Vibration-based piezoelectric energy harvesting provides a potential power source for low-consumption devices; however, its prediction requires a consistent representation of localized structural properties and experimentally identified modal behavior. This study presents the structural and modal qualification of an analytical electromechanical model for a 6061-T6 aluminum cantilever beam carrying a finite one-sided PZT-5J piezoelectric patch, with unequal beam and patch widths, under base excitation. The specific contribution is the traceable integration of local neutral-axis relocation, spatially varying mass and flexural rigidity, a finite-patch indicator function, $d_{31}$ electromechanical coupling, multimodal projection, and mode-specific reduced-order equations. Two beam lengths, $275$ and $250 \mathrm{m}\mathrm{m}$, were investigated using broadband shaker excitation, accelerometry, and scanning laser vibrometry. The measured first and second bending frequencies were $16.56$ and $110.31 \mathrm{H}\mathrm{z}$ for the $275 \mathrm{m}\mathrm{m}$ beam and $19.14$ and $125.00 \mathrm{H}\mathrm{z}$ for the $250 \mathrm{m}\mathrm{m}$ beam. Experimental damping ratios obtained from the frequency-response functions ranged from $6.54\times {10}^{-3}$ to $1.55\times {10}^{-2}$. The analytical formulation reproduced the increase in modal frequencies produced by reducing the beam length and captured the measured transverse mode-shape trends. Experimentally identified frequencies, base accelerations, and damping ratios were subsequently introduced into the reduced model to obtain experimentally parameterized model outputs. The largest calculated peak voltage and estimated average electrical power were $155.99 \mathrm{m}\mathrm{V}$ and $1.22 \mathsf{\mu }\mathrm{W}$, respectively, for the first mode of the $275 \mathrm{m}\mathrm{m}$ beam across a reference $10 \mathrm{k}\mathsf{\Omega }$ resistive load. The reported qualification is restricted to the structural and modal response of the two tested configurations; the electrical quantities are calculated outputs rather than independent electrical measurements.

In nanotechnology, one of the powerful tools is the atomic force microscope (AFM). Instrument used to characterize materials superficially. Nanoscale hardness (nanohardness) using nanoindentation method spectroscopy mode is considered when evaluating these characteristics. The suitable equipment to measure the hardness in materials such as thin films, with thicknesses on the order of tens of nanometers is the AFM. In this article, the authors propose a first approach to some models used to evaluate the hardness, using the AFM, based on the elastic model.

Molecular dynamics (MD) simulations of nanoindentation using the hard sphere potential were carried out for Cr, Ni and Ni/Cr bilayer thin films with interaction of BCC and FCC single-crystal and the contact between the Cr-Ni. On the other hand, fixed boundary conditions were used and the repulsive radial potential was employed for modeling the interaction between the tip and sample surface. Mechanical properties of the material at 300 K were obtained for Cr and Ni thin films and Ni/Cr bilayers. Hardness and elastic parameters were determined from the load-unload curves obtained by means of the simulations. These results show a better mechanical response in the case of bilayers compared to the Ni and Cr monolayers.