A novel approach to investigate and evaluate the damping loss factor of a planar multilayered structure is presented. A statistical analysis reveals the connection between the damping properties of the structure and the transmission of sound through the thickness of its laterally infinite counterpart.The obtained expression for the panel loss factor involves all the derivatives of the transmission and reflection coefficients of the layered structure with respect each layer damping. The properties of the fluid for which the sound transmission is evaluated are chosen to fulfil the hypotheses on the basis of the statistical formulation. A transfer matrix approach is used to compute the required transmission and reflection coefficients, making it possible to deal with structures having arbitrary stratifications of different layers and also granting high efficiency in a wide frequency range. Comparison with alternative formulations and measurements demonstrates the effectiveness of the proposed methodology.Passive damping treatments are widely used in engineering applications 2 to reduce noise radiation, the amplitude of vibrations and the risk of fa-3 tigue failure. In particular, viscoelastic laminates have found application in 4 many areas of structural acoustics due to the high damping levels that can 5 be attained when the cross-sectional properties of the laminate are appropri-6 ately chosen. A key requirement for determining the optimal cross-sectional 7 properties of a given laminate is an accurate model of its dynamics. 8 Typically, at low frequencies, a finite element (FE) model provides a good 9 description of the structural-acoustic behavior of the laminate. A Modal 10 Strain Energy (MSE) analysis on the FE model can provide the loss factor of 11 the structure in terms of the strain energy field of each mode [1]. At higher 12 frequencies, the wavelengths of interest become small with respect to the lat-13 eral dimensions of the laminate and then the FE approach becomes impracti-14 cal. Indeed, Statistical Energy Analysis (SEA) [2] is a more suitable method 15 for estimating the high-frequency responses of a structure under acoustic or 16 mechanical excitation. In order to model a subsystem in SEA, it is necessary 17 to determine the dispersion properties and the Damping Loss Factor (DLF) 18 of each propagating wave type of the subsystem. An approach for evaluating 19 the DLF of a structure is to simplify a real world component down to an 20 equivalent 3-layer beam or plate system. This was first suggested by Ross, 21 Kerwin, Ungar (RKU) [3, 4, 5], involving a fourth order differential equation 22 tion of the 3-layer laminate system represented as an equivalent, frequency 24 dependent, complex stiffness. Several authors have described extensions to 25 RKU analysis by involving different displacement fields to characterize the 26 response of more general laminates [6, 7]. Typically, the assumption of a 27 low-order displacement field is required in order to reduce analytical com-28 plexity. While simplified ...
The paper presents a full-potential model for nonisentropic unsteady transonic flows extending a parent formulation based on an independent approximation of the density and velocity potential fields. It retains the advantage of the existence of a velocity potential while granting a unique solution by combining a correction of the stagnation pressure behind a shock with a new form of Kutta condition. The solution procedure relies on an unstructured, node-based, finite volume approximation, with linear shape functions and nonreflecting far-field boundary conditions. An improved upwind density biasing allows the solution in supersonic regions to be stabilized. A new proof is given for the linearized unconditional stability of the implicit solver adopted for subsupersonic asymptotic conditions. Numerical results show that the method can model Euler solutions more accurately than an isentropic full-potential formulation, for both steady and unsteady conditions. Applications to asymptotically supersonic flows complete the numerical validation
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