Nonlinear forced vibration of fluid-conveying microtubes with viscoelastic boundary conditions based on couple-stress theory

This study examines the nonlinear vibrational response of a fluid-conveying microtube subjected to distributed harmonic excitation. A central novelty of the work lies in the incorporation of viscoelastic supports, which enables a more realistic representation of boundary conditions and inherent damping mechanisms in micro-scale systems. Size-dependent effects are accounted for by the modified couple stress theory, while the microtube is modeled using Timoshenko beam kinematics to include both rotary inertia and transverse shear deformation. The governing nonlinear partial differential equations are attained utilizing Hamilton’s principle, considering the contributions of strain energy, kinetic energy, external work, and dissipation introduced by the viscoelastic supports. For numerical implementation, spatial discretization is performed using the Generalized Differential Quadrature Method (GDQM), after which the resulting system is transformed into first-order ordinary differential equations and analyzed using the MATCONT continuation package in MATLAB. The results reveal pronounced influences of both the viscoelastic support parameters and the material length-scale parameter – arising from couple stress theory – on the system’s dynamic response. These effects lead to substantial deviations from predictions, drawing on the classical Timoshenko beam theory with idealized supports. Moreover, the investigation systematically evaluates the roles of support properties, microtube geometry, internal fluid velocity, and excitation characteristics in shaping the frequency response. The findings highlight a high sensitivity of the dynamic behavior to viscoelastic support parameters, underscoring the crucial importance of realistic support modeling in accurately predicting micro-scale fluid–structure interaction phenomena.