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Nanomechanical cantilever sensors (NMCSs) have recently emerged as an effective means for label-free chemical and biological species detection. They operate through the adsorption of species on the functionalized surface of mechanical cantilevers. Through this functionalization, molecular recognition is directly transduced into a micromechanical response. In order to effectively utilize these sensors in practice and correctly relate the micromechanical response to the associated adsorbed species, the chief technical issues related to modeling must be resolved. Along these lines, this paper presents a general nonlinear-comprehensive modeling framework for piezoelectrically actuated microcantilevers and validates it experimentally. The proposed model considers both longitudinal and flexural vibrations and their coupling in addition to the ever-present geometric and material nonlinearities. Utilizing Euler-Bernoulli beam theory and employing the inextensibility conditions, the coupled longitudinal-flexural equations of motion are reduced to one nonlinear partial differential equation describing the flexural vibrations of the sensor. Using a Galerkian expansion, the resulting equation is discretized into a set of nonlinear ordinary differential equations. The method of multiple scales is then implemented to analytically construct the nonlinear response of the sensor near the first modal frequency (primary resonance of the first vibration mode). These solutions are compared to experimental results demonstrating that the sensor exhibits a softening-type nonlinear response. Such behavior can be attributed to the presence of quadratic material nonlinearities in the piezoelectric layer. This observation is critical, as it suggests that unlike macrocantilevers where the geometric hardening nonlinearities dominate the response behavior, material nonlinearities dominate the response of microcantilevers yielding a softening-type response. This behavior should be accounted for wh- en designing and employing such sensors for practical applications. [ABSTRACT FROM PUBLISHER]

Over the past decade, microcantilever-based mass sensing has grown to become a significant field of research in the engineering community. The ability of microcantilevers to detect extremely small biochemical particles is being investigated for a number of industrial applications. This paper presents an adaptive self-sensing strategy for ultrasmall tip mass estimation using piezoelectrically actuated microcantilevers. A piezoelectric patch actuator deposited on the cantilever surface actuates the beam through a capacitance bridge mechanism. The same patch is used to measure shifts in the beam natural frequency associated with increase in the mass, which is due to the addition of biochemical particles. The ability to measure frequency shifts due to tip masses as small as 1 fg (10-15 g) is demonstrated through extensive numerical simulations. Uncertainty in the measurement of system parameters makes implementation of the self-sensing bridge network difficult at the microscale. The piezoelectric capacitance is also known to vary with temperature. To overcome these difficulties, a novel adaptive mechanism is presented to dynamically balance the capacitance bridge network. Lyapunov-based stability analysis demonstrates the global stability of the adaptation laws. Simulation results demonstrate the feasibility of this mechanism to perform self-sensing at the microscale. Experimental validation of the adaptation mechanism at the microscale involves a number of technical challenges, and hence, is performed on a macroscale cantilever system. This paper aims to motivate research in the development of a powerful, yet portable frequency shift detection-based microcantilever sensor for use in a variety of biochemical applications, where ultrasmall mass detection is a key requirement. [ABSTRACT FROM PUBLISHER]