Nonlinear vibration analysis of pre/post-buckled 3D-printed tubular metastructures

Medical devices utilize auxetic tubes with a negative Poisson's ratio in esophageal and vascular stents to guard against embolism. Designing stents with auxetic structures provides several advantages compared to traditional stents. Therefore, the current investigation focuses on analyzing the small/large amplitude vibration of the pre/post-buckled geometrically imperfect re-entrant auxetic tube. In order to achieve this, von-K & aacute;rm & aacute;n nonlinear assumption along with the first order shear deformation Timoshenko beam theory are employed to obtain the governing equations of the auxetic tube with geometrical imperfection subjected to axial mechanical load. These motion equations are established by applying the Hamilton's principle. Based on Malek-Gibson relations, the effective elastic characteristics of the auxetic honeycomb tube are extracted. Then, the mechanical properties of polylactic acid (PLA) biopolymer are derived experimentally through tensile tests and the digital image correlation (DIC) method. In addition, to investigate the factors affecting the difference in Young's modulus as well as ultimate tensile strength values in dogbone specimens, scanning electron microscopy (SEM) images are taken. The nonlinear equations, using the Ritz method with Chebyshev polynomials, are discretized. The direct displacement control strategy and the Newton-Raphson iterative method are applied to assess the small/large amplitude vibration of the re-entrant auxetic tube. After verifying the created mathematical model, a detailed analysis is undertaken to evaluate the impact of cell angle, vertical to inclined cell wall length ratio, cell thickness to inclined cell wall length ratio, the proportion between the inner and the outer radius of the tube, imperfection parameter, and edge supports on the vibrational behavior of the tubular metastructure.