Second Mode Of Vibration Research Articles

An approach to design and fabrication of resonant giant magnetostrictive transducer

The paper provides a comprehensive procedure for the mechanical and magnetic design of Langevin transducer based on giant magnetostrictive material. The the transducer is designed to work at its second mode of vibration, having high mechanical quality factor and low damping coefficient. The design procedure is based on an analytical model and it is verified by finite-element analysis. Experimental tests based on impedance response analysis in first and second modes are carried out on the prototype. Results confirm the appropriate design of this transducer, demonstrating the highest mechanical quality factor between the resonant transducers in the literature.

Even nanomechanical modes transduced by integrated photonics

We demonstrate the actuation and detection of even flexural vibrational modes of a doubly clamped nanomechanical resonator using an integrated photonics transduction scheme. The doubly clamped beam is formed by releasing a straight section of an optical racetrack resonator from the underlying silicon dioxide layer, and a step is fabricated in the substrate beneath the beam. The step causes uneven force and responsivity distribution along the device length, permitting excitation and detection of even modes of vibration. This is achieved while retaining transduction capability for odd modes. The devices are actuated via optical force applied with a pump laser. The displacement sensitivities of the first through third modes, as obtained from the thermomechanical noise floor, are 228 fm Hz−1/2, 153 fm Hz−1/2, and 112 fm Hz−1/2, respectively. The excitation efficiency for these modes is compared and modeled based on integration of the uneven forces over the mode shapes. While the excitation efficiency for the first three modes is approximately the same when the step occurs at about 38% of the beam length, the ability to tune the modal efficiency of transduction by choosing the step position is discussed. The overall optical force on each mode is approximately 0.4 pN μm−1 mW−1, for an applied optical power of 0.07 mW. We show a potential application that uses the resonant frequencies of the first two vibrational modes of a buckled beam to measure the stress in the silicon device layer, estimated to be 106 MPa. We anticipate that the observation of the second mode of vibration using our integrated photonics approach will be useful in future mass sensing experiments.

On the vibrational characteristics of single- and double-walled carbon nanotubes containing ice nanotube in aqueous environment

The properties and behavior of carbon nanotubes (CNTs) in aqueous environment due to their considerable potential applications in nanobiotechnology and designing nanobiosensors have attracted the attention of researchers. In this study, molecular dynamics simulations are carried out to investigate the vibrational characteristics of single- and double-walled CNTs containing ice nanotubes (a new phase of ice) in vacuum and aqueous environments. The results demonstrate that formation of ice nanotubes inside the CNTs reduces the natural frequency of pure CNTs. Moreover, it is demonstrated that increasing the number of walls considerably reduces the sensitivity of frequency to the presence of ice nanotube inside CNT. Additionally, it is shown that increasing the length decreases the effect of ice nanotube on reducing the frequency. The calculation of natural frequency of CNTs in aqueous media demonstrates that the interaction of CNTs with water molecules considerably reduces the natural frequency up to 50 %. Finally, it is demonstrated that in the case of CNTs with one free end in aqueous environment, the CNT does not vibrate in its first mode, and its frequency is between the frequencies of first and second modes of vibration.

Basic dynamic characteristics and seismic design of anchorage system

Based on some assumptions, the dynamic governing equation of anchorage system is established. The calculation formula of natural frequency and the corresponding vibration mode are deduced. Besides, the feasibility of the theoretical method is verified by using a specific example combined with other methods. It is found that the low-order natural frequency corresponds to the first mode of vibration, and the high-order natural frequency corresponds to the second mode of vibration, while the third mode happens only when the physical and mechanical parameters of anchorage system meet certain conditions. With the increasing of the order of natural frequency, the influence on the dynamic mechanical response of anchorage system decreases gradually. Additionally, a calculating method, which can find the dangerous area of anchorage engineering in different construction sites and avoid the unreasonable design of anchor that may cause resonance, is proposed to meet the seismic precautionary requirements. This method is verified to be feasible and effective by being applied to an actual project. The study of basic dynamic features of anchorage system can provide a theoretical guidance for anchor seismic design and fast evaluation of anchor design scheme.

Modelling and analysis of damped vibration in hydraulic cylinder

The study presents a formulation on the basis of Hamilton’s principle and solution for the problem of damped vibration in hydraulic cylinders. The physical model took into consideration the energy dissipation in a vibrating cylinder as a result of external viscous damping and internal damping of viscoelastic material in beams used to construct a model of a cylinder (rheological model by Kelvin–Voigt). Constructional damping in the points of the cylinder connection with the components of the basic structure was also considered. The example computation was made for a cylinder used in a mining prop. The results of the computations concern the determination of the relationships between the first eigenvalue of transverse vibration in the cylinder and its extension length with two values of load and determination of the amplitude decay factor for the first and the second eigenvalue versus the extension length. Furthermore, the study also focused on determination of the relationships between the amplitude decay factor of the first and second mode of vibration for a particular length of the cylinder.

Vibration Control of Smart Cantilever Beam Using Strain Rate Feedback

In this paper simulation and experimental results of Strain rate feedback for active vibration control of a cantilever beam are presented. The piezoelectric patches are fixed on the surface of the host beam based on the Harmonic and Modal analysis done in a Finite Element tool (ANSYS). The dynamic model of the smart beam for the first two modes is obtained using a System Identification technique. The feedback control algorithm is analyzed and is implemented in real-time using National Instruments cRIO 9022 controller. It is observed that with this feedback law 49.29% and 52.84% reduction are obtained for first and second modes of vibration respectively. The result verifies the effectiveness of the controller to suppress the vibration of the smart beam.

Driving modes and material stability of a double membrane rheometer and density sensor

Abstract. This contribution presents the analysis of an earlier proposed double membrane sensor for measuring mass density and rheological properties of liquids with respect to different driving modes. Concerning practical implementation the sensor mounting and the stability of the polyethylene foil, currently used as membrane material, are investigated. The sensor is based on two opposed membranes vibrating in parallel where a sample liquid is enclosed between the membranes. The excitation and read-out mechanisms of the membrane vibration are based on Lorentz forces induced in a static magnetic field. Each membrane carries three conductive paths for excitation, which can be separately connected to the excitation currents. This allows the excitation of the first and second modes of vibration and enables prestressing the second mode of oscillation. Analyzing the material-stability of the used polyethylene foil shows a strong long-term drift of the modulus of elasticity and an increase of internal damping with increasing temperature. Comparing the resonance frequency of the fundamental mode with earlier measurements achieved with the second mode of resonance indicates an increased sensitivity to density featuring a reasonably sustained quality factor for high viscosities. Thereby, the sensitivity can be adjusted by varying the distance between the membranes.

Simplified Mechanical Model for the Seismic Vulnerability Evaluation of Belfries

The systematic observation of damage caused by recent Italian earthquakes has highlighted the high seismic vulnerability of belfries, the inner part of bell towers. In this study, the authors propose a simplified methodology for safety checks of belfries that is usable for risk analysis at territorial level for the whole bell tower, according to the method proposed by the Italian Directive of October 12, 2007, Guidelines for the Evaluation and the Reduction of the Seismic Vulnerability of Cultural Heritage. The new mechanical method takes into account the possible activation of two different collapse mechanisms, connected to combined actions of compression and bending or shear action, supposing different static schemes in relation to the real belfry configuration. The seismic force at the base of the belfry is calculated also considering the influence of the second mode of vibration through a correction factor obtained by spectral analyses on several bell towers damaged by the 1976 Friuli earthquake. A validation of the proposed approach has been shown for two belfries damaged by the 2002 Molise earthquake and by the 2009 Abruzzi earthquakes, to highlight the reliability of the method in comparison to the simplified approach proposed in the literature.

Forced Vibration Behavior of Adhesively Bonded Single-Lap Joint

This paper deals with forced vibration behavior of adhesively bonded single-lap joint theoretically and experimentally. The finite element analysis (FEA) software was used to predict the natural frequencies and frequency response functions (FRFs) of the joint. The dynamic test software and the data acquisition hardware were used in experimental measurement of the dynamic response of the joint. It is shown that the natural frequencies of the joint from experiment are lower than those predicted using finite element analysis. It is also found that the measued FRFs are close to the predicted FRFs for the first two modes of vibration of the joint. Above the second mode of vibration, there is considerable discrepancy between the measured and predicted FRFs.

Fracture Analysis of a First Stage Turbine Blade by FRANC3D

The premature failure of a blade occurred after a service life of 8127 EOH operation houre. This paper presents the fracture analysis of the first stage blade through fractographic and mechanical analysis. Crack growth mechanisms were evaluated based on the microscopic observations of the fracture surfaces by SEM. The analysis of the different region of the fracture surface shows that crack propagation is mainly related with fatigue mechanism. The crack propagation occurred in the pressure-suction side direction. The dynamic characteristics of the blade were evaluated by FEM in order to identify the cause of blade failure. The result depicts that the second mode of vibration might be excited and the vibratory stresses cause to HCF damage of the blade. Eventully fracture analysis of the blade under the presence of a fatigue crack was analyzed by FRACNC3D software.

Controlling damping and quality factors of silicon microcantilevers by selective metallization

Ceramic microresonators coated with relatively thin metallic films are widely used for sensing, scanning probe microscopy, signal processing and vibration energy harvesting. The metallization improves optical reflectivity and electrical conductivity, but invariably degrades the quality factor (Q) of resonance by increasing the amount of energy dissipated during vibration. Developing strategies for controlling damping due to metallization is vital for the design of high-performance microresonators. This paper presents a strategy based on the insight that dissipation is a function of the deformation experienced by the thin film during oscillation. Therefore, damping can be controlled by patterning the metal in regions of low strain. A simple analytical model is developed to quantify the change in damping as a function of selective metallization along the length of a microcantilever. The predictions of this model are in good agreement with measurements of damping in single-crystal silicon microcantilevers that are partially coated on one surface with 100 nm thick aluminum films. Crucially, damping due to clamping, support and viscous losses is minimized in these structures to enable a careful comparison of theory with experiments. Coating 20% of the length of the beam starting from the tip has no significant impact on damping in either the first or the second mode of vibration. In contrast, placing the same size of metallization at the root leads to considerable dissipation; in the first mode, the damping due to this patch is ∼60% of that caused by a full coat.

Experiments on chaotic vibrations of a post-buckled cantilevered beam connected by a string to an axial spring

Experimental results are presented on chaotic vibrations of a post-buckled cantilevered beam constrained by a string. The string is stretched between the top end of the beam and an axial spring. The axial spring consists of a leaf spring with an attached mass and is fixed on a base frame close to the clamped end of the beam. The length of the string is less than that of the beam. The beam is excited by lateral periodic acceleration. By increasing the attached mass on the axial spring, nonlinear responses of the beam are examined. Nonperiodic response is observed in a typical frequency region. The response is examined by the Fourier spectrum, maximum Lyapunov exponents, Poincaré projection, and principal component analysis. Predominant chaotic response is generated by the internal resonance with a frequency ratio of one-to-three. The fundamental mode and the second mode of vibration are strongly coupled in the chaotic response. When the attached mass of the axial spring is increased, the natural frequency of the axial spring approaches the region of chaotic response. Therefore, the number of vibration modes that contribute to the chaos increases. Furthermore, the Poincaré projection of the chaotic response shows more scattered figures.

Nondestructive detection of the effect of drilling on acoustic performance of wood

The aim of this paper is to determine the effect of hole diameter (LR Direction) on acoustic performance indicators such as acoustic coefficient and acoustic conversion efficiency of wooden beams using flexural vibration of a free-free bar test.The drilling from 0 to 8 millimetres diameter was made exactly at the middle of the bar, on the node of the second mode of vibration. The results revealed that holes of diameter from 0 to 8 millimeters didn’t cause any sever change on acoustic coefficient and acoustic conversion efficiency when the beam was impacted on both radial and tangential surfaces. Nevertheless, these acoustic properties changed a bit when the beam was impacted on the tangential surface. Thus, the changes of the acoustic coefficient and acoustic conversion efficiency for both radial and tangential impacts were not significant, even with an 8 mm hole. Therefore, hole diameter not only didn’t cause any severe effect on acoustic coefficient and acoustic conversion efficiency but also somewhat increased their values. So, a hole having a relatively small diameter may cause improved acoustical performance of a wooden beam.

Simultaneous Vibration Control Using an Impact Damper System in Horizontal and Vertical Directions

We applied the impact damper system to the vibration model of a cantilever beam. The impact damper system consists of an impactor and walls placed in a container, which vibrates in the horizontal and vertical directions when the first and second modes of vibration are excited at the same time. The damping effects are influenced by a clearance between an inpactor and walls of a container. We changed the clearance and the acceleration of the foundation and investigated the damping characteristics of the impact damper system when the system vibrated in two directions at the same time. We calculated the vibration response of the impact damper numerically, and found that the calculation results were in accordance with the experimental ones. The impact damper system converts the vibration energy of the vibrating body to the kinetic energy of the impactor by collision. Therefore, to investigate the damping effects of two directions in the simultaneous vibration, we calculated the mechanical energy of the vibration system. We found that the damping effects of the horizontal direction were not affected by the vertical vibration when a horizontal clearance was larger than the optimum clearance. On the other hand, we found that the damping effects of vertical direction were not affected by the horizontal vibration when the impactor did not collide to the ceiling. In other words, we found that using an impactor reduced the vibrations of both the horizontal and the vertical direction at the same time when the clearance was properly adjusted.

Experimental Measurement of Resonance Frequencies of Asymmetric Micro-bridge Resonators

The experiment results on the resonance frequencies of micro-bridge resonators with attached electrostatic comb-drives are reported in this article. The resonators include a novel design of asymmetric resonators, in which the comb-drives are attached to off-midpoint of the beam. The experiment results confirm that by properly designing the location and mass of the comb-drives, the natural frequencies can exceed those of conventional symmetric resonators. Moreover, it has been shown that the second mode of vibration of asymmetric resonators, in contrast to that of symmetric resonators, can be excited, hence exploited for applications in which multiple working frequencies are desired. The experiment results are in good agreement with the analytical model. The deviations between these two are discussed in detail.

Experiments on Chaotic Vibrations of a Thin Circular Plate with Outer Clamped Edge and a Circular Center Hole

This paper presents experimental results on chaotic vibrations of a thin circular plate with a circular center hole. The plate has an asymmetric curved configuration due to an initial imperfection, an in-plane compressive stress and lateral deformation by the gravity. First, linear natural frequencies and natural modes of vibration are measured. The second and the third modes of vibration have one nodal diameter with different natural frequencies. These nodal diameters are perpendicular to each other. The linear natural frequencies of the lowest and the second modes satisfy the condition of one-to-two internal resonance, closely. Characteristics of restoring force of the plate show the type of a softening-and-hardening spring. Next, the plate is excited with periodic acceleration, laterally. Sweeping the excitation frequency, nonlinear responses of the plate are measured. In a restricted frequency range of the principal resonance of the lowest mode, non-periodic responses with amplitude modulation are generated. The time histories of the response are measured for a long-time interval at four positions, simultaneously. The time histories are inspected by the Fourier spectrum, the Poincare projection, the maximum Lyapunov exponents and the principal component analysis. The non-periodic response is found to be the chaotic response generated from the one-to-two internal resonance coupled with the lowest and the second modes. The results of the principal component analysis with the time histories of the multiple positions on the plate show that the lowest, second and third modes predominantly contribute to the chaotic response. Applying the calculation with short-time intervals cut out from the time histories, it is found that the nodal patterns of the second and the third modes of vibration are fluctuated along the circumferential direction. Furthermore, the exchange of the contribution ratio is shown between the lowest and the second modes of vibration.

Development of microcantilever-based biosensor array to detect Angiopoietin-1, a marker of tumor angiogenesis

Microcantilever biosensors have been proposed in the last years as very sensitive mass detectors, but few works focused on the precision and specificity of such tools. We measured the repeatability and reproducibility of our cantilever-based system, proponing the combination of results coming from both the first and second mode of vibration. Then, we optimized two biodesigns (a receptor-based and an antibody-based) to the detection of Angiopoietin-1, a possible marker in tumor progression. The reported results show that our microcantilever-based system can detect Angiopoietin-1 masses of the order of few hundreds of picograms with less than 0.5% of relative uncertainty. We showed that the evaluation of the protein surface density (number of molecules per cm 2) could reveal interesting features concerning the multimerization state of the targeted protein. We also performed negative controls (dipping the sample in PBS without proteins) and specificity tests (dipping the sample in PBS with a “false” antigen). The related frequency shifts coming from non-specific interactions were found to be at least one order of magnitude lower than typical variations due to specific protein binding. Thanks to its fine precision and optimal specificity, our microcantilever-based system can be successfully applied as a quantitative tool for systems biology studies such as the comprehension of angiogenic machinery and cancer progression.

Dynamic Behaviour of Single Lap-Jointed Cantilevered Beams

The aim of this study is to predict the dynamic behaviour of single lap-jointed cantilevered beams theoretically and to validate the predictions via experimental tests. The ABAQUS finite element analysis (FEA) software was used to predict the natural frequencies, mode shapes and frequency response functions (FRFs) of lap-jointed beams. The LMS (Leuven Measurement System) CADA-X dynamic test software and the LMS-DIFA Scadas II 48 channel data acquisition hardware were used in experimental measurement of the dynamic response of the lap-jointed beams. It is shown that the natural frequencies of the single lap-jointed cantilevered beams from experiment are lower than those predicted using FEA. It is also found that the measued FRFs are close to the predicted FRFs for the first two modes of vibration of the single lap-jointed cantilevered beam. Above the second mode of vibration, there is considerable discrepancy between the measured and predicted FRFs.

Compensating for frequency change in flowmeters

Motion is induced in a conduit that contains a fluid. The motion is induced such that the conduit oscillates in a first mode of vibration and a second mode of vibration. The first mode of vibration has a corresponding first frequency of vibration and the second mode of vibration has a corresponding second frequency of vibration. At least one of the first frequency of vibration or the second frequency of vibration is determined. A phase difference between the motion of the conduit at a first point of the conduit and the motion of the conduit at a second point of the conduit is determined. A quantity based on the phase difference and the determined frequency is determined. The quantity includes a ratio between the first frequency during a zero-flow condition and the second frequency during the zero-flow condition. A property of the fluid is determined based on the quantity.

Performance of Simple and Sophisticated Control in Energy-recycling Semi-active Vibration Suppression

The semi-active energy-recycling methods studied in this article suppress vibration by controlling switches in inductive shunt circuits connected to piezoelectric transducers in vibrating structures. This article compares the performances of simple and sophisticated methods that can be used for multiple-mode vibration. Although it should be obvious that the performance of the latter is superior, we need to know whether the superior performance of the sophisticated method justifies the expense incurred by its complexity. The performance comparisons were done by numerically simulating the vibration suppression of a truss structure with a piezoelectric transducer. We simulated transient free vibrations, forced sinusoidal vibrations, and forced random vibrations. In all cases, both methods were shown to be effective for the first and second modes of vibration. The ways and situations in which the sophisticated method is superior to the simple method were also elucidated. A vibration suppression experiment using a truss was also carried out and demonstrated that the sophisticated method worked well under random excitation.