Modelling and nonlinear analysis of frictional jointed beams with inerter-based dynamic vibration absorber

This study investigates the effectiveness of an inerter-based dynamic vibration absorber (IDVA) in suppressing vibrations in a nonlinearly jointed beam structure. The governing partial differential equations are derived and discretized using the finite element method, followed by transformation into ordinary differential equations via the Galerkin method. To efficiently compute the steady-state dynamic response and vibration power flow variables, the harmonic balance method with an alternating frequency–time (HB-AFT) scheme is employed. The results demonstrate that the proposed grounded IDVA design achieves superior vibration reduction and energy absorption compared to other designs. The nonlinear frictional joint exhibits distinct behaviour depending on the limit friction force: at smaller limit friction forces, the joint behaves as a frictional damper, resulting in lower response peaks and potential stick-slip motion at the beam tips; at larger limit friction forces, the joint acts as a stiffener, inducing full-stick behaviour and increasing the natural frequency. Additionally, the stiffness nonlinearity primarily influences the system response near the third and fifth resonant peaks, whereas the inertance value significantly affects the first resonant peak. The power dissipation characteristics vary with excitation frequency, with the IDVA dissipating the majority of energy between the first and second resonant frequencies. A design suggestion is to position the IDVA away from the fixed boundary to minimize both the dynamic response and the kinetic energy of the system.