Resonance frequency of a cantilever beam is given by

f=(kn/2pi)*sqrt(EI/mL4)

where, kn=3.52 for cantilever, E is Young's Modulus, I is moment of Inertia, m is mass, L is beam length.

The equation is available in Raymond J. Roark and Warren C. Young, “Formulas for Stress and Strain”, McGraw-Hill, Kogakusha, 5th Edition, (1976).

resonance (natural) frequency of a cantilever beam is given by

f=[kn/2pi][sqrt(EI/wL^4)] where, kn=3.52 for mode 1, E is Young's modulus, I is moment of Inertia, w is beam width, L is beam length. (this is from Formulas for Stress and Strain, 5th edition by Raymond J. Roark and Warren C. Young).

 I would like to derive this formula. Can any one suugest me any book or any link?  

We have recently reported the label-free detection of HCV (Hepatitis C Virus) helicase by using a resonating microcantilever whose surface is functionalized by RNA aptamers as receptor molecules. This work was accepted for publication at Biosensors & Bioelectronics.

Abstract

We have recently reported the piezoelectric thick film microcantilever, which enables the in-situ real-time detection of the protein related to disease (e.g. C reactive protein) in liquid environment. This work was published at APL (click here).

"In-situ real-time monitoring of biomolecular interactions based on resonating microcantilevers immersed in a viscous fluid"

We recently reported the mass sensing by using resonating microcantilevers. The characterization of mass-sensing and its related sensitivity was suggested on the basis of elasticity theory. This work was published online at Sensors and Actuators A (click here).

Microcantilevers have taken much attention as devices for label-free detection of molecules and/or their conformations in solutions and air. Recently, microcantilevers have allowed the nanomechanical mass detection of thin film [1-3], small molecules [4, 5], and biological components such as viruses [6] and vesicles [7] in the order of a pico-gram to a zepto-gram. The great potential of microcantilevers is the sensitive, reliable, fast label-free detection of proteins and/or protein conformations. Specifically, microcantilevers are capable of label-free detection of marker proteins related to diseases, even at a low concentration in solution [8-17]. Microcantilevers, operated in a viscous fluid, have also enabled the real-time monitoring of protein-protein interactions [8, 12-15]. Furthermore, microcantilevers are able to recognize the specific protein conformations [18] and/or reversible conformation changes of proteins/polymers [19, 20].