scispace - formally typeset
Search or ask a question
Journal ArticleDOI

On the Vibrations of an Elastic Plate in Contact with Water

TL;DR: In this paper, the pitch of the fundamental note of a thin circular plate or diaphragm of given material and dimensions, filling an aperture in a plane wall which is in contact on one side with an otherwise unlimited mass of water, was investigated.
Abstract: In connection with the problem of submarine signalling the question arose as to the pitch of the fundamental note of a thin circular plate or diaphragm of given material and dimensions, filling an aperture in a plane wall which is in contact on one side with an otherwise unlimited mass of water. The following investigation, which includes some extensions, is now published by permission. To simplify the theoretical treatment, the wall is supposed to be rigid, and the plate to be firmly clamped to it along the circumference, although these conditions are only imperfectly fulfilled in practice. Even with these limitations an exact solution is out of the question, but a sufficient approximation can be obtained by Rayleigh’s method of an assumed type, which gives good results if the type be suitably chosen. It is known that the frequency estimated in this way will be somewhat too high.
Citations
More filters
Journal ArticleDOI
TL;DR: In this article, fabrication arid characterization results of piezoelectric micromachined ultrasonic transducers (pMUTs) based on 2-spl mu/m-thick Pb(Zr/sub 0.53/Ti/sub 3/) (PZT) thin films are described.
Abstract: This paper describes fabrication arid characterization results of piezoelectric micromachined ultrasonic transducers (pMUTs) based on 2-/spl mu/m-thick Pb(Zr/sub 0.53/Ti/sub 0.47/O/sub 3/) (PZT) thin films. The applied structures are circular plates held at four bridges, thus partially undamped. A simple analytical model for the fully clamped structure is used as a reference to optimize design parameters such as thickness relations and electrodes, and to provide approximate predictions for coupling coefficients related to previously determined thin film properties. The best coupling coefficient was achieved with a 270-/spl mu/m plate and amounted to k/sup 2/=5.3%. This value compares well with the calculated value based on measured small signal dielectric (/spl epsi/=1050) and piezoelectric (/spl epsi//sub 31,f/=15 Cm/sup -2/) properties of the PZT thin film at 100 kV/cm dc bias. The resonances show relatively large Q-factors, which can be partially explained by the small diameters as compared to the sound wavelength in air and in the test liquid (Fluorinert 77). A transmit-receive experiment with two quasiidentical pMUTs was performed showing significant signal transmission up to a distance of 20 cm in air and 2 cm in the test liquid.

279 citations


Cites result from "On the Vibrations of an Elastic Pla..."

  • ...This is close to the estimation obtained from Lamb’s theory [43] (extended to double-side immersion) which yields a decrease by a factor of 5....

    [...]

Journal ArticleDOI
TL;DR: In this paper, a mathematical model for the structure is developed using a combination of the finite element method and Sanders' shell theory, and the in-plane and out-of-plane displacement components are modelled using bilinear polynomials and exponential functions, respectively.

145 citations

Journal ArticleDOI
TL;DR: In this paper, the effect of fluid on the natural frequencies of circular plates vibrating axisymmetrically in contact with fluid was investigated. And the authors obtained the non-dimensionalized added virtual mass incremental (NAVMI) factor for circular plates having simply supported, clamped and free edges using the integral transformation technique in conjunction with the dual integral equation method.

138 citations

Journal ArticleDOI
TL;DR: In this paper, a semi-analytical method is developed to investigate free vibrations of circular plates immersed in fluids and a series of experimental tests are presented to validate the model. But the results obtained from the present method agree with those obtained from modal test and the finite element analysis.

122 citations

Journal ArticleDOI
Moon K. Kwak1
TL;DR: In this paper, the authors used the Rayleigh-Ritz method combined with the Green function method to estimate the virtual mass effect on the natural frequencies and mode shapes of rectangular plates in the presence of water on one side of the plate.
Abstract: This paper is concerned with the virtual mass effect on the natural frequencies and mode shapes of rectangular plates due to the presence of the water on one side of the plate. The approximate formula, which mainly depends on the so-called nondimensionalized added virtual mass incremental factor, can be used to estimate natural frequencies in water from natural frequencies in vacuo. However, the approximate formula is valid only when the wet mode shapes are almost the same as the one in vacuo. Moreover, the nondimensionalized added virtual mass incremental factor is in general a function of geometry, material properties of the plate and mostly boundary conditions of the plate and water domain. In this paper, the added virtual mass incremental factors for rectangular plates are obtained using the Rayleigh-Ritz method combined with the Green function method. Two cases of interfacing boundary conditions, which are free-surface and rigid-wall conditions, and two cases of plate boundary conditions, simply supported and clamped cases, are considered in this paper. It is found that the theoretical results match the experimental results. To investigate the validity of the approximate formula, the exact natural frequencies and mode shapes in water are calculated by means of the virtual added mass matrix. It is found that the approximate formula predicts lower natural frequencies in water with a very good accuracy.

113 citations