A Discrete Two-Dimensional Model of a Loaded Cantilever Influenced by Time-Dependent Forces

TL;DR

This paper presents a discrete 2D model of a loaded cantilever that accounts for inhomogeneity, geometry, and external time-dependent forces, with validation against continuous models and applications to complex geometries.

Contribution

The authors introduce a novel discrete 2D cantilever model that incorporates inhomogeneity, geometry, and external forces, providing detailed analysis and numerical validation.

Findings

Discrete model aligns well with continuous solutions

Model effectively captures effects of external time-dependent forces

Useful for complex cantilever geometries and external influences

Abstract

We developed a discrete two-dimensional model of a cantilever which incorporates the effects of inhomogeneity, the geometry of an attached particle, and the influence of external time-dependent forces. We provide a comparison between the solutions for our discrete model and its continuous limit. The rotational-vibrational mode is studied in detail. The results of numerical simulations demonstrate usefulness of our model for many applications when a cantilever has a complicated geometry and is affected by time-depended and distributed external forces.