Cantilever

About: Cantilever is a research topic. Over the lifetime, 19032 publications have been published within this topic receiving 265886 citations.

An experimentally validated bimorph cantilever model for piezoelectric energy harvesting from base excitations

Abstract: Piezoelectric transduction has received great attention for vibration-to-electric energy conversion over the last five years. A typical piezoelectric energy harvester is a unimorph or a bimorph cantilever located on a vibrating host structure, to generate electrical energy from base excitations. Several authors have investigated modeling of cantilevered piezoelectric energy harvesters under base excitation. The existing mathematical modeling approaches range from elementary single-degree-of-freedom models to approximate distributed parameter solutions in the sense of Rayleigh–Ritz discretization as well as analytical solution attempts with certain simplifications. Recently, the authors have presented the closed-form analytical solution for a unimorph cantilever under base excitation based on the Euler–Bernoulli beam assumptions. In this paper, the analytical solution is applied to bimorph cantilever configurations with series and parallel connections of piezoceramic layers. The base excitation is assumed to be translation in the transverse direction with a superimposed small rotation. The closed-form steady state response expressions are obtained for harmonic excitations at arbitrary frequencies, which are then reduced to simple but accurate single-mode expressions for modal excitations. The electromechanical frequency response functions (FRFs) that relate the voltage output and vibration response to translational and rotational base accelerations are identified from the multi-mode and single-mode solutions. Experimental validation of the single-mode coupled voltage output and vibration response expressions is presented for a bimorph cantilever with a tip mass. It is observed that the closed-form single-mode FRFs obtained from the analytical solution can successfully predict the coupled system dynamics for a wide range of electrical load resistance. The performance of the bimorph device is analyzed extensively for the short circuit and open circuit resonance frequency excitations and the accuracy of the model is shown in all cases.

Cantilever transducers as a platform for chemical and biological sensors

Abstract: Since the late 1980s there have been spectacular developments in micromechanical or microelectro-mechanical (MEMS) systems which have enabled the exploration of transduction modes that involve mechanical energy and are based primarily on mechanical phenomena. As a result an innovative family of chemical and biological sensors has emerged. In this article, we discuss sensors with transducers in a form of cantilevers. While MEMS represents a diverse family of designs, devices with simple cantilever configurations are especially attractive as transducers for chemical and biological sensors. The review deals with four important aspects of cantilever transducers: (i) operation principles and models; (ii) microfabrication; (iii) figures of merit; and (iv) applications of cantilever sensors. We also provide a brief analysis of historical predecessors of the modern cantilever sensors.

Bernoulli–Euler beam model based on a modified couple stress theory

Abstract: A new model for the bending of a Bernoulli–Euler beam is developed using a modified couple stress theory. A variational formulation based on the principle of minimum total potential energy is employed. The new model contains an internal material length scale parameter and can capture the size effect, unlike the classical Bernoulli–Euler beam model. The former reduces to the latter in the absence of the material length scale parameter. As a direct application of the new model, a cantilever beam problem is solved. It is found that the bending rigidity of the cantilever beam predicted by the newly developed model is larger than that predicted by the classical beam model. The difference between the deflections predicted by the two models is very significant when the beam thickness is small, but is diminishing with the increase of the beam thickness. A comparison shows that the predicted size effect agrees fairly well with that observed experimentally.

Method for the calibration of atomic force microscope cantilevers

Abstract: The determination of the spring constants of atomic force microscope (AFM) cantilevers is of fundamental importance to users of the AFM. In this paper, a fast and nondestructive method for the evaluation of the spring constant which relies solely on the determination of the unloaded resonant frequency of the cantilever, a knowledge of its density or mass, and its dimensions is proposed. This is in contrast to the method of Cleveland et al. [Rev. Sci. Instrum. 64, 403 (1993)], which requires the attachment of masses to the cantilever in the determination of the spring constant. A number of factors which can influence the resonant frequency are examined, in particular (i) gold coating, which can result in a dramatic variation in the resonant frequency, for which a theoretical account is presented and (ii) air damping which, it is found, leads to a shift of -4% in the resonant frequency down on its value in a vacuum. Furthermore, the point of load on the cantilever is found to be extremely important, since a small variation in the load point can lead to a dramatic variation in the spring constant. Theoretical results that account for this variation, which, it is believed will be of great practical value to the users of the AFM, are given. © 1995 American Institute of Physics.

Energy dissipation in tapping-mode atomic force microscopy

Abstract: A method is presented to measure the energy dissipated by the tip–sample interaction in tapping-mode atomic force microscopy (AFM). The results show that if the amplitude of the cantilever is held constant, the sine of the phase angle of the driven vibration is then proportional to changes in the tip–sample energy dissipation. This means that images of the cantilever phase in tapping-mode AFM are closely related to maps of dissipation. The maximum dissipation observed for a 4 N/m cantilever with an initial amplitude of 25 nm tapping on a hard substrate at 74 kHz is about 0.3 pW.