Vibrational frequencies and tuning of the African mbira

The acoustic spectrum of the mbira, a musical instrument from Africa that produces sound by the vibration of cantilevered metal rods, has been measured. It is found that the most prominent overtones present in the spectrum have frequencies that are approximately 5 and 14 times the lowest frequency. A finite-element model of the vibration of the key that takes into account the acoustic radiation efficiency of the various normal modes reveals that the far-field power spectrum is dominated by modes involving predominately transverse motion of the key. Modes involving longitudinal motion do not radiate efficiently, and therefore contribute little to the sound produced. The high frequencies of the dominant overtones relative to the fundamental make it unlikely that the tunings of the mbira that are used by expert musicians are determined by matching the fundamental frequencies of the upper keys with the overtones of the lower keys.     

Objective estimation of the tuning features of historical carillons

The carillons of the Mafra National Palace are undergoing a restoration project. Together, the pair of carillons represent the largest surviving 18th century carillons in Europe. To guarantee the historical significance of these outstanding musical instruments, a detailed diagnosis of their current physical tuning state was achieved and results were analyzed with respect to historical, acoustical and musical concerns. In a first stage, we developed a suitable polyreference modal identification technique to infer the tuning status of bells from their modal parameters and we then systematically performed in-field modal testing experiments on a selection of historical bells of the Mafra carillons. For each carillon bell, tuning charts displaying the internal frequency relationships between its most important partials were obtained, as well as the mode shapes, decay times and beating frequencies between modal-doublets for every single musical partial of the bell. In a second part, since carillon bells also must be tuned very accurately one relative to the others in order to play in tune, the important topic of estimating the reference pitch and musical temperament of carillons was addressed by devising optimization techniques, here tentatively based on the actual modal frequencies of the bells. After presenting the modal identification procedure and optimal strategies developed for this work, the feasibility and interests of this instrumental approach are finally illustrated for the two carillons of Mafra.     

Adaptive non-linear control of a clamped rectangular plate with PZT patches

The dynamic behavior and control of a clamped rectangular plate with bonded piezoelectric ceramic patches are investigated in this paper. The dynamic behavior is studied experimentally, showing that the plate exhibits dense modes, varying residual stress and non-linearity. An adaptive non-linear control scheme is then presented, which introduces a non-linear function into the normal adaptive feedforward control to non-linearize a reference signal. Vibration reductions using both the normal adaptive feedforward control and the adaptive non-linear control are compared in the cases of sinusoidal excitations at the first nine modal frequencies of the plate and a swept-frequency harmonic excitation below 100 Hz, indicating that the adaptive non-linear control can suppress not only the fundamental frequency vibration that the normal adaptive feedforward control can only attenuate, but also its higher harmonic components. Significant vibration reduction achieved by the adaptive non-linear control demonstrates its validity and reliability.     

Vibrational characteristics of Balinese gamelan metallophones

A study of the eight metallophone pairs from a Balinese gamelan semara dana has been conducted. Acoustical recordings of metallophone bars being struck were used to examine ratios of overtone frequencies to the fundamental. Results showed large variability in the number and ratios of overtones present. Scanning laser Doppler vibrometry measurements made on several bars also revealed great variability in mode shapes present. The distribution of prominent overtones and their modal shapes do not appear to match those of Western metallophones. Notably, the overall gamelan metallophone characteristics are quite dissimilar to the glockenspiel, which disagrees with previous studies.     

Influence of residual surface stress on the fracture of nanoscale piezoelectric materials with conducting cracks

In this paper,we analyze the stress and electric field intensity factors affected by residual surface stress for conducting cracks in piezoelectric nanomaterials.The problem is reduced to a system of non-linear singular integral equations,whose solution is determined by iteration technique.Numerical results indicate that the residual surface stress can significantly alter the crack tip fields at nanometer length scales.Due to the residual surface stress,281he electric field can produce stress around crack tip.This suggests a strong electromechanical coupling crack tip field for nanoscale piezoelectric materials.Such a finding is considerably different from the classical fracture mechanics results.A transit electric field to stress load ratio is identified,for which influences of residual surface stresses vanish.The research is useful for the applications of nanoscale piezoelectric devices.     

Periodic contact between piezoelectric materials and a rigid body with a wavy surface

An exact analysis is conducted for periodic, two-dimensional (2D) contact of piezoelectric materials in contact with a rigid body with a wavy surface pressed by uniform stresses at infinity. For three cases of eigenvalue distribution, three harmonic functions automatically satisfying the periodicity conditions are carefully constructed to facilitate the derivation of the solution of the considered problem. The stresses and electric displacements are obtained as infinite series. It is found that for the full contact case, the disturbance stress and electric displacement fields remain only the first harmonic which has the slowest decay in the y-direction. The convergence behaviours of the infinite series are checked, which shows that the external loading p and different positions have a great effect on the convergence behaviours of the infinite series and 400 terms are enough to get accurate solution at each position. Numerical results are presented to justify the validity of the present derivation and show the effect of the external loading on the contact behaviours.     

Laser cutting of holes in thick sheet metals: Development of stress field

Laser cutting of hole in a mild steel thick sheet metal is investigated. Temperature and stress fields developed around the cutting section are simulated using the finite element method. An experimental is carried out accommodating the simulation parameters. The residual stress developed in the cutting section is measured using the XRD technique and findings are compared with the predictions. Optical microscopy and SEM are carried out to examine the morphological changes in the cutting sections. It is found that temperature decays sharply in the region of the laser heat source, which results in high temperature gradient in this region. This causes the development of high stress levels around the cut edges. The residual stresses predicted are in agreement with the measured results.     

Analysis by speckle interferometry of the dependency of yield stress on residual stress

We used electronic speckle pattern interferometry (ESPI) to measure in situ displacement fields nondestructively and with high resolution (10⁻² μm) by using the interferometry principle and the phase-shift technique. We measured the depth profile of the residual stress in steel pipe manufactured by thermomechanically controlled processing using a quantitative model, which explains the relationship between residual stress and displacement measured by ESPI in chemical etching. We analyzed the variation of yield stresses measured by the indentation technique and the residual stresses at various depths. The relationship between the residual stresses and the yield stresses was consistent with simulated results and can be used for indirect evaluation of the residual stresses from the yield stresses.     

Quantitative nondestructive measurements of residual stresses

A stress maintained in the bulk of a material without application of an external traction (excluding gravity) or other sources, such as a thermal gradient, is called a residual stress. All residual stress systems have zero resultant force, the body being in equilibrium. The distance or range over which the stresses achieve this balance may be grouped into three classes as presented in Table 1. Also shown are the effects that the given examples exhibit using x-ray diffraction, the most popular technique to investigate residual stresses.     

The design of bells with harmonic overtones

Musical bells have had limited application due to the presence of inharmonic partials in the lower part of their acoustic spectra. A series of bells has been designed that contains up to seven partial frequencies in the harmonic series beginning at the fundamental frequency. This was achieved by choosing geometries for finite-element analysis models in which as many purely circumferential bending modes as possible occurred at frequencies below any mode with an axial ring node. The bell models were then fine tuned using gradient projection method shape optimization and the resulting profiles were cast in silicon bronze. A range of bell geometries and timbres is analyzed using psycho-acoustic models and is discussed in relation to European carillon bells.     

Reactions and stresses in polycrystalline diamond-metal and diamond-carbide compacts

Abstract

The kind of bonding phase has a significant influence on the microstructure and mechanical properties of diamond compacts. Microstructural studies of diamond with 5% wt. Ti and 5%wt. Tic (and also 30%wt. Tic) were carried out with a Transmission Electron Microscope. The TEM microstructural observations show differences between the metal and metal carbide bonding phase in diamond compacts. The mismatch of thermal expansion coefficients between diamond and the bonding metal or the compound induces significant internal stresses and may generate micro-cracks in polycrystalline diamond compacts. Twins and dislocations are the important details of microstructures in diamond crystals after HPHT sintering. They can appear as a result of residual stress relaxation. Results of measurements of residual stresses on a diamond compact surface by means of the “sin²ψ X-ray diffraction method are reported.     

Analysis of a non-linear structure by considering two non-linear formulations

In recent years, modal synthesis methods have been extended for solving non-linear dynamic problems subjected to harmonic excitation. These methods are based on the notion of non-linear or linearized modes and exploited in the case of structures affected by localized non-linearity. Actually, the experimental tests executed on non-linear structures are time consuming, particularly when repeated experimental tests are needed. It is often preferable to consider new non-linear methods with a view to decrease significantly the number of attempts during prototype tests and improving the accuracy of the dynamic behaviour.This article describes two fundamental non-linear formulations based on two different strategies. The first formulation exploits the eigensolutions of the associated linear system and the dynamics characteristics of each localized non-linearity. The second formulation is based on the exploitation of the linearized eigensolutions obtained using an iterative process. This article contains a numerical and an experimental study which examines the non-linear behaviour of the structure affected by localized non-linearities. The study is intended to validate the numerical algorithm and to evaluate the problems arising from the introduction of non-linearities. The complex responses are evaluated using the iterative Newton-Raphson method and for a series of discrete frequencies. The theory has been applied to a bi-dimensional structure and consists of evaluating the harmonic responses obtained using the proposed formulations by comparing measured and calculated transfer functions.     

Computational prediction of modal damping ratios in thin-walled structures

Modal analysis in finite element packages gives natural frequencies and mode shapes, but not modal damping values. Given a constitutive relation for specific material dissipation, volume integrals of the per cycle dissipation can be used to estimate the modal damping. Here, we adopt a well known power law model for such specific dissipation. We develop a modal damping estimation procedure for thin-walled components using shell elements in a commercial finite element package. We validate our shell element results against both analytical results and a solid elements approach developed elsewhere. Our computational approach allows complex geometries in a study of the effects of shape on damping. Finally, we demonstrate the efficacy of both stress concentrations and small tuned resonant appendages in increasing damping.     

Resonant vibration control of rotating beams

Rotating structures, like e.g. wind turbine blades, may be prone to vibrations associated with particular modes of vibration. It is demonstrated, how this type of vibrations can be reduced by using a collocated sensor-actuator system, governed by a resonant controller. The theory is here demonstrated by an active strut, connecting two cross-sections of a rotating beam. The structure is modeled by beam elements in a rotating frame of reference following the beam. The geometric stiffness is derived in a compact form from an initial stress formulation in terms of section forces and moments. The stiffness, and thereby the natural frequencies, of the beam depend on the rotation speed and the controller is tuned to current rotation speed to match the resonance frequency of the selected mode. It is demonstrated that resonant control leads to introduction of the intended level of damping in the selected mode and, with good modal connectivity, only very limited modal spill-over is generated. The controller acts by resonance and therefore has only a moderate energy consumption, and successfully reduces modal vibrations at the resonance frequency.     

Dynamic stability of a sandwich plate with a constraining layer and electrorheological fluid core

The dynamic stability problems of a sandwich plate with a constraining layer and an electrorheological (ER) fluid core subjected to an axial dynamic force are investigated. The rectangular plate is covered in an ER fluid core and a constraining layer to improve the stability of the system. Effects of the natural frequencies, static buckling loads, and loss factors on the dynamic stability behavior of the sandwich plate are studied in the paper. Rheological property of an ER material, such as viscosity, plasticity, and elasticity may be changed when applying an electric field. The modal damper and the natural frequencies for the sandwich plate are calculated for various electric fields. When an electric field is applied, the damping of the system is more effective. In this study, finite element method and the harmonic balance method are used to calculate the instability regions of the sandwich plate. The ER fluid core is found to have a significant effect on the dynamic stability regions.     

Noise-driven switching and chaotic itinerancy among dynamic states in a three-mode intracavity second-harmonic generation laser operating on a Lambda transition

We studied the antiphase self-pulsation in a globally coupled three-mode laser operating in different optical spectrum configurations. We observed locking of modal pulsation frequencies, quasiperiodicity, clustering behaviors, and chaos, resulting from the nonlinear interaction among modes. The robustness of [p:q:r] three-frequency locking states and quasiperiodic oscillations against residual noise has been examined by using joint time-frequency analysis of long-term experimental time series. Two sharply antithetical types of switching behaviors among different dynamic states were observed during temporal evolutions; noise-driven switching and self-induced switching, which manifests itself in chaotic itinerancy. The modal interplay behind observed behaviors was studied by using the statistical dynamic quantity of the information circulation. Well-organized information flows among modes, which correspond to the number of degeneracies of modal pulsation frequencies, were found to be established in accordance with the inherent antiphase dynamics. Observed locking behaviors, quasiperiodic motions, and chaotic itinerancy were reproduced by numerical simulation of the model equations.     

A role of fringe pattern catalogue in the course of interferometrically based determination of residual stresses by the hole-drilling method

A further development of the technique for residual stresses determination in thick-walled structures, which is based on a combination of the hole-drilling method and reflection hologram interferometry, is presented. A plane specimen welded from two equal parts of dimensions 130×80 mm² in plane and thickness 12 mm is the object of investigation. Weld seam is performed along the shortest side of the specimen. Residual stress field of interest is formed by a superposition of initial welding-induced field and secondary stress field caused by plastic deformation of the specimen. A set of actual fringe patterns, which corresponds to a wide variety of residual stress components both ratio and sign, are reconstructed and presented as illustrations. A series of reference fringe patterns is simulated for the most typical cases inherent in residual stress field under study. It is shown that actual interferograms obtained belong to three main groups depending on a typical form of fringes configuration. On this base the main principles of creating the general catalogue of fringe patterns are established and the first version of this catalogue, which is related to reflection hologram interferometry, is developed. A structure of the catalogue that consists of both actual interferograms and reference fringe patterns is described. Possible ways of further catalogue completing and its direct implementing in the course of quantitative determination of residual stresses are discussed. It is shown that both experimental and numerical data aggregated into the first version of the catalogue can be effectively used for a verification of various coherent optics techniques with respect to a determination of residual stress components by means of hole drilling. An analysis of capabilities of reflection hologram interferometry in the field of residual stresses determination comparing with dual-beam speckle-interferometric techniques is presented. Superimposed residual stress field is quantitatively described in detail for both specimen sides of dimensions 260×80 mm². It is shown that fine nuances inherent in residual stress distributions over different specimen faces can be reliably derived from recorded fringe patterns of any type. This study serves as an example of residual stress components determination in real structure with a type of residual stress field to be investigated is unknown before the experiment.     

Short pulse laser microforming of thin metal sheets for MEMS manufacturing

Continuous and long-pulse lasers have been used for the forming of metal sheets for macroscopic mechanical applications. However, for the manufacturing of micro-electro-mechanical systems (MEMS), the applicability of such type of lasers is limited by the long-relaxation-time of the thermal fields responsible for the forming phenomena. As a consequence of such slow relaxation, the final sheet deformation state is attained only after a certain time, what makes the generated internal residual stress fields more dependent on ambient conditions and might make difficult the subsequent assembly process for MEMS manufacturing from the point of view of residual stresses due to adjustment.The use of ns laser pulses provides a suitable parameter matching for the laser forming of an important range of sheet components used in MEMS that, preserving the short interaction time scale required for the predominantly mechanic (shock) induction of deformation residual stresses, allows for the successful processing of components in a medium range of miniaturization but particularly important according to its frequent use in such systems.In the present paper, a discussion is presented on the specific features of laser interaction in the timescale and intensity range needed for thin sheet microforming with ns-pulse lasers along with relevant modelling and experimental results and a primary delimitation of the parametric space of the considered class of lasers for the referred processes.