Paolo Gardonio

1 – Waves in Fluids and Solid Structures

To understand the process of acoustic interaction between solid structures and fluids, it is essential to appreciate the wave nature of responses of both media to time-dependent disturbances from equilibrium, whether these are transient or continuous. This chapter gives an introduction to the general mathematical description of unidirectional harmonic wave motion. Various forms and characteristics of the principal types of wave that are important in vibroacoustics are discussed in the chapter, along with their behaviors in a number of archetypal forms of structure. The chapter introduces the unified mathematical description of temporal and spatial distributions of wavefield variables and illustrates the forms of vibrational waves that travel in various ideal forms of structure, such as uniform beams, flat plates, and thin-walled, circular cylindrical shells. The phenomenon of wave dispersion that relates wave speed and frequency form the basis to categorize regimes of wave interaction at interfaces between different media and different forms of structure. The phenomena of natural frequencies and modes of bounded elastic systems and the related phenomenon of resonance are illustrated and explained in the chapter in terms of wave reflection and interference. The chapter provides a brief overview to probabilistic modeling of natural frequency distributions and related quantities that are employed in statistical energy analysis.

Transmission of Sound through Partitions

There are two main methods to inhibit the transmission of sound energy from one region of fluid to another. In the first, sound energy is absorbed in transit by materials that are specially chosen to accept energy efficiently from waves in the contiguous fluid, and then efficiently to dissipate it into heat. In the second, sound in transit is reflected by means of introducing a large change of acoustic impedance into transmission path. Many forms of sound transmission control system employ both methods in combination—for example, double-leaf partitions in buildings and sound insulation trim in vehicles. This chapter discusses the transmission of normally incident plane waves through an unbounded partition, the transmission of obliquely incident plane waves through an unbounded flexible partition, and the transmission of diffuse sound through a bounded partition in a baffle. The two principal factors that cause the diffuse-field transmission performance of a real, bounded panel in a rigid baffle to differ significantly from the theoretical performance of an unbounded partition include (1) the existence of standing-wave modes and associated resonance frequencies and (2) diffraction by the aperture in the baffle that contains the panel.

Sound Radiation by Vibrating Structures

Surfaces that vibrate in contact with fluids displace fluid volume at the interface. The time-average sound power radiated per unit area of a vibrating surface is equal to the time average of the product of surface pressure and normal particle velocity. The pressure at any point on a surface receives contributions from acoustic disturbances generated by the motion of all other points on the surface.This phenomenon of “mutual acoustic interaction” is one of the most important mechanisms that govern the effectiveness of sound radiation by vibrating surfaces. Sound radiation by the vibrational modes of baffled, flat plates is analyzed by using two different formulations: the first is based upon the representation of an array of elementary sources of fluid volume acceleration; the second is based upon the Fourier decomposition of surface vibration field in terms of spatially harmonic traveling waves. This chapter discusses the analysis of radiations by flat plates that are exerted by localized forces and the influence of nonuniformities, such as stiffeners, corrugations, and multi-layer composition. The radiation characteristics of circular cylindrical shells are then described in the chapter and their differences from those of flat plates are explained.

Introduction to Active Control of Sound radiation and Transmission

This chapter focuses on a new approach of actively controling sound radiation, which has emerged from previous work on active noise control. The basic idea behind this new technology is to modify or reduce the vibration of a radiating structure to diminish the radiated sound. Control schemes are classified into two main families: feed-forward and feedback control architectures. Single-input single-output control systems (SISO) have been extended to more complex multi-input multi-output (MIMO) controllers, which enable the implementation of control systems that can operate on complex multi-resonant systems. The chapter discusses the main features of the most common types of structural actuators and sensors. For the purpose of active control, mechanical vibrations is both generated and detected by strainTransducers—such as piezoelectric laminae or films—or generated by electrodynamic inertial actuators and detected by inertial sensors (accelerometers).The chapter presents an extensive and detailed review of the various stages that have brought the development of active noise control (ANC) systems into active structural acoustic (ASAC) systems and AVC systems for the control of sound radiation.

Introduction to Numerically Based Analyses of Fluid-Structure Interaction

The chapter discusses the vibration fields in solid structures and sound fields in fluids with the aim of providing tools for the vibroacoustic analysis of systems in which the two forms of field are coupled. The analysis of vibrations in structures and sound fields in closed or nearly closed volumes is most commonly accomplished by using finite element analysis (FEA). In FEA, the structure or fluid space are theoretically divided into contiguous elements of linear dimension that are substantially smaller than a structural or acoustic wavelength at the highest frequency of interest. It is also possible to apply finite difference analysis (FDA) to sound fields. The main practical problem with FDA in application to sound fields in volumes of arbitrary geometry is that it does not readily accommodate boundaries that do not conform to the grid line pattern. In addition, it is much more sensitive to local errors of field representation than FEA. The evaluation of the acoustic field generated by a vibrating surface in an infinitely extended volume of fluid is commonly accomplished by the application of boundary element analysis (BEA) to the evaluation of the field on the surface of radiator, through the approximate solution of the Kirchhoff–Helmholtz integral.

Structural Mobility, Impedance, Vibrational Energy and Power

This chapter discusses the concepts of structural impedance and mobility that characterize the response of beams, flat plates, and circular cylindrical shells to excitation by harmonic point forces. The mobility and impedance concepts refer to variables that can be measured. This feature helps analysts to build models that explicitly represent the physics of problems. They are very valuable in the design of experiments and in the interpretation of experimental results. “Modal approach” is used to derive mobility expressions for the finite beam. This approach is particularly suited for the study of distributed structures at low frequencies, where the response is determined by the superposition of responses of a few low frequency modes. The chapter illustrates the derivation of the mobility functions of both infinite and finite thin flat rectangular plates in bending. Small amplitude bending waves in a thin-flat plate are uncoupled from the in-plane longitudinal and shear waves to separately treat out of-plane vibrations. Complex networks of point-connected structural components are represented by matrix models that incorporate impedances or mobilities of the components at the connection points. Their application is illustrated by analysis of the flow of vibrational energy through a beam network. The chapter provides a brief analysis of wave energy propagation in beams and plates.

Fluid Loading of Vibrating Structures

Fluid loading refers to the force field that a fluid exerts on a vibrating structure with which it is in contact and its effects on the vibrational and acoustic behavior of the structure. This chapter discusses various methods of mathematical analysis of fluid loading and its effects on vibrating plate and cylindrical shell structures and sound radiation. The problem of evaluating the reaction forces (fluid loading) applied by a fluid to a vibrating body is discussed in the chapter. The concept of complex acoustic radiation impedance is illustrated in the chapter by some simple examples. The effects of fluid loading on the natural frequencies and sound radiation by point-excited plates and circular cylindrical shells are then described and illustrated in the chapter. The effect of fluid loading on the vibration and sound radiation of a thin-walled circular, cylindrical shell of finite length subject to point force excitation has been studied by using a series expansion of in-vacuo shell modes to represent the structural vibration field.