Forced vibration response of a micro-cantilever beam with moving loads

Analyzing vibration characteristics of micro-cantilever beams under different loading conditions including moving loads is required in various MEMS applications such as wind speed sensors, bio-sensors and chemical sensor arrays. This paper, therefore presents a mathematical model to evaluate the vibratory response of rectangular cross-section micro-cantilever beams in time domain for any time and space varying loads. The model gives transverse deflection of micro-cantilever beam at any time and any location along its length with deflection resolution in the range of nano-meters. The developed model is validated by comparing natural frequencies of a micro-cantilever beam obtained by the model with the corresponding experimental values of a step-up micro-cantilever beam given in the literature. A step-up geometry condition slightly changes the boundary condition of a normal cantilever beam. This explains the observed error of 15 to 19 % in the natural frequencies of micro-cantilever beam obtained by model and the corresponding experimental values for step-up micro-cantilever beam given in the literature.