Dynamic Behavior of Mass Sensor Based on Switchable Dual-Mode Composite Strips

Micro- and nanoscale mass sensing is crucial for applications such as molecular detection and wearable monitoring. However, the observation of mass perturbations in flexible composite structures requires systematic theoretical evaluation. This study develops a dual-mode vibration-based mass-sensing model based on a film–substrate composite strip. By releasing and re-stretching pre-strain in the soft substrate, the ribbon can reversibly switch between a two-dimensional flat configuration (Mode 1) and a three-dimensional buckled configuration (Mode 2), leading to distinct dynamic responses. Under a finite-deformation Euler–Bernoulli beam assumption, displacement fields and kinematic relations are formulated for both configurations. An energy-based approach is employed to decompose the total energy into stretching and bending contributions, while an added-mass block is incorporated into the kinetic energy as a lumped mass. The governing equations of motion are derived using the Lagrange equations and the Hamiltonian function. Based on these results, the influence of the added mass on displacement signatures is examined, and the mode-dependent observability in the flat versus buckled states is compared, providing an analytical basis for mass sensor evaluation.