The free vibration analysis of rotating functionally graded (FG) nano-beams under an in-plane thermal loading is provided for the first time in this paper. The formulation used is based on Euler-Bernoulli beam theory through Hamilton’s principle and the small scale effect has been formulated using the Eringen elasticity theory. Then, they are solved by a generalized differential quadrature meth...

This paper focuses on the development of a complete model of an atomic force microscope (AFM) micro-cantilever beam, based on considering the effects of four major factors in modeling the cantilever. They are: rotary inertia and shear deformation of the beam and mass and rotary inertia of the tip. A method based on distributed-parameter modeling approach is proposed to solve the governing equat...

Measurement of gas density and viscosity was conducted using a micro-cantilever beam. In parallel, the validity of the proposed modeling approach was evaluated. This study also aimed to widen the database of the gases on which the model development of the micro-cantilever beams is based. The density and viscosity of gases are orders of magnitude lower than liquids. For this reason, the use of a...

A working model has been developed which can be used to significantly increase the accuracy of cantilever deflection measurements using optical beam techniques (used in cantilever-based sensors and atomic force microscopes), while simultaneously simplifying their use. By using elementary geometric optics and standard vector analysis it is possible, without any fitted or adjustable parameters, t...

In this investigation an elastic stress analysis is carried out a woven steel fiber reinforced thermoplastic cantilever beam loaded uniformly at the upper surface. The composite beam material consists of low density polyethylene as a thermoplastic (LDFE, f.2.12) and woven steel fibers. Granules of the polyethylene are put into the moulds and they are heated up to 160°C by using electrical resis...

5 Simple example problems 20 5.1 Cantilever beam . . . . . . . . . . . . . . . . . . . . . . . . . . . 20 5.2 Frequency calculation of a beam loaded by compressive forces . . 27 5.3 Frequency calculation of a rotating disk on a slender shaft . . . . 29 5.4 Thermal calculation of a furnace . . . . . . . . . . . . . . . . . . 35 5.5 Seepage under a dam . . . . . . . . . . . . . . . . . . . . . . ...

The frequency response of a cantilever beam is strongly dependent on the fluid in which it is immersed. In a companion study, Sader @J. Appl. Phys. 84, 64, ~1998!# presented a theoretical model for the flexural vibrational response of a cantilever beam, that is immersed in a viscous fluid, and excited by an arbitrary driving force. Due to its relevance to applications of the atomic force micros...

Electrostatic actuators are used as voltage-controlled oscillators or resonators in high frequency applications. The change in deflection of a cantilever beam due to an applied voltage leads to change in capacitance between the plates of the beam. However, the range of operation of these devices is limited due to the nonlinear nature of the applied electrostatic forces as the cantilever beam mo...

Theoretical models for the frequency response of a cantilever beam immersed in a viscous fluid commonly assume that the fluid is unbounded. Experimental measurements show, however, that proximity to a surface can significantly affect the frequency response of a cantilever beam. In this article, we rigorously calculate the effect of a nearby surface on the frequency response of a cantilever beam...