Nonlinear response of a microplate on soft visco-hyperelastic micropillar arrays under base excitation

Abstract Soft visco-hyperelastic micropillar arrays, elastomeric nanocomposites reinforced with graphene, MXene, or carbon nanotubes, provide tunable mechanical compliance essential for wearable sensors, soft robotics, and bio-integrated microdevices. Nevertheless, the nonlinear vibrational dynamics of rigid microstructures supported by such compliant foundations under operational base excitations remain poorly characterized, particularly when finite deformations activate strong geometric and material nonlinearities. This work develops a physics-based model that couples incompressible neo-Hookean hyperelasticity with Kelvin–Voigt viscoelasticity to capture large-strain dynamics of PDMS-based micropillar arrays supporting a metallic microplate under harmonic base excitation. Through Galerkin projection of the governing equation of motion, frequency–amplitude responses reveal four quantified design principles for engineering predictable dynamics: (i) nanofiller incorporation that raises the effective modulus from 0.4 to 1.5 MPa suppresses classical jump phenomena and reduces bifurcation interval lengths by up to 90%; (ii) enhanced viscoelastic damping attenuates resonance amplitudes by 45% while promoting linearized response; (iii) geometric tuning via pillar height increase (from $$\\:5\\:\\mu\\:m$$ to $$\\:7\\:\\mu\\:m$$ ) linearizes system dynamics and shrinks nonlinear intervals by 70%; and (iv) the static acceleration component elevates the effective natural frequency through pre-compression stiffening, whereas the harmonic component governs bifurcation onset. Notably, at the lowest modulus ( $$\\:{E}_{m}=\\:0.4\\:MPa$$ ), softening permits sufficiently large deflections to activate nonlinearities, triggering a Neimark–Sacker bifurcation and quasiperiodic response, a regime absent in stiffer configurations. This identification is based on the characteristic frequency response signature where the periodic solution loses stability, consistent with the creation of an invariant torus as described in nonlinear dynamics theory. These principles establish a rational framework for designing soft-supported microsystems with predictable vibrational behavior under real-world excitations, a prerequisite for signal fidelity in next-generation wearable and implantable sensors.