Analytic and Numerical Modeling of the Transient Dynamics of a Microcantilever Sensor

Sarit Barhen

Supervisor: Professor Arye Nehorai

Department of Electrical and Systems Engineering
Washington University in St. Louis
Summer - Fall 2006

 

Abstract

Microcantilevers have recently emerged as sensor components that hold the promise for robust detection of biological, chemical, and other security-related threats. Consequently, there has been a growing need to develop accurate and sophisticated methods for predicting a microcantilever's transient response to an arbitrary spatio-temporal load. To model the spatio-temporal dynamics of the microcantilever, the nonhomogeneous beam equation, a fourth-order partial differential equation, is used. This Letter presents an innovative analytical solution of this equation, including damping and spatio-temporal shifts. This solution is compared to a numerical, stable finite-differences implementation. Excellent agreement is shown for two examples of forcing by shifted spatio-temporal loads, including a finite-width Gaussian pulse. The computer code implementation is also discussed.

Reference

Sarit Barhen, “Analytic and numerical modeling of the transient dynamics of a microcantilever sensor”, Physics Letters A, Volume 372, Issue 7, 11 February 2008, Pages 947-957.

 

Fig. 1. Schematic representation of a microcantilever.

Fig. 2. Finite differences grid. It includes virtual grid points (on vertical dashed lines) to accommodate boundary conditions. Domain boundaries are in bold lines.

 

Fig. 3. Microcantilever transient impulse beam dynamics (shifted temporal profile). Analytical results were obtained for a 10 modes expansion.

 

 

Fig. 4. Comparison of the longitudinal spatial profiles of a micro cantilever's responses to a finite-size Gaussian distribution load.