Influence of agglomeration and CNT waviness on the natural frequencies of porous multi-scale hybrid weightlifting sport annular plates

The present study investigates the vibrational properties of a weightlifting sport plate, which is modeled as an annular plate composed of an epoxy matrix reinforced with carbon nanotubes (CNTs) and carbon fibers (CFs). This study pioneers the analysis of free vibration in porous multi-scale hybrid composite plates, explicitly addressing the previously unexplored effects of CNT agglomeration and waviness. The mechanical properties of the nanocomposite are assessed using a modified Halpin–Tsai micromechanics model, which incorporates considerations of agglomeration and waviness of CNTs within the matrix. Subsequently, the enhanced nanocomposite matrix is integrated with unidirectional and oriented CFs. Based on an energy-based Hamiltonian approach; equations of motion are derived using higher-order shear deformation theory. The key parameters being investigated include weight fraction of CNTs, CNT patterns, CNT agglomeration and waviness, CF volume fraction, CF orientation, porosity parameters, boundary conditions, and dimensions of the annular plate. It is found that increasing the CNT weight fraction enhances natural frequencies, with the introduction of CFs further amplifying this effect. Among the CNT patterns, CNT-O pattern is observed to have the most significant impact, while CNT-X pattern shows the least. Under severe agglomeration and waviness, influence of waviness becomes dominant, leading to a decrease in natural frequency for CNT weight fractions exceeding 1%. The presence of CNTs is found to mitigate the negative effects of porosity, particularly at lower porosity coefficients.