Nonlocal elasticity-based torsional vibration analysis of short-fiber-reinforced nanorods with elliptical and triangular cross-sections

Abstract This study investigates the torsional vibration of short-fiber-reinforced composite (SFRC) nanorods with non-circular cross-sections under deformable boundary conditions using nonlocal elasticity theory. Governing equations of motion and force boundary conditions are derived via Hamilton’s principle. Unlike most existing studies, this work incorporates elliptical and triangular geometries with warping effects, and determines the properties of randomly oriented short fibers using the Halpin–Tsai micromechanics model. A semi-analytical solution is then formulated, in which the rotation function is defined with two constants at the boundaries and a Fourier sine series over the domain, while Stokes’ transformation allows systematic incorporation of arbitrary boundary spring stiffnesses. The resulting unified eigenvalue matrix includes material, geometric, nonlocal, and boundary parameters. A key novelty of this approach is that different support conditions can be obtained by simply tuning the spring stiffnesses, eliminating the need to repeatedly solve the boundary value problem. Infinite and zero limits recover clamped and free boundaries, respectively, while intermediate values enable examination of boundary deformations. Numerical analyses are conducted to investigate the influence of key parameters, including the fiber volume fraction, aspect ratio, elastic modulus ratio, mass density ratio, nonlocal parameter, nanorod length, and cross-sectional geometry. The findings and the developed solution method can significantly aid in the design and analysis of nanomechanical systems utilizing composite nanorods.