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Vibro-acoustic analysis of complex systems at higher frequencies faces two challenges: how to compute the response without using an excessive number of degrees of freedom (DOFs), and how to quantify the uncertainty of the response due to small spatial variations in geometry, material properties, and boundary conditions, which have a wave scattering effect? In this study, a general method of analysis is presented that provides an answer to both questions while overcoming most limitations of statistical energy analysis. The fundamental idea is to numerically compute an artificial ensemble of realizations for the components of the built-up system that are highly sensitive to small random wave scatterers. This can be efficiently performed because their eigenvalue spacings and mode shapes conform to Gaussian orthogonal ensemble spacings and Gaussian random fields, respectively. The DOFs of the overall system are therefore limited to those of the deterministic components and the interface DOFs of the random components. The method is extensively validated by application to plate structures. Good agreement between the predicted response probability distributions and the results of detailed parametric probabilistic models is obtained, also for cases of low modal overlap, single point loading, and strong subsystem coupling. [ABSTRACT FROM AUTHOR]

In this paper a numerical approach is presented to compute dispersion curves for solid waveguides coupled to an infinite medium. The derivation is based on the scaled boundary finite element method that has been developed previously for waveguides with stress-free surfaces. The effect of the surrounding medium is accounted for by introducing a dashpot boundary condition at the interface between the waveguide and the adjoining medium. The damping coefficients are derived from the acoustic impedances of the surrounding medium. Results are validated using an improved implementation of an absorbing region. Since no discretization of the surrounding medium is required for the dashpot approach, the required number of degrees of freedom is typically 10 to 50 times smaller compared to the absorbing region. When compared to other finite element based results presented in the literature, the number of degrees of freedom can be reduced by as much as a factor of 4000. [ABSTRACT FROM AUTHOR]

The idea of predicting the future from the knowledge of the past is quite natural, even when dealing with systems whose equations of motion are not known. This long-standing issue is revisited in the light of modern ergodic theory of dynamical systems and becomes particularly interesting from a pedagogical perspective due to its close link with Poincaré's recurrence. Using such a connection, a very general result of ergodic theory--Kac's lemma--can be used to establish the intrinsic limitations to the possibility of predicting the future from the past. In spite of a naive expectation, predictability is hindered more by the effective number of degrees of freedom of a system than by the presence of chaos. If the effective number of degrees of freedom becomes large enough, whether the system is chaotic or not, predictions turn out to be practically impossible. The discussion of these issues is illustrated with the help of the numerical study of simple models. [ABSTRACT FROM AUTHOR]

An optimal design of a hybrid vibration absorber (HVA) with a displacement and a velocity feedback for minimizing the velocity response of the structure based on the H2 optimization criterion is proposed. The objective of the optimal design is to reduce the total vibration energy of the vibrating structure under wideband excitation, i.e., the total area under the velocity response spectrum is minimized in this criterion. One of the inherent limitations of the traditional passive vibration absorber is that its vibration suppression is low if the mass ratio between the absorber mass and the mass of the primary structure is low. The active element of the proposed HVA helps further reduce the vibration of the controlled structure, and it can provide very good vibration absorption performance even at a low mass ratio. Both the passive and active elements are optimized together for the minimization of the mean square velocity of the primary system as well as the active force required in the HVA. The proposed HVA was tested on single degree-of-freedom (SDOF) and continuous vibrating structures and compared to the traditional passive vibration absorber. [ABSTRACT FROM AUTHOR]

In the first part of the paper, a single degree-of-freedom model of a vibrating membrane with piezoelectric inserts is introduced and is initially applied to the case when a plane wave is incident with frequency close to one of the resonance frequencies. The model is a prototype of a device which converts ambient acoustical energy to electrical energy with the use of piezoelectric devices. The paper then proposes an enhancement of the energy harvesting process using a nonlinear processing of the output voltage of piezoelectric actuators, and suggests that this improves the energy conversion and reduces the sensitivity to frequency drifts. A theoretical discussion is given for the electrical power that can be expected making use of various models. This and supporting experimental results suggest that a nonlinear optimization approach allows a gain of up to 10 in harvested energy and a doubling of the bandwidth. A model is introduced in the latter part of the paper for predicting the behavior of the energy-harvesting device with changes in acoustic frequency, this model taking into account the damping effect and the frequency changes introduced by the nonlinear processes in the device. [ABSTRACT FROM AUTHOR]

Human perception of sonic booms is a major impediment to commercial supersonic flight. Shaping, which reduces the audible shock waves of a boom, can make outdoor perception of booms acceptable. Perception of sonic booms experienced indoors is of concern, and it is not yet established whether shaped booms offer benefit to indoor listeners. A better understanding of the transmission of shaped booms into building structures is needed. In the authors’ earlier work the vibration response of house elements subjected to different sonic boom wave shapes was evaluated using a single degree of freedom model. This paper expands that approach with a modal analysis model. The acceleration of building elements and the resulting sound pressure inside a room are computed in the time and frequency domains. Analytical results are compared with experimental data measured by NASA during sonic boom tests conducted at Edwards Air Force Base in 2007. The effects of wave signature parameters on transmission are studied to evaluate the advantages of various kinds of minimized boom shapes. [ABSTRACT FROM AUTHOR]

The development of a tunable, multiple degree of freedom (MDOF) electromechanical Helmholtz resonator (EMHR) is presented. An EMHR consists of an orifice, backing cavity, and a compliant piezoelectric composite diaphragm. Electromechanical tuning of the acoustic impedance is achieved via passive electrical networks shunted across the piezoceramic. For resistive and capacitive loads, the EMHR is a 2DOF system possessing one acoustic and one mechanical DOF. When inductive ladder networks are employed, multiple electrical DOF are added. The dynamics of the multi-energy domain system are modeled using lumped elements and are represented in an equivalent electrical circuit, which is used to analyze the tunable acoustic input impedance of the EMHR. The two-microphone method is used to measure the acoustic impedance of two EMHR designs with a variety of resistive, capacitive, and inductive shunts. For the first design, the data demonstrate that the tuning range of the second resonant frequency for an EMHR with non-inductive shunts is limited by short- and open-circuit conditions, while an inductive shunt results in a 3DOF system possessing an enhanced tuning range. The second design achieves stronger coupling between the Helmholtz resonator and the piezoelectric backplate, and both resonant frequencies can be tuned with different non-inductive loads. [ABSTRACT FROM AUTHOR]

This analysis is concerned with the derivation of a “diffuse field” reciprocity relationship between the diffuse field excitation of a connection to a structural or acoustic subsystem and the radiation impedance of the connection. Such a relationship has been derived previously for connections described by a single degree of freedom. In the present work it is shown that the diffuse–field reciprocity relationship also arises when describing the ensemble average response of connections to structural or acoustic subsystems with uncertain boundaries. Furthermore, it is shown that the existing diffuse–field reciprocity relationship can be extended to encompass connections that possess an arbitrary number of degrees of freedom. The present work has application to (i) the calculation of the diffuse field response of structural–acoustic systems modeled by Finite Elements, Boundary Elements, and Infinite Elements; (ii) the general calculation of the Coupling Loss Factors employed in Statistical Energy Analysis (SEA); and (iii) the derivation of an alternative analysis method for describing the dynamic interactions of coupled subsystems with uncertain boundaries (a generalized “boundary” approach to SEA). © 2005 Acoustical Society of America. [ABSTRACT FROM AUTHOR]

When the bulk and shear moduli of the mineral frame are set to zero, the full Biot theory of wave propagation in a porous medium such as a marine sediment reduces to Williams' "effective density fluid" (EDF) model [J. Acoust. Soc. Am. 110, 2276-2281 (2001)]. Although eight material variables appear in the EDF model, it is in fact tightly constrained, possessing just three degrees of freedom: the phase speeds in the limits of low and high frequency, c0 and c∞, respectively, and a transition frequency, fT, separating the low- and high-frequency regimes. In this paper, an algebraic approximation to the EDF model is formulated, which is termed the "modified viscous fluid" (MVF) model, involving only the three parameters (c0, c∞, fT). Expressions are developed for (c0, c∞, fT) in terms of the eight material properties; and a comparison of the MVF and EDF dispersion curves is performed, showing that they are essentially identical at all frequencies. Apart from its computational simplicity, the MVF model provides insight into the effect of each material parameter on the shape of the dispersion curves. For instance, the transition frequency scales as the ratio of the pore-fluid viscosity to the permeability, but neither the viscosity nor the permeability affects the limiting phase speeds c0 and c∞. [ABSTRACT FROM AUTHOR]

Estimating the direction of arrival of sound in three-dimensional space is typically performed by generalized time-delay processing on a set of signals from a fixed array of omnidirectional microphones. This requires specialized multichannel A/D hardware, and careful arrangement of the microphones into an array. This work is motivated by the desire to instead only use standard two-channel audio A/D hardware and portable equipment. To estimate direction of arrival of persistent sound, the position of the microphones is made variable by mounting them on one or more computer-controlled pan-and-tilt units. In this paper, we describe the signal processing and control algorithm of a device with two omnidirectional microphones on a fixed baseline and two rotational degrees of freedom. Experimental results with real data are reported with both impulsive and speech sounds in an untreated, normally reverberant indoor environment. [ABSTRACT FROM AUTHOR]