, according to the mechanical characteristics of heterogeneous coatings along the length, having damage inside due to their physical structure and, finally, a system in contact with a viscoelastic medium. Taking into account one of the existing models (Winkler or Pasternak), the contact conditions between the coating and the reinforcement elements and the influence of the medium on the coating, the frequency equation of oscillation was solved, the results were analyzed. Theory of hereditary type damage under the action of external force is often used for taking into account the damages in the structure of a cylindrical shell forced to vibration. The Hamilton-Ostrogradsky variational principle is used for solving the problem. The results obtained can be used in the foundations of bridges built across mountain rivers. Such support is cost-effective. It should be noted that reinforcement and concrete mortar are also used in the internal parts of the cylindrical supports used. The article proposes to fill the inside of the cylindrical lid under study with clay.