Cantilever resonator with integrated actuation and sensing fabricated using a single step lithography

Micro- and nano-mechanical resonators have been proposed for a variety of applications ranging from mass sensing to signal processing. Often their actuation and/or detection involve external subsystems that are much larger than the resonator itself. We have designed a simple microcantilever resonator with integrated sensor and actuator, facilitating the integration of large arrays of resonators. This unique design can be manufactured with a low-cost fabrication process, involving just a single step of lithography. The bilayer cantilever of gold and silicon dioxide is used as piezoresistive sensor as well as thermal bimorph actuator. The ac current used for actuation and the dc current used for piezoresistive detection are separated in the frequency-domain using a bias-tee circuit configuration. The resonant response is measured by detecting the second harmonic of the actuation current using a lock-in amplifier.

Analysis of grating inscribed micro-cantilever for high resolution AFM probe

We present a mathematical modelling and analysis of reflection grating etched Si AFM cantilever deflections under different loading conditions. A simple analysis of the effect of grating structures on cantilever deflection is carried out with emphasis on optimizing the beam and gratings such that maximum amount of diffracted light remains within the detector area.

VIBRATIONAL CHARACTERISTICS OF ZIGZAG, ARMCHAIR AND CHIRAL CANTILEVER SINGLE-WALLED CARBON NANOTUBES

Finite element analysis has been performed to study vibrational characteristics of cantilever single walled carbon nanotubes. Finite element models are generated by specifying the C-C bond rigidities, which are estimated by equating energies from molecular mechanics and continuum mechanics. Bending, torsion, and axial modes are identified based on effective mass for armchair, zigzag and chiral cantilever single walled carbon nanotubes, whose Young's modulus is evaluated from the bending frequency. Empirical relations are provided for frequencies of bending, torsion, and axial modes.

Fabrication and Experimentation of a Cantilever Beam Based Piezoelectric Actuator and Sensor for Vibration Energy Harvesting

In the immediate surroundings of our daily life, we can find a lot of places where the energy in the form of vibration is being wasted. Therefore, we have enormous opportunities to utilize the same. Piezoelectric character of matter enables us to convert this mechanical vibration energy into electrical energy which can be stored and used to power other device, instead of being wasted. This work is done to realize both actuator and sensor in a cantilever beam based on piezoelectricity. The sensor part is called vibration energy harvester. The numerical analyses were performed for the cantilever beam using the commercial package ANSYS and MATLAB. The cantilever beam is realized by taking a plate and fixing its one end between two massive plates. Two PZT patches were glued to the beam on its two faces. Experiments were performed using data acquisition system (DAQ) and LABVIEW software for actuating and sensing the vibration of the cantilever beam.

Exploring isospectral cantilever beams using electromagnetism inspired optimization technique

Isospectral beams have identical free vibration frequency spectrum for a specific boundary condition. The problem of finding non-uniform beams which are isospectral to a given uniform beam, with fixed-free boundary condition, leads to a multimodal optimization problem. The first Q natural frequencies of the given uniform Euler-Bernoulli beam are determined using analytical solution. The first Q natural frequencies of a non-uniform beam are obtained with the help of finite element modeling. In order to obtain the non-uniform beams isospectral to a given uniform beam, an error function is designed, which calculates the difference between the spectra of the given uniform beam and the non-uniform beam. In our study, this error function is minimized using electromagnetism inspired optimization technique, a population based iterative algorithm inspired by the attraction-repulsion physics of electromagnetism. Numerical results show the existence of the isospectral non-uniform beams for a given uniform beam, which occur as local minima. Non-uniform beams isospectral to a damaged beam, are also explored using the proposed methodology to illustrate the fact that accurate structural damage identification is difficult by just frequency measurements. (C) 2012 Elsevier B.V. All rights reserved.

Note: A resonating reflector-based optical system for motion measurement in micro-cantilever arrays

A robust, compact optical measurement unit for motion measurement in micro-cantilever arrays enables development of portable micro-cantilever sensors. This paper reports on an optical beam deflection-based system to measure the deflection of micro-cantilevers in an array that employs a single laser source, a single detector, and a resonating reflector to scan the measurement laser across the array. A strategy is also proposed to extract the deflection of individual cantilevers from the acquired data. The proposed system and measurement strategy are experimentally evaluated and demonstrated to measure motion of multiple cantilevers in an array. (C) 2015 AIP Publishing LLC.

Instability of laminated composite thin-walled open-section beams

Instability of thin-walled open-section laminated composite beams is studied using the finite element method. A two-noded, 8 df per node thin-walled open-section laminated composite beam finite element has been used. The displacements of the element reference axis are expressed in terms of one-dimensional first order Hermite interpolation polynomials, and line member assumptions are invoked in formulation of the elastic stiffness matrix and geometric stiffness matrix. The nonlinear expressions for the strains occurring in thin-walled open-section beams, when subjected to axial, flexural and torsional loads, are incorporated in a general instability analysis. Several problems for which continuum solutions (exact/approximate) are possible have been solved in order to evaluate the performance of finite element. Next its applicability is demonstrated by predicting the buckling loads for the following problems of laminated composites: (i) two layer (45°/−45°) composite Z section cantilever beam and (ii) three layer (0°/45°/0°) composite Z section cantilever beam.

Analysis of laminated shells with laminated stiffeners using rectangular shell finite elements

A finite element analysis of laminated shells reinforced with laminated stiffeners is described in this paper. A rectangular laminated anisotropic shallow thin shell finite element of 48 d.o.f. is used in conjunction with a laminated anisotropic curved beam and shell stiffening finite element having 16 d.o.f. Compatibility between the shell and the stiffener is maintained all along their junction line. Some problems of symmetrically stiff ened isotropic plates and shells have been solved to evaluate the performance of the present method. Behaviour of an eccentrically stiffened laminated cantilever cylindrical shell has been predicted to show the ability of the present program. General shells amenable to rectangular meshes can also be solved in a similar manner.

Analysis of laminated shells of revolution with laminated stiffeners using a doubly curved quadrilateral finite element

A finite element analysis of laminated shells of revolution reinforced with laminated stifieners is described here-in. A doubly curved quadrilateral laminated anisotropic shell of revolution finite element of 48 d.o.f. is used in conjunction with two stiffener elements of 16 d.o.f. namely: (i) A laminated anisotropic parallel circle stiffener element (PCSE); (ii) A laminated anisotropic meridional stiffener element (MSE). These stifiener elements are formulated under line member assumptions as degenerate cases of the quadrilateral shell element to achieve compatibility all along the shell-stifiener junction lines. The solutions to the problem of a stiffened cantilever cylindrical shell are used to check the correctness of the present program while it's capability is shown through the prediction of the behavior of an eccentrically stiffened laminated hyperboloidal shell.

Rotating Beams and Nonrotating Beams With Shared Eigenpair

In this paper, we look for rotating beams whose eigenpair (frequency and mode-shape) is the same as that of uniform nonrotating beams for a particular mode. It is found that, for any given mode, there exist flexural stiffness functions (FSFs) for which the jth mode eigenpair of a rotating beam, with uniform mass distribution, is identical to that of a corresponding nonrotating uniform beam with the same length and mass distribution. By putting the derived FSF in the finite element analysis of a rotating cantilever beam, the frequencies and mode-shapes of a nonrotating cantilever beam are obtained. For the first mode, a physically feasible equivalent rotating beam exists, but for higher modes, the flexural stiffness has internal singularities. Strategies for addressing the singularities in the FSF for finite element analysis are provided. The proposed functions can be used as test-functions for rotating beam codes and for targeted destiffening of rotating beams.

Analysis of laminated shells with laminated stiffeners using rectangular shell finite elementsstar

A finite element analysis of laminated shells reinforced with laminated stiffeners is described in this paper. A rectangular laminated anisotropic shallow thin shell finite element of 48 d.o.f. is used in conjunction with a laminated anisotropic curved beam and shell stiffening finite element having 16 d.o.f. Compatibility between the shell and the stiffener is maintained all along their junction line. Some problems of symmetrically stiffened isotropic plates and shells have been solved to evaluate the performance of the present method. Behaviour of an eccentrically stiffened laminated cantilever cylindrical shell has been predicted to show the ability of the present program. General shells amenable to rectangular meshes can also be solved in a similar manner.

Structural Damage Detection Using Modal Curvature and Fuzzy Logic

A fuzzy logic system (FLS) with a new sliding window defuzzifier is proposed for structural damage detection using modal curvatures. Changes in the modal curvatures due to damage are fuzzified using Gaussian fuzzy sets and mapped to damage location and size using the FLS. The first four modal vectors obtained from finite element simulations of a cantilever beam are used for identifying the location and size of damage. Parametric studies show that modal curvatures can be used to accurately locate the damage; however, quantifying the size of damage is difficult. Tests with noisy simulated data show that the method detects damage very accurately at different noise levels and when some modal data are missing.

Automated estimation of fatigue crack length and closure/opening stress

An experimental technique is proposed for the estimation of crack length as well as crack closure/opening stress during fatigue crack growth. A specially designed, single cantilever, crack opening displacement gauge is used to monitor these variables during fatigue crack propagation testing. The technique was experimentally validated through electronfractography.

A new probe for three-dimensional flow measurements

A new four-hole cylindrical cantilever probe is described which could be used for three-dimensional flow surveys. The probe is more compact than the usual cylindrical type allowing for closer approach to a boundary. The probe is robust and gives good reproducibility. It can be used for a wide range of pitch angle. Review of Scientific Instruments is copyrighted by The American Institute of Physics.

Vibrations of a Beam in Variable Contact With a Flat Surface

We study small vibrations of cantilever beams contacting a rigid surface. We study two cases: the first is a beam that sags onto the ground due to gravity, and the second is a beam that sticks to the ground through reversible adhesion. In both cases, the noncontacting length varies dynamically. We first obtain the governing equations and boundary conditions, including a transversality condition involving an end moment, using Hamilton's principle. Rescaling the variable length to a constant value, we obtain partial differential equations with time varying coefficients, which, upon linearization, give the natural frequencies of vibration. The natural frequencies for the first case (gravity without adhesion) match that of a clamped-clamped beam of the same nominal length; frequencies for the second case, however, show no such match. We develop simple, if atypical, single degree of freedom approximations for the first modes of these two systems, which provide insights into the role of the static deflection profile, as well as the end moment condition, in determining the first natural frequencies of these systems. Finally, we consider small transverse sinusoidal forcing of the first case and find that the governing equation contains both parametric and external forcing terms. For forcing at resonance, w find that either the internal or the external forcing may dominate.