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This paper investigates the vibration characteristics of the coupling system of a microscale fluid-loaded rectangular isotropi plate attached to a uniformly distributed mass. Previous literature has, respectively, studied the changes in the plate vibratio induced by an acoustic field or by the attached mass loading. This paper investigates the issu...
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... Extensive analyses for the vibration of homogeneous plate structures in fluid environment have been carried out due to its wide applications in ocean engineering, biomedical engineering, and aerospace engineering. In these research works, different fluid properties including the compressible and incompressible fluid [37][38][39][40], viscid and inviscid fluid [41][42][43][44], are considered. Up to date, most studies on the plate-fluid coupling system mainly focused on the ideal fluid for the purpose of simplifying the theoretical analysis procedures. ...
This paper presents a free vibration analysis of functionally graded material (FGM) plates that are partially submerged in an incompressible, inviscid fluid. The FGM plates with four gradient types of continuously varying material properties along the thickness direction, including the power law, exponential, sinusoidal and cosine forms, are studied to examine various distributions of material properties. The plate is modeled based on the Mindlin Plate Theory (MPT), and the fluid loading effect on the FGM plates is modeled using the method of added mass. The variational principle is applied to derive the governing equations of this fluid-plate interaction system. The differential quadrature (DQ) method is used to solve this problem by converting the governing equations into a system of linear equations. The fundamental frequency and the corresponding mode shape are obtained using an iterative procedure. Numerical results for several examples are obtained and presented to investigate the vibration characteristics of the submerged FGM plates in terms of the gradient index, gradient type, immersed depth, fluid density, aspect ratio and slenderness ratio. Results indicate that the larger aspect ratio and immersed depth increase the fundamental frequency of the FGM plate, while larger gradient index, fluid density and slenderness ratio decrease the fundamental frequency. Among four different material gradient types, the FGM plate with power law type gradient has the smallest fundamental frequency, while the one with sinusoidal form has the largest value. The mode shape in fluid deviates from that in vacuum and shows an unsymmetrical shape for CCCC and SSSS FGM plates.
... If the mode shape is assumed to be the same in vacuum and liquid, an approximation that can be confirmed by vibrometer measurements in air and liquid as seen in Figure 1, the frequency of the vibration in the fluid can be calculated using equation (3) [4]. ...
... In order to calculate ? for a particular mode shape of a rectangular plate, equation (4) can be used [4]. ...
... h L p b f mn (4) In the above equation, ? mn is the non-dimensionalized added virtual mass incremental (NAVMI), ? is the plate aspect ratio L b /L a , ? ...
A piezoelectrically transduced MEMS resonator capable of operating in a liquid and fabricated using standard thin film fabrication processes is presented. The optical and electrical characterization of the (1,2) flexural mode of the device in air and liquid matches analytical predictions. Furthermore, the device shows an improvement in Q in liquid over air. The mass sensitivity of the device is 135 cm2/g, higher than typical QCM values, showing promise for liquid sensing applications.
... Extensive research is being carried on in the field of plate vibrations due to its applications in various fields like aircraft, aerospace and ship building industries. Cohen [7]. Mali and Singru formulated analytical models for free vibration of perforated plated by using Heaviside functions to represent perforations [8,9,10]. ...
Various structural components used in the engineering domain such as the aircraft and aerospace industries can be effectively modeled as beams, plates, and shells and are subjected to vibrations frequently. Free and forced vibration analysis of plates with added patches of mass and various boundary conditions is encountered in various applications from printed circuit boards in electronics to the plates used in ocean engineering systems. The printed circuit boards and plate like chassis can be approximated as flat rectangular plates carrying distributed patch mass and subjected to vibration. The concept of added mass is often used for the consideration of the accelerometer mass in calculation of vibration frequencies of plates during experimentation. It is also applied in the field of micro-plate dynamics for design of bio-MEMS. This paper is concerned with determination of fundamental frequency of free vibration. Plates considered in this study are thin, homogeneous rectangular with clamped edges. Analysis is done for patch masses mounted on various locations on the plate. The analytical procedure using the Rayleigh-Ritz approach is adopted in which polynomial terms are used to represent the shape function. We have analysed the effect of position and magnitude of added patches of circular masses on the modal frequencies of the plate. The results have been validated by comparing with those obtained by the finite element analysis (FEA).
... Une approche souvent reprise pour déterminer ces fréquences de résonance est la méthodologie de Lindholm [82] qui permet d'évaluer la masse ajoutée à partir d'une correction empirique. Parmi les travaux qui utilisent les résultats de Lindholm comme référence, on peut citer l'étude de Liang et al. [81] qui propose une formulation empirique de la masse ajoutée, et celle de Wu et al. [141] qui présente une solution analytique des fréquences de résonance et des déformées d'une structure sous chargement lourd. L'approche à laquelle nous nous intéressons ici consiste à calculer la masse ajoutée par le fluide sur la base modale de la plaque à vide, ce qui rejoint la méthode décrite dans le Code Aster [32], ou encore par Vu et al. [135]. ...
L’objectif de la thèse est de développer une méthode de calcul pour prédire le rayonnement acoustique, en fluide léger ou en fluide lourd, d’une structure excitée par une Couche Limite Turbulente (CLT) en présence d’un gradient de pression statique. La méthodologie proposée comporte trois étapes : la caractérisation de l’écoulement moyen par un calcul RANS stationnaire, la modélisation des fluctuations de pression pariétale à l’aide de modèles semi-empiriques et le calcul vibro-acoustique en réponse aux pressions fluctuantes.Nous portons dans ce travail une attention particulière aux effets d’un gradient de pression statique dans l’écoulement, présent dans la plupart des cas industriels. Pour mettre en lumière ces effets nous proposons l’analyse d’un cas d’écoulement avec gradient de pression négatif puis positif correspondant à des mesures réalisées en tunnel aérodynamique. Cette étape de validation souligne l’importance de la prise en compte du gradient de pression dans la modélisation globale.Une des difficultés pour estimer la réponse vibro-acoustique de la structure excitée par la CLT dans les basses et moyennes fréquences repose sur le couplage entre le modèle déterministe vibro-acoustique et les modèles statistiques de pression pariétale. Plusieurs approches sont étudiées pour introduire l’excitation hydrodynamique dans le modèle vibro-acoustique : a) en modélisant l’excitation par une distribution de forces ponctuelles ; b) en modélisant l’excitation par un champ d’ondes planes ; c) en utilisant un principe de réciprocité ; d) en utilisant des échantillons d’ondes planes auxquelles sont associées des phases aléatoires. L’application de ces différentes approches sur un cas test en fluide lourd permet d’étudier l’influence des paramètres de calcul et d’établir les avantages et inconvénients propres à chacune des méthodes. Les calculs vibro-acoustiques sont alors réalisés par l’approche PTF (Patch Transfer Functions) qui permet de traduire le couplage structure-fluide lourd sans trop augmenter le coût des calculs. Par ailleurs, pour traiter les hautes fréquences en utilisant la méthode SEA (Statistical Energy Analysis), des développements théoriques sont proposés avec les hypothèses simplificatrices associées qui permettent d’estimer la puissance injectée par la CLT à partir de fluctuations de pression exprimées dans le domaine des nombres d’onde.La dernière partie est consacrée à l’adaptation des méthodes pour prendre en compte l’évolution spatiale de la CLT en présence d’un gradient de pression. Le formalisme repose sur une décomposition de la structure en différentes zones auxquelles on associe des interspectres de fluctuations de pression différents. Cette approche est appliquée sur un cas industriel d’écoulement sur un massif de sous-marin. La décomposition suppose que l’on néglige l’effet des corrélations des pressions entre les zones. L’influence de cette hypothèse est tout d’abord étudiée avec un cas d’excitation homogène. Enfin l’intérêt de prendre en compte l’évolution spatiale de la CLT dans les calculs de la pression rayonnée est mis en évidence sur ce cas.
... The rectangular plate is one of the most widely used structures in the industrial world. The sound radiation from vibrating unbaffled panels [2][3][4], baffled panels [4][5][6][7][8][9] and submerged panels [10][11][12] has been the subject of active research for many years. Particularly, the sound radiation from vibrating plates is a common problem in automobiles, airplanes, industrial machinery, buildings and electro-acoustical devices, to name a few. ...
... The damped point force response of a rectangular composite plate due to a harmonic point force at ðx p ; y p Þ is given by Eq. (11), where m a is estimated based on Eq. (12). We consider the simply supported boundary conditions in the analysis of composite panels, where the mode shapes are given by [42] ...
... Galerkin procedure and Rayleigh-Ritz method are the most commonly used systematic approaches to study vibrations of plates with attached masses, in which the bending stiffness of the attached mass is usually ignored. [15][16][17] However, different from those studies, bending stiffness of attached masses on MAMs cannot be neglected. Instead, such attached masses would be rigid compared with the thin rubber membrane. ...
... Since a plane sound wave can only induce symmetric modes on the MAM, we choose the double cosine series expansion to satisfy boundary conditions in Eq. (15) and Eq. (16) as , (17) . (18) Substituting Eq. (17) ...
By considering the membrane's dissipation, the membrane-type acoustic
metamaterial (MAM) has been demonstrated as a super absorber for low-frequency
sound. In the paper, a theoretical vibroacoustic plate model is developed to
reveal sound energy absorption mechanism within the MAM under a plane normal
incidence. Based on the plate model in conjunction with the point matching
method, the in-plane strain energy of the membrane due to the resonant and
antiresonant motion of the attached masses can be accurately captured by
solving the coupled vibroacoustic integrodifferential equation. Therefore, the
sound absorption of the MAM is obtained and discussed, which is also in good
agreement with the prediction from the finite element method. In particular,
microstructure effects including eccentricity of the attached masses, the
depth, thickness and loss factor of the membrane on sound absorption peak
values are quantitatively investigated.
... The transverse displacement (w) is expanded into a series and is required to satisfy the plate boundary conditions [29], ...
... Within the parameter range defined by the present sensors and the working fluid (air) the frequency shift is small and can be regarded as constant over the considered frequency range. According to Wu (2009) the added mass shifts the resonance frequency by approximately 2% for the 1 st mode (diaphragm size 1.8mm). For the 2 nd and 3 rd mode the frequency shift is less than 1%. ...
A novel pressure measurement technique is presented for wireless recording of time-averaged surface pressure distributions
in wind tunnel surveys. An array of silicon micro-plate resonators acts as pressure sensing element. The pressure is recorded
by measuring the sensor diaphragms’ resonance frequency using optical interferometry. Dependent on the quasi-static deflection
caused by a pressure load, the resonance frequency varies with an average pressure sensitivity of 3Hz/Pa in a frequency range
between 30 and 150kHz. A smart-pixel CMOS camera, narrow-band acoustic noise excitation and a specific sensor surface structure
allow for the interrogation of a large number of sensors in parallel without the need for alignment between sensor and detector.
Experimental tests reveal increased sensing performance with acoustic excitation of the higher vibration modes.
This paper investigates the characteristics of higher-order transverse mode fully clamped membrane resonators that are piezoelectrically transduced as a class of resonators that completely seal the domain above the resonator from the domain below. Such isolation between the top and bottom of a resonator is preferable when encasing the device in a microfluidic cell for liquid-phase sensing measurements, a setup that can be beneficial for sensing applications. Most fully clamped membrane resonators are hampered by low liquid-phase quality factor (Q) and large motional resistance (R m). This paper describes the design of higher-order transverse (2, 2) mode square membrane and (2, 0) mode circular membrane resonators, and the effect of device scaling on liquid-phase Q and R m. We show a best-case liquid-phase R m of 54 kΩ and Q of 270 among the various membrane sizes tested. This level of liquid-phase Q is higher than some contour mode resonators. Compared to other fully clamped membrane resonators in the literature, the results here represent a significant improvement in both R m and Q, highlighting the potential of these membrane resonators for liquid-phase mass sensing applications.
This paper studies the vibrational behaviors of a distributive mass-loaded microscale circular diaphragm submerged in a fluid. The vibration of the diaphragm involving loadings simultaneously induced by an acoustic field and the adhesion of distributive mass has been investigated. Two different types of adsorbates, namely, in the form of discrete particles (mass only) and a uniform layer (mass and rigidity), are considered and compared. Moreover, the pre-existing stress in the diaphragm has also been taken into consideration. Based on Lamb's hypotheses of the fluid-loaded structure in conjunction with the Rayleigh–Ritz theorem, an analytical solution for the dynamic characteristics of the coupling system, including the resonant frequency, mode shape, and the quality factor, is developed. The results have been compared with those of the finite element simulations, and a good agreement has been obtained. The results reveal that the adsorbate properties contribute differently to the dynamic response of the micro-diaphragm in the fluid, and the contribution may be intervened by tuning the pre-stress. The theoretical model and novel analytical solution are of interest in the design of micro-diaphragm-based biosensing devices.
