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This research focuses on examining the vibrational properties of intelligent curved microbeams (CMBs) that incorporate metal foams and are enhanced with carbon nanotubes-reinforced piezoelectric (CNTRP) actuators. An advanced four-variable theory for shear and normal deformation is applied in the polar coordinate framework to investigate the microstructure, thereby negating the need for a shear correction factor. Additionally, the modified couple stress theory (MCST) is utilized to account for scale effects. The structural attributes exhibit thickness-dependent alterations following predefined functions. The governing equations of motion are deduced using Hamilton’s principle. In instances where the structure has simply supported ends, Fourier series functions are utilized to solve these equations. The outcomes are cross-validated in contradiction with previously documented works with more straightforward setups. The inquiry investigates the effects of critical parameters on the vibrational response of the structure. The results are corroborated in simpler scenarios using existing data in the literature to ensure accuracy.

This study delves into the dynamic characteristics of intelligent arches composed of metal foams, augmented with piezoelectric nanocomposite actuators. These arches are represented within the polar coordinate system, utilizing a higher-order shear and normal deformation theory that eliminates the need for shear correction factors. The structural properties exhibit thickness-dependent variations following predetermined functions. The model operates within a thermal environment and is supported by a Winkler–Pasternak elastic substrate. Hamilton’s principle is employed to derive the equations governing the structure’s motion. In solving these equations for a scenario with simply supported ends, Fourier series functions are employed as an analytical method. The outcomes are cross-verified against previously published studies with simpler configurations. The investigation explores the impacts of various critical parameters on the dynamic response of the structure. Findings reveal that an increase in pores within the metal foam core decreases the frequency, whereas an increase in the volume fraction of carbon nanotubes has the opposite effect. The primary objective of this study is to design and fabricate more efficient smart structures, through a comprehensive understanding and optimization of the behavior of metal foam arches when integrated with piezoelectric components.

With the demand of lightweight structure, more and more metal foams were employed as impact protection and efficient energy absorption materials in engineering fields. But, results from different impact experiments showed that the strain rate sensitivity of metal foams were different or even controversial. In order to explore the true hiding behind the controversial experimental data about the strain rate sensitivity of metal foams, numerical simulations of split Hopkinson pressure bar (SHPB) tests of the metal foams were carried out by finite element methods. In the analysis, cell structures of metal foams were constructed by means of 3D Voronoi, and the matrix metal was assumed to be no strain rate sensitivity, which helps to learn the strain rate effects quantitatively by the foam structures. Numerical simulations showed that the deformation of the metal foam specimen is not uniform during the SHPB tests along the specimen, and the strain–stress relations of the metal foams at two ends of the specimen are different; there exists strain rate sensitivity of the metal foams even the matrix metal has no strain rate sensitivity, when the strain of the metal foams is defined by the displacement difference between the ends of the specimen; localized deformation of the metal foams and the inertia effect of matrix metal are the two main contributions to the strain rate sensitivity of the metal foams.