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.

A hollow microcantilever is used instead of a conventional microcantilever to dispense and aspirate liquids in the femto-litre (10^-15 L) volume range in an atomic force microscope (AFM) setup. The inherent force sensing capability of the cantilever is used to monitor the fluid manipulation in-situ. At this small scale, parameters like: surface energy, evaporation, viscosity and temperature become important for controlled manipulation. In a conventional AFM, these parameters are usually not taken into consideration as feedback parameters. In the present work, we report initial experimental results on the dosing process and an analytical dynamic model of the process. The model is based on the liquid bridge between the cantilever tip and the substrate, which can describe the dosing process with variance accounted for (VAF) larger than 90%. We aim to use this model and implement a control system for precise dispensing and aspiration.

In situ stiffness adjustment in microelectromechanical systems is used in a variety of applications such as radio-frequency mechanical filters, energy harvesters, atomic force microscopy, vibration detection sensors. In this review we provide designers with an overview of existing stiffness adjustment methods, their working principle, and possible adjustment range. The concepts are categorized according to their physical working principle. It is concluded that the electrostatic adjustment principle is the most applied method, and narrow to wide ranges in stiffness can be achieved. But in order to obtain a wide range in stiffness change, large, complex devices were designed. Mechanical stiffness adjustment is found to be a space-effective way of obtaining wide changes in stiffness, but these methods are often discrete and require large tuning voltages. Stiffness adjustment through stressing effects or change in Young's modulus was used only for narrow ranges. The change in second moment of inertia was used for stiffness adjustment in the intermediate range.