Linear and non-linear vibrations of fluid-filled hollow microcantilevers interacting with small particles

Linear and non-linear vibrations of a U-shaped hollow microcantilever beam filled with fluid and interacting with a small particle are investigated. The microfluidic device is assumed to be subjected to internal flowing fluid carrying a buoyant mass. The equations of motion" are derived via extended Hamilton's principle and by using Euler-Bernoulli beam theory retaining geometric and inertial non-linearities. A reduced-order model is obtained applying Galerkin's method and solved by using a pseudo arc-length continuation and collocation scheme to perform bifurcation analysis and obtain frequency response curves. Direct time integration of the equations of motion has also been performed by using Adams-Moulton method to obtain time histories and analyze transient cantilever-particle interactions in depth. It is shown that exploiting near resonant non-linear behavior of the microcantilever could potentially yield enhanced sensor metrics. This is found to be due to the transitions that occur as a matter of particle movement near the saddle-node bifurcation points of the coupled system that lead to jumps between coexisting stable attractors.