This paper presents an elasticity theory solution for computation of acoustic radiation by a point- or line-excited fluid-loaded laminated plate, which may consist of a stack of an arbitrary number of different isotropic material layers. A one-side water-loaded three-layer sandwich plate, which consists of a hard rubber core sandwiched between two steel plates of equal thickness, was used as an example of the laminated plates. The approximated equivalent sandwich plate solutions were compared with the elasticity theory solutions. These results show that the approximated solutions are, as expected, valid only at frequencies much lower than the coincidence frequency. The numerical result also shows that, even at about one-tenth of the coincidence frequency, the approximated solutions suffer substantial error. The differences between the dry-side- and the wet-side-excited radiated fields of a single-layer uniform plate and a sandwich plate were investigated and compared, and found to be significantly different at frequencies above the coincidence frequency. [S0739-3717(00)01803-1]
This paper examines the wavevector-frequency spectrum of the turbulent boundary layer wall pressure in the incompressive, inviscid domain in the intermediate and high frequencies range, i.e, wS'/l]^ > > 0.5. It is shown that the wavevectorfrequency spectrum can be normalized by a factor so that it becomes simply a function of nondimensional Strouhal wavenumber U c k,/ij) and U c k 3 /w, where U c is the convective flow velocity, and ki and k 3 are the wavenumbers in the plane of the wall along the streamwise and the crossflow directions, respectively. The normalization factor is the point pressure frequency spectrum times (U c /w) 2 . It follows that the normalized wavevector-frequency spectrum can be scaled with respect to the Strouhal wavenumbers U c k]/w and U c k 3 /o>. The rationale of using a linear regression model for estimating the normalized wavevector-frequency spectrum with a set of measured response data from a wavevector filter is presented. The contention is that the actual spectrum can be obtained by the multiplication of a trial spectrum with a correction spectrum. The correction spectrum is approximated by a polynomial in U c k,/w with a set of coefficients to be determined. The multiple linear regression model relates the response of a measuring system to these coefficients which are determined by least square minimization of a set of measured response data. The advantages of the regression approach are that it relaxes the requirements of the wavevector filter's ability to discriminate against the spectral elements outside the wavenumber bandwidth of the filter, and this approach is capable of better estimating the entire wavevector spectrum as compared to the existing methods which are limited to measurements of the low-wavenumber spectra. Some preliminary numerical results are presented.
Some drums have, typically, a hollow trunk (or a barrel) with a circular membrane at each of the two ends. In this type of drum structure, the two membranes interact with each other through the air between them inside the body. Even if the two membranes have an identical fundamental resonance frequency, the interaction results in two resonance frequencies. At the lower resonance, the two membranes vibrate in phase. Since the membranes must move the internal air, the frequency at the lower resonance is lower than that of the original resonance (without air loading). At the higher resonance, they vibrate out-of-phase, causing compression or expansion of the internal air simultaneously. The frequency at this resonance is higher than that of the original resonance since, in this case, the air works as a spring. In this paper, resonance frequencies and mode shapes of the coupled membranes are investigated using an analytical model. The membranes are assumed to be ideal (i.e., no bending stiffness) and the body is assumed to be ideally rigid. Since it is a common practice that the two membranes are slightly (intentionally) miss-tuned, the main interest of this paper is to simulate the effect of this miss-tuning on the resulting resonance frequencies and mode shapes. Numerical results for the case of a 48 cm diameter and 50 cm length Japanese drum are presented.
This paper presents an exploratory study of using external fluid loading on a vibrating tube for measuring the suspended sediment concentration (SSC) in bodies of water such as rivers and reservoirs. This new measuring concept provides an opportunity for an automated on-site monitoring of the conditions in a body of water by taking the fluid sample instantaneously in the area surrounding the vibrating tube. The physical properties of the fluid sample are those of the fluid that naturally flows around the tube, and are more representative of those of the water with SSC to be measured. The theoretical analysis presented in this paper shows that the resonance frequencies of an immersed vibrating tube change significantly with mass density variations that normally occur in bodies of water with suspended sediment. These changes are sensitive enough to have a possible 1% resolution of the measured fluid density. The signal processing issues are discussed, and a schematic of a conceptual measuring setup is proposed. Based on the theoretical analyses and other measurement issues presented in the paper, using the loading by external fluid on a vibrating tube is feasible for measuring the SSC in water bodies.
An analysis of sound and vibratory transmission and reflection losses in a fluid filled planar piping system which consists of straight pipe segments, flexible hose, elbows and/or U-joints is discussed in this paper. The transfer matrix approach is used for the analysis. The wave propagation constants for various types of waves calculated from the transfer matrix method were verified with an exact elasticity theory. Although calculation of the transmission losses for a hose-pipe system has been widely discussed in the literature, the reflection characteristics of a hose-pipe system, however, have not received proper attention. In this paper, we calculate the reflection, absorption, and transmission coefficients of a piping system simultaneously. The numerical example shows that very large pressure and bending wave transmission losses that occur in a hose-pipe system are not only caused by attenuation and dissipation but also by the reflection from the system.
This paper presents a finite-element analysis on the free vibration of Japanese drum wood barrels under insufficient material property data. Unlike isotropic material such as steel, wood behaves like an orthotropic composite material, whose elastodynamic characterization in a cylindrical shell needs Young's modulus in the longitudinal (in-grain) and circumferential (cross-grain) directions, shear modulus, and Poisson ratios. Due to measurement difficulty encountered during the process of testing, only the longitudinal Young's modulus and the specific gravity of the wood were measured. In the analysis, the finite-element models of the drum were constructed using conical shell elements. The required unknown elastic constants were estimated consecutively by a try-and-error approach, and the estimated values were reached when the computed resonance frequencies matched simultaneously with those of the seven lower modes measured in experiments. In order to accomplish this, both the estimated constants and the finite-element analysis must be within acceptable range of accuracy. It was found that the values of the circumferential (cross-grain) Young's modulus, which was unknown at the beginning of the study, turns out to be crucial in determining the lower mode resonance frequencies. The usefulness of this analysis is that the estimated elastic constants can now be used for updating the finite-element model. The updated model can then be used calculating the higher order modes which cannot be practically obtained through measurements.
A numerical approach for computing the eigenvalues and eigenfunctions of an axisymmetric shell with a nonaxisymmetric edge constraint is presented. The shell structures are modeled without constraint by an assemblage of axisymmetric shell elements. The constraint at any point along the edge circumference may be imposed by two linear springs acting against the axial and the radial degrees of freedom, and by a torque spring acting against the rotational degree of freedom. The nonuniform constraint is thus represented by the arbitrary distribution of these spring constants per unit length along the circumference. This arbitrary distribution of spring constants is then resolved by a Fourier series expansion. Utilizing the natural modes of the unconstrained shell as the generalized coordinates, the equations of motion which include the effects of a nonuniform constraint are derived. The mass and the stiffness matrices of these equations of motion are used as inputs for solving the linear numerical eigenvalue problem. A circular plate, which can be considered as an extreme case of an axisymmetric shell, is used as a numerical example. For a simply supported circular plate with a sinusoidal variation of rotational edge constraint, the computed results agree well with the data available in the literature.
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