Sound and Structural Vibration Radiation, Transmission and Response

Fahy, F.J.; Thoma, Jean U.

doi:10.1115/1.3143810

Cited by 115 publications

(198 citation statements)

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“…Therefore, in accordance with the formulae , and , we come to the expressions

{\overset{q}{true}}_{*} + {\overset{q}{true}}_{1} = - i ρ_{1} ω \sum_{m, n = 1, 3, . .}^{M, N} ([] 2 f_{m n} - \frac{c_{1}^{*} R_{m n}}{L_{m n}}) A_{*}, {\overset{q}{true}}_{2} = - i ρ_{2} ω \sum_{m, n = 1, 3, . .}^{M, N} \frac{c_{2}^{*} R_{m n}}{L_{m n}} A_{*} .

With the prescribed value

A_{*}

and obtained values

{\overset{q}{true}}_{*}, {\overset{q}{true}}_{1}

and

{\tilde{q}}_{2}

the sound insulation properties of the plate and levels of acoustic pressure in the points of boundary planes will have the following parameters

\begin{matrix} true \\ right R_{p} = - 20 prefixlg (||, \frac{{\tilde{q}}_{2}}{{\tilde{q}}_{*}}), R_{p}^{0} = - 20 prefixlg (||, \frac{{\tilde{q}}_{2}}{{\overset{q}{true}}_{*} + {\overset{q}{true}}_{1}}) . \end{matrix}

…”

Section: Equations Of Motions Of a Thin Plate Adapted For Dissipationsupporting

confidence: 52%

“…Figure 2 and 3 illustrate the dependences of the parameter of sound insulation

R_{p}

on the frequency of sound wave

f = ω / false(2 π false)

for steel and duralumin plates obtained at

η = 0

within the frequency range

= 20 \div 1000

Hz. The solid lines indicate curves corresponding to the use of three‐dimensional wave equations, while the dashed lines mean the using the hypothesis of the flat reflection of acoustic waves, and dotted lines designate the corresponding to the use of mass law under normal incidence of sound according which the parameter of noise insulation is determined by the formula

\begin{matrix} true \\ right R_{p} = 20 prefixlg \frac{ρ_{p} t ω}{2 ρ} . \end{matrix}

…”

Section: Analysis Of Calculations Results Of Plate Sound Insulation Pmentioning

confidence: 99%

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Free and forced bending vibrations of a thin plate in a perfect compressible fluid with energy dissipation taken into account

et al. 2020

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A refined statement of stationary dynamic acoustoelasticity problems of thin isotropic plates surrounded from both sides by acoustic media assumed to be perfect compressible fluids has been studed. The problem statement takes into account the energy dissipation in the material of the plate and fluid on the basis of the Kelvin-Voigt hysteresis model. The refinement of the fluid behavior is based on the assumption that the pressure increment is proportional not only to volumetric strain, but also to the rate of its volumetric strain. This assumption allows us to obtain the generalized Helmholtz wave equation by introducing Skudrzyk's complex sound velocity into consideration to take account of the energy dissipation. The motion equations of the plate are based on the classical Kirchhoff-Love model and are obtained in two versions. In the first version unsimplified three-dimensional wave equations are used to determine the aerohydrodynamic load acting on a plate. The second version is based on simplifying the equations of fluid motion by the introduction of the well-known hypothesis of plane reflection and emission of sound waves. On the basis of the derived equations, exact analytical solutions of two types of problems are obtained. The first type is related to the problem of free vibrations of a rectangular plate hinged around the contour when complex eigenfrequencies were defined. The second type is related to the problem of forced vibrations of the plate under the action of a flat mono-harmonic incident sound wave when sound transmission loss, the stress-strain state parameters of the plate as well as the laws of change in sound pressure in a fluid were determined. It is shown that correct and more meaningful solutions of acoustoelasticity problems of the considered class are possible only in case of describing the behavior of a fluid with unsimplified three-dimensional wave equations with consideration of the energy dissipation. K E Y W O R D Sacoustoelasticity problems, complex oscillation frequency, complex sound velocity, energy dissipation, free and forced vibrations, generalized Helmholtz equation, Kelvin-Voigt model, perfect compressible fluid, plate, sound pressure, sound transmission loss

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“…Therefore, in accordance with the formulae , and , we come to the expressions

{\overset{q}{true}}_{*} + {\overset{q}{true}}_{1} = - i ρ_{1} ω \sum_{m, n = 1, 3, . .}^{M, N} ([] 2 f_{m n} - \frac{c_{1}^{*} R_{m n}}{L_{m n}}) A_{*}, {\overset{q}{true}}_{2} = - i ρ_{2} ω \sum_{m, n = 1, 3, . .}^{M, N} \frac{c_{2}^{*} R_{m n}}{L_{m n}} A_{*} .

With the prescribed value

A_{*}

and obtained values

{\overset{q}{true}}_{*}, {\overset{q}{true}}_{1}

and

{\tilde{q}}_{2}

the sound insulation properties of the plate and levels of acoustic pressure in the points of boundary planes will have the following parameters

\begin{matrix} true \\ right R_{p} = - 20 prefixlg (||, \frac{{\tilde{q}}_{2}}{{\tilde{q}}_{*}}), R_{p}^{0} = - 20 prefixlg (||, \frac{{\tilde{q}}_{2}}{{\overset{q}{true}}_{*} + {\overset{q}{true}}_{1}}) . \end{matrix}

…”

Section: Equations Of Motions Of a Thin Plate Adapted For Dissipationsupporting

confidence: 52%

“…Figure 2 and 3 illustrate the dependences of the parameter of sound insulation

R_{p}

on the frequency of sound wave

f = ω / false(2 π false)

for steel and duralumin plates obtained at

η = 0

within the frequency range

= 20 \div 1000

\begin{matrix} true \\ right R_{p} = 20 prefixlg \frac{ρ_{p} t ω}{2 ρ} . \end{matrix}

…”

Section: Analysis Of Calculations Results Of Plate Sound Insulation Pmentioning

confidence: 99%

Free and forced bending vibrations of a thin plate in a perfect compressible fluid with energy dissipation taken into account

et al. 2020

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“…A significant increase can be seen over the entire frequency range, remarkably at 4 kHz with more than 15 dB, due to the aerogel constraint layers. The dip in the STL values of the gypsum‐only panel at 4 kHz can be explained using thin plate theory . According to this theory, for an unbounded flexible partition, at a certain frequency, the incident wave is coincident with the bending wave in the partition.…”

Section: Resultsmentioning

confidence: 99%

“…According to this theory, for an unbounded flexible partition, at a certain frequency, the incident wave is coincident with the bending wave in the partition. This coincidence frequency ( f c ) is approximated as:

f_{c} = \frac{c_{0}^{2}}{2 π \sin^{2} θ} \sqrt{\frac{ρ t_{0}}{D},}

where

D = E_{0} t_{0}^{3} / 12 true(1 - v_{0}^{2} true),

is the partition's bending stiffness with E 0 , v 0 , and t 0 being the Young's modulus, the Poisson's ratio and the thickness of the partition, respectively. Using Equation , the estimated coincidence frequencies for an unbounded gypsum panel at incident angles less than 90° are entirely above 2000 Hz.…”

Section: Resultsmentioning

confidence: 99%

Sound Transmission Loss Enhancement in an Inorganic‐Organic Laminated Wall Panel Using Multifunctional Low‐Density Nanoporous Polyurea Aerogels: Experiment and Modeling

et al. 2018

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Recently, the authors have reported an exceptional normal incidence sound transmission loss characteristic for a class of low density, highly porous, and mechanically strong polyurea aerogels. Herein, a laminated composite comprising the organic low-density aerogels bonded with an inorganic compound (e.g., gypsum materials) is considered to investigate the constrained damping effects of the aerogels on the airborne sound insulation behavior of the composite using the standard chamber-based diffuse sound field measurements. Huge improvement in the sound transmission loss is obtained due to the use of aerogel without a significant increase in the overall weight and thickness of the composite panel (e.g., more than 10 dB increase by reaching 40 dB sound transmission loss at 2 kHz after the implementation of only two 5 mm-thick aerogel layers at bulk densities 0.15 and 0.25 g cm À3 ). This uncommon behavior breaks the empirical "Mass Law" nature of the most conventional acoustic materials. In addition, an exact analytical time-harmonic plane-strain solution for the diffused wave propagation through the multilayered structure is provided using theories of linear elasticity and Biot's dynamic poroelasticity. The theoretical results are well supported by the experiments which can be utilized for the design of the future light-weight multifunctional composite structures.

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“…To calculate the STL, the first resonance frequency (ω 0 ) needs to be defined. Fahy and Gardonio introduced the frequency of the first resonance for a rigid panel with flexible supports as follows:

ω_{0} = \sqrt{k_{s} / m}

where k s is the stiffness per unit area for the panel's support and the surface density ( m ) can be replaced by ρ h (where ρ and h are the density and thickness of the panel, respectively). The natural frequencies for a circular flexible plate (ω m,n 's) are as follows:

ω_{m, n} = \frac{{true(λ r true)}_{m, n}^{2}}{r^{2}} \sqrt{\frac{D}{ρ h}} m, n = 0, 1, 2, \dots

where r is the radius and (λ r ) m,n is obtained from the plate's characteristic equation.…”

Section: Theoretical Formulationmentioning

confidence: 99%

Experimental and theoretical investigation of sound transmission loss for polycarbonate, poly(methyl methacrylate), and glass

Sabet

Ohadi

2015

J of Applied Polymer Sci

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In this study, the effects of the soundproofing properties of polycarbonate (PC), poly(methyl methacrylate) (PMMA), and glass were investigated. We fabricated the specimens into 3 mm thick sheets by direct hot compression molding as a monolithic sample and also by gluing three thin sheets together into a multilayer. Sound transmission loss (STL) was measured by an impedance tube over the frequency range 63-1600 Hz. The results indicate that because of the close density, the STLs for PC and PMMA were almost the same above 1200 Hz. Also, PMMA had a greater STL than PC in the range 63-300 Hz. In a comparison of the monolithic and multilayered samples, we demonstrated that the epoxy-based adhesive interlayers had more efficient bonding than the siliconebased ones. The multilayered polymer/silicone specimens showed a sharp drop in the STL values compared to the monolithic samples. However, the multilayered polymer/epoxy specimens revealed similar behavior to the monolithic polymers. V C 2015 Wiley Periodicals, Inc. J. Appl. Polym. Sci. 2016, 133, 42988.

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Sound and Structural Vibration Radiation, Transmission and Response

Cited by 115 publications

References 0 publications

Free and forced bending vibrations of a thin plate in a perfect compressible fluid with energy dissipation taken into account

Free and forced bending vibrations of a thin plate in a perfect compressible fluid with energy dissipation taken into account

Sound Transmission Loss Enhancement in an Inorganic‐Organic Laminated Wall Panel Using Multifunctional Low‐Density Nanoporous Polyurea Aerogels: Experiment and Modeling

Experimental and theoretical investigation of sound transmission loss for polycarbonate, poly(methyl methacrylate), and glass

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