Parametric effects in nanobeams and AFM
Vibration dynamics of forced cantilever beams that are used in nanotechnology such as atomic force microscope modeling and carbon nanotubes is considered in terms of a fundamental response within a matrix framework. The modeling equations are written as a matrix differential equation subject to tip-sample general boundary conditions. At the junctions, where there are discontinuities due to different material or beam thickness, compatibility conditions are prescribed. Forced responses are given by convolution of the input load with the time domain Green matrix function. The corresponding matrix transfer function and modes of a multispan cantilever beam are determined in terms of solution basis of the same shape generated by a fundamental solution. Simulations were performed for a three stepped beam with a piezoelectric patch subject to pulse forcing terms and with surface effects.