Akademik Veri Yönetim Sistemi
INDIAN JOURNAL OF PHYSICS, cilt.99, sa.3, ss.1077-1089, 2025 (SCI-Expanded)
In this paper, Casimir
force sensitivity is investigated by utilizing a micro-cantilever under the
driving forces in heptamodal operations. A novel forced Van der
Pol-Rayleigh-Helmholtz nonlinear oscillator model is developed to describe the
nonlinear dynamics of the micro-cantilever which is subject to the excitation
and Casimir forces simultaneously. Demonstrating the effectiveness of the
heptamodal operations, single- and tetramodal-frequency excitation schemes are
also applied separately to resonate the micro-cantilever at the fundamental and
higher eigenmodes. The oscillation observables of the externally driven
micro-cantilever are determined in the presence of the Casimir forces in the
separation distance range of 200-800 nm. Remarkable variations in amplitude
ratio, phase shift, and frequency shift for different effective masses of the
micro-cantilever are explored for the higher eigenmodes. In this current work, the AFM micro-cantilever exhibits the
amplitude response of 0.82 nm to Casimir force at the fourth eigenmode for the
separation distance ranging between 200 nm and 300 nm. The stable frequency
shifts ranging between 103 and 106 Hz are also observed
at the first four eigenmodes for larger separation distances (above around 500
nm). Moreover, the maximum phase shift response of around 150 degrees at
the sixth eigenmode is achieved using heptamodal-frequency excitation of the
lightest micro-cantilever (3.6 x 10-12 kg) at
the separation distance of 200 nm. Thus, implementing heptamodal-frequency
excitation schemes has considerable potential to improve the phase shift
sensitivity to Casimir forces when compared with other excitation schemes.
Additionally, the parameters of the nonlinear oscillator determine
significantly the patterns of the time-domain sensitivities to the external
forces. Correspondingly, displacements of the micro-cantilever under the
driving and Casimir forces at different eigenmodes are obtained to investigate
diverse system nonlinearities. Furthermore, the virial and dissipated power are
also determined for different effective masses of the micro-cantilever to
explain the energy dissipation process in the measurement of Casimir forces.
Therefore, in the present work, the observable responses and energy quantities
for particular system nonlinearities are introduced to be utilized for
nanometrological applications.