Design and analysis of curved wire for biomedical device applications

In this study, the dynamic behavior of curved wires is investigated and optimized with a focus on biomedical applications. To solve the integral boundary value problem of the curved wire, a spectral Chebyshev approach is developed in conjunction with the first-order shear deformation theory for beams. The wire shapes are categorized into two main groups: (i) with curvature and (ii) without curvature. In the former category, the curved segment is located in the middle of the wire, flanked by two straight segments, resulting in a complex geometric equation. The proposed method is validated by comparing the obtained natural frequencies with those reported in the literature and results from the finite element method. The results for different boundary conditions and various geometric properties show excellent agreement with both the literature and finite element method. Furthermore, a design process is conducted to optimize the maximum displacement response of the wire distal tip relative to the base excitation amplitude. This process involves varying the length ratios of the tapered wire, defined as design variables, for different lengths of straight wires and various curvature amounts of curved wires. The design results indicate that the ratio of distal tip displacement to base excitation amplitude can be increased by up to 600% for straight wires and 240% for curved wires at an excitation frequency of 40 kHz.