gdqem analysis for free vibration of v-shaped atomic force microscope cantilevers

v-shaped and triangular cantilevers are widely employed in atomic force microscope (afm) imaging techniques due to their stability. for the design of vibration control systems of afm cantilevers which utilize patched piezo actuators, obtaining an accurate system model is indispensable prior to acquiring the information related to natural modes. a general differential quadrature element method (gdqem) analysis based on layer-wise displacement beam theory was performed to obtain the natural frequencies of v-shaped afm cantilevers with piezoelectric actuators. a finite element analysis was applied to validate the accuracy of numerical results. finally, a parametric investigation of the sensitivity of natural frequencies with respect to beam geometry was performed. simulations show that presented approach is considerably accurate and does not need a lot computational costs. based on the governing equations, general differential quadrature method (gdqm) and gdqm could be applied for uniform and stepped plates, respectively. thus, presented approach covers the v-shaped and triangular cantilevers perfectly and could be utilized to derive the dynamic response of such systems with a little substitution.