Flexural Eigenfrequencies Research Articles

A theoretical-experimental framework for the analysis of the dynamic response of a QEPAS tuning fork device immersed in a fluid medium

Quartz-enhanced photoacoustic spectroscopy (QEPAS) is a trace gas sensing technique that employs a designed high-quality factor quartz tuning fork (QTF) as acousto-electric transducer. The first in-plane skew-symmetric flexural mode of the QTF is excited when weak resonant sound waves are generated between the QTF prongs. Thus, the performance of a QEPAS sensor strongly depends on the resonance properties of the QTF, namely the determination of flexural eigenfrequencies and air damping loss.In this work, we present a mixed theoretical-experimental framework to study the dynamic response of a QTF while vibrating in a fluid environment. Due to the system linearity, the dynamic response of the resonator immersed in a fluid medium is obtained by employing a Boundary Element formulation based on an ad hoc calculated Green’s function. In particular, the QTF is modelled as constituted by a pair of two Euler-Bernoulli cantilevers partially coupled by a distributed linear spring. As for the forces exerted by the fluid on QTF structure, the fluid inertia and viscosity as well as an additional diffusivity term, whose influence is crucial for the correct evaluation of the system response, have been taken into account.By corroborating the theoretical analysis with the experimental outcomes obtained by means of a vibro-acoustic setup, the fluid response coefficients and the dynamics of the QTF immersed in a fluid environment are fully determined.

Stress control of tensile-strained In1−xGaxP nanomechanical string resonators

We investigate the mechanical properties of freely suspended nanostrings fabricated from tensile-stressed, crystalline In1−xGaxP. The intrinsic strain arises during epitaxial growth as a consequence of the lattice mismatch between the thin film and the substrate, and is confirmed by x-ray diffraction measurements. The flexural eigenfrequencies of the nanomechanical string resonators reveal an orientation dependent stress with a maximum value of 650 MPa. The angular dependence is explained by a combination of anisotropic Young's modulus and a change of elastic properties caused by defects. As a function of the crystal orientation, a stress variation of up to 50% is observed. This enables fine tuning of the tensile stress for any given Ga content x, which implies interesting prospects for the study of high Q nanomechanical systems.

Design and fabrication of a flexural harmonic AFM probe with an exchangeable tip

While harmonic probes are essential characterization tools in dynamic mode Atomic Force Microscopy, precise fabrication of harmonic probes is a challenge, and their replacement is relatively expensive. This paper reports the design, fabrication and evaluation of harmonic AFM probes with exchangeable tips that address these issues. The probe comprises a cantilever of non-uniform geometry that carries an exchangeable tip held by a liquid meniscus. The cantilever and the liquid meniscus interface are designed so that the tip is held firmly and the tip exchange can be performed with precise control over its position and orientation. A systematic approach is proposed for the design and fabrication of probes with specified eigen-frequencies. The approach consists of adopting an appropriate initial geometry, and iteratively modifying its dimensions so that the specified eigen-frequencies are achieved. To correct for errors in fabrication of the designed probe, an iterative fabrication scheme is also proposed. To facilitate implementation of this scheme, a simple lumped parameter model is developed for the overall probe. The proposed approach is employed to design and fabricate a harmonic probe with exchangeable tip whose first two flexural eigen-frequencies are in the ratio 1:4. Finally, the fabricated probe is evaluated, and the ratio of eigen-frequencies is found to match the desired harmonic ratio to an accuracy of over 99.8%.

Shape and topology optimization for tailoring the ratio between two flexural eigenfrequencies of atomic force microscopy cantilever probe

In an operation mode of atomic force microscopy that uses a higher eigenmode to determine the physical properties of material surface, the ratio between the eigenfrequency of a higher flexural eigenmode and that of the first flexural eigenmode was identified as an important parameter that affects the sensitivity and accessibility. Structure features such as cut-out are often used to tune the ratio of eigenfrequencies and to enhance the performance. However, there lacks a systematic and automatic method for tailoring the ratio. In order to deal with this issue, a shape and topology optimization problem is formulated, where the ratio between two eigenfrequencies is defined as a constraint and the area of the cantilever is maximized. The optimization problem is solved via the level set based method.

Dynamic behavior of a new surface-micromachined piezoelectric material actuated micro-mirror device

In this paper, a finite element method is used to analyze the dynamic behavior of a piezoelectric micro-mirror taking into account both anisotropic properties of silicon chip and technologically induced stress. We propose a special arrangement of piezoelectric and substrate components to build-up the micro-mirror device. In conjunction with a special arrangement of electrodes and cuts the piezoelectric actuator layer can be used to deflect the mirror in certain directions. The numerical analysis focuses on the computation of eigenfrequencies with special attention to the influence of the anisotropic material parameters. The eigenfrequencies has been shifted to higher eigenmodes when anisotropic material parameters are considered. Technologically induced stress has resulted in substantial influence on eigenfrequencies. The out-of-plane dimension (thickness) of thin-film has shown significant influence on the eigenfrequencies of micro-mirror. The fundamental eigenfrequencies increased and the flexural eigenfrequencies decreased with increasing the thickness of PZT film. Evidently, the calculated eigenfrequencies were also found to increase with increasing the thickness of silicon layer (underneath the diaphragm area).

The effect of axial inertia on the bending eigenfrequencies of a timoshenko two‐bar frame

AbstractThe equations of free lateral vibrations of a uniform Timoshenko two‐bar frame including the effects of axial motion and joint mass with its rotational inertia are presented. The influence on the flexural eigenfrequencies of the axial motion alone or in combination with other parameters is fully assessed and thoroughly discussed. These parameters are: the translational and rotational inertia of the joint mass, the transverse shear deformation and rotatory inertia, the length, stiffness and slenderness ratios of the two bars of the frame.The variety of numerical results presented herein leads to the important finding that for framed structures the effect of axial inertia on the flexural eigenfrequencies alone or in combination with the foregoing parameters may be considerable. In particular, if the joint mass should be accounted for, the foregoing effect cannot be ignored, since it leads, in general, to considerable errors even for frames with relatively slender bars.

On the discontinuity of the flutter load for various types of cantilevers

In this investigation, using an energy (variational) approach, the flutter instability for various types of elastically restrained uniform cantilevers carrying up to three concentrated masses and subjected to a follower compressive force, is presented. The effects of transverse shear deformation and rotatory inertia of the mass of the column and of the positioning of the concentrated masses with or without their rotational inertia, are also included in the analysis.In all cases, where the flutter load is obtained from the coincidence of the second and third flexural eigenfrequencies a discontinuity with a finite jump in this load is possible; the lower value of the flutter load at this discontinuity is obtained from the coincidence of the first and second eigenfrequencies, while the upper value of this load is obtained from the coincidence of the second and third eigenfrequencies. Subsequently, it is found that the flutter load is a sectionally continuous function of certain of the varying parameters. Finally, the effect of several parameters upon the magnitude of the jump in the flutter load, is also discussed.