Robert J. Bernhard

Mechanical energy flow models of rods and beams

Abstract It has been proposed that the flow of mechanical energy through a structural/acoustic system may be modeled in a manner similar to that of flow of thermal energy in a heat conduction problem [1]. If this hypothesis is true, it would result in relatively efficient numerical models of structure-borne energy in large built-up structures. Fewer parameters are required to approximate the energy solution than are required to model the characteristic wave behavior of structural vibration by using traditional displacement formulations. The energy flow hypothesis is tested in this investigation for both longitudinal vibration in rods and transverse flexural vibrations of beams. The rod is shown to behave approximately according to the thermal energy flow analogy. However, the beam solutions behave significantly differently than predicted by the thermal analogy unless locally space averaged energy and power are considered. Several techniques for coupling dissimilar rods and beams are also discussed. Illustrations of the solution accuracy of the methods are included.

Models of space-averaged energetics of plates

The analysis of high-frequency vibrations of plates is of particular interest for many cases of structure-borne noise in aircraft. The current methods of analysis are either too expensive (finite element method) or may have a confidence band wider than desirable (statistical energy analysis). An alternative technique to model the spaceand time-averaged response of structural acoustics problems with enough detail to include all significant mechanisms of energy generation, transmission, and absorption is highly desirable. The focus of this paper is the development of a set of equations that govern the space- and time-averaged energy density in plates. To solve this equation, a boundary value problem must be considered in terms of energy density variables using energy and intensity boundary conditions. A verification study of the energy governing equation is performed. A finite element formulation of the new equations is also implemented and several tests cases are analyzed and compared to analytical solutions. cg D E e 6j F [F] h / [K] [P] q q(x, w 17 v p

Review of numerical solutions for low-frequency structural-acoustic problems

Abstract Numerical methods for predicting the behavior of structural acoustic systems are becoming increasingly practical. In this paper, the theoretical basis of the most popular state-of-the-art numerical structural-acoustic analysis techniques, the finite element methods and boundary element methods, are described in general terms. Typical approximations are described to identify both the best utilization and the limitations of the methods. Models for cases of heavy and light fluid loading are discussed. The methods are compared to each other and to analytical methods. A comprehensive literature review is included for identification of more complete references describing the methods.

Prediction of sound fields in cavities using boundary element methods

Two boundary element formulations of acoustical behavior exist; the Direct Boundary Element Methods (DBEM) based on the Helmholtz Integral Equations and the Indirect Boundary Element Methods (IBEM) based on Huygens Principle. In this investigation, both methods are implemented utilizing a simple linear superparametric element. In addition the IBEM is studied using a quadratic isoparametric element. The accuracy and relative efficiency of the various techniques are examined. In order to properly model aircraft interior cavities the additional capability to model wall treatments and internal point sources is added to the methods. The procedures are verified for several well-understood cavity problems. The relative merits of each boundary element method and the finite element method are examined.

Robust feedback control of flow–induced structural radiation of sound.

A significant component of the interior noise of aircraft and automobiles is a result of the turbulent boundary layer excitation of the vehicular structure. In this investigation the feasibility of active control of wind noise is studied. Initial studies are made by considering the idealized case of sound radiation from a simply supported panel excited by a turbulent flow boundary layer. To study various control system alternatives, a wind noise model is developed. The model consists of a modal model of the excitation of a plate from a turbulent boundary layer, a model of plate vibrations, and a model of the sound radiated from the plate. A frequency‐domain approach, similar to quantitative feedback theory, is utilized in the design of a robust feedback controller. The controller utilizes plate acceleration feedback while maintaining sound‐pressure‐level reduction as the primary design objective. The design method insures that performance and control effort objectives are met for plant and disturbance unc...

A finite element method for synthesis of acoustical shapes

Abstract Classical finite element procedures are not well suited to the development of optimal acoustical shapes. Typical procedures require a complete analysis of each candidate acoustical geometry in the search for an optimal shape. This paper presents a method for decomposing the original finite element matrices into matrices which may be multiplied by shape change parameters to develop a model of the revised geometry. The method is also used to synthesize the geometry required for desired acoustical behavior of a complicated coupled cavity system.

Basics of Noise Generation for Pavement Engineers

This paper is intended as a brief basic primer on tire-pavement noise generation and measurement. It is particularly directed toward pavement and materials engineers who are aware that noise is an issue of concern to the public but have not been able to invest the time needed to investigate and learn about noise control fundamentals. This paper defines sound and noise, illustrates the publics growing awareness of noise issues, explains the units of measurement and measurement techniques, outlines some of the mechanisms of noise generation at the tire-pavement interface, and briefly discusses how pavements can help to mitigate noise problems. Significant progress has been made to reduce tire-pavement noise, and, with more applications and an increased understanding of noise generation and propagation, economical pavements are possible that control noise while maintaining safety and durability.

Controlled continuous tuning of an adaptively tunable vibration absorber incorporating shape memory alloys

Controlled continuous tuning of the stiffness of shape memory alloy (SMA) spring elements of an adaptively tunable vibration absorber (ATVA) is a novel concept for adaptive-passive vibration control. Minimization of the vibration of a primary system is achieved indirectly via stiffness control of the SMA structural elements supporting a secondary mass. Stiffness control is further achieved via the heating of the SMA elements. In this paper a control law to achieve phase- tracking by controlling the heating of the SMA elements is developed and implemented. Successful analytical and experimental results demonstrate the feasibility of continuous control of the SMA ATVA. Performance of the SMA ATVA is compared to the performance of comparable passive tuned vibration absorbers (TVA). The comparison shows that substantial improvements in vibration attenuation can be achieved through the implementation of the SMA ATVA.

An investigation of the modal characteristics of nonrectangular reverberation rooms

The finite element method is used to study the modal characteristics of a class of reverberation rooms with parallel floors and ceilings. Special numerical procedures are developed to express acoustic finite element matrices as functions of room shape and to reduce the computational requirements for room evaluation. The modal distribution function proposed by Louden [M. M. Louden, Acustica 24, 101–104 (1971)] is used to evaluate room performance. Two studies of rooms with one nonparallel wall illustrate the typical influence of room shape on the modal distribution in the room. A global optimization is attempted for a room with five independent shape variables. A solution 40% better than the best rectangular reverberation room was found using approximately 450 000 room evaluations.

A finite element procedure for design of cavity acoustical treatments

The design of acoustical treatments for small or close‐fitting cavity enclosures is significantly complicated by nearfield effects and standing wave behavior. In this article, the finite element method is used to model the acoustical behavior in such situations. Additional calculations are made to compute the sensitivity of certain acoustical design objective functions, particularly radiated power through apertures or total energy in the cavity, to certain design parameters, in this case, the reactance and resistance of the acoustical treatment materials. The sensitivity calculation results are used to identify which design parameters are most effective and which design philosophy most effectively improves the objective function. The article illustrates two examples of the application of the design sensitivity information to an automated design optimization.