Multiscale nonlinear dynamics of DNA-grafted microcantilevers driven by electro-chemo-mechanical strain-stiffening

A multiscale continuum framework is developed to couple the nonlinear Poisson–Boltzmann electrochemical field with the entropic elasticity of polymer brushes, establishing the electro-chemo-mechanical constitutive behavior of DNA-functionalized microcantilevers. This constitutive relation is incorporated into the macroscopic beam dynamics through an effective stiffness that accounts for surface-induced nonlinearity. The analysis shows that the effective flexural rigidity exhibits a non-monotonic dependence on ionic conditions, resulting from the competition between electrostatic screening and entropic repulsion. This dependence modifies the nonlinear restoring force and alters the structure of the dynamic response, leading to a transition from weakly nonlinear oscillations to bistable behavior associated with saddle–node bifurcations of periodic solutions. Based on this mechanism, a bifurcation-based sensing scheme is examined, in which DNA hybridization acts as a slowly varying parameter that drives the system across stability boundaries. The resulting transition between coexisting periodic attractors produces a pronounced change in oscillation amplitude. The dynamic response is computed using a hybrid harmonic balance and pseudo-arc-length continuation (HBM–PALC) method, which captures both stable and unstable solution branches. In addition, the global response is analyzed in the excitation amplitude–frequency parameter space. The results indicate that increasing excitation amplitude leads to a sequence of period-doubling bifurcations and eventual transition to aperiodic motion, thereby defining a bounded region of stable periodic operation. The influence of stochastic perturbations near bifurcation points is also discussed in terms of noise-induced transitions between attractors. These results provide a consistent dynamical description of the coupled electro-chemo-mechanical system and clarify the role of bifurcation behavior in sensing applications.