  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.
