Modeling Frequency Shifts in Small-Scale Beams with Multiple Eccentric Masses

TL;DR

This paper introduces a stress-driven nonlocal model to analyze how attached eccentric masses affect the vibrational frequencies and mode shapes of small-scale beams, aiding the design of ultrasensitive sensors.

Contribution

It presents a novel nonlocal modeling approach for small-scale beams with multiple eccentric masses, including inverse problem analysis for mass and location detection.

Findings

Excellent agreement with experimental and numerical data.

Insights into frequency shifts and mode shapes for multiple attached masses.

Method for detecting mass and position of attached particles.

Abstract

Studying the dynamics of small-scale beams with attached particles is crucial for sensing applications in various fields, such as bioscience, material science, energy storage devices, and environmental monitoring. Here, a stress-driven nonlocal model is presented for the free transverse vibration of small-scale beams carrying multiple masses taking into account the eccentricity of the masses relative to the beam axis. The results show excellent agreement with the experimental and numerical data in the literature. New insights into the frequency shifts and mode shapes of the first four vibrational modes of stress-driven nonlocal beams with up to three attached particles are presented. The study investigates the inverse problem of detecting the location and mass of an attached particle based on natural frequency shifts. The knowledge acquired from the present study provides valuable guidance for the design and analysis of ultrasensitive mechanical mass sensors.