Recent Development of the Fast Multipole Boundary Element Method for Modeling Acoustic Problems

Some recent development of the fast multipole boundary element method (BEM) for modeling acoustic wave problems in both 2-D and 3-D domains are presented in this paper. First, the fast multipole BEM formulation for 2-D acoustic wave problems based on a dual boundary integral equation (BIE) formulation is presented. Second, some improvements on the adaptive fast multipole BEM for 3-D acoustic wave problems based on the earlier work are introduced. The improvements include adaptive tree structures, error estimates for determining the numbers of expansion terms, refined interaction lists, and others in the fast multipole BEM. Examples involving 2-D and 3-D radiation and scattering problems solved by the developed 2-D and 3-D fast multipole BEM codes, respectively, will be presented. The accuracy and efficiency of the fast multipole BEM results clearly demonstrate the potentials of the fast multipole BEM for solving large-scale acoustic wave problems that are of practical significance.

Analysis of In-Plane Modal Characteristics of an Annular Disk With Multiple Point Supports

In-plane free vibrations of an isotropic, elastic annular disk constrained at some points on the inner and outer boundaries are investigated. The presented study is relevant to various practical problems including disks clamped by bolts along the inner and outer edges or the railway wheel vibrations. The boundary characteristic orthogonal polynomials are employed in the Rayleigh-Ritz method to obtain the frequency parameters and the associated mode shapes. The boundary characteristic orthogonal polynomials are generated for the free boundary conditions of the disk while artificial springs are used to realize clamped conditions at discrete points. The frequency parameters for different point constraint conditions are evaluated and compared with those computed from a finite element model to demonstrate the validity of the proposed method. The computed mode shapes are presented for a disk with different point constraints at the inner and outer boundaries to demonstrate the free in-plane vibration behavior of the disk. Results show that addition of point supports causes some of the modes to split into two different frequencies with different mode shapes. The effects of different orientations of multiple point supports on the frequency parameters and mode shapes are also discussed.

Tunable Band Gaps of Acoustic Waves in Two-Dimensional Phononic Crystals With Reticular Band Structures

The excellent applications and researches of so-called photonic crystals raise the exciting researches of phononic crystals. By the analogy between photon and phonon, repetitive composite structures that are made up of different elastic materials can also prevent elastic waves of some certain frequencies from passing by, i.e., the frequency band gap features also exist in acoustic waves. In this paper, we present the results of the tunable band gaps of acoustic waves in two-dimensional phononic crystals with reticular band structures using the finite element method. Band gaps variations of the bulk modes due to different thickness and angles of reticular band structures are calculated and discussed. The results show that the total elastic band gaps for mixed polarization modes can be enlarged or reduced by adjusting the orientation of the reticular band structures. The phenomena of band gaps of elastic or acoustic waves can potentially be utilized for vibration-free, high-precision mechanical systems, and sound insulation.

Multidisciplinary Optimization of a Car Component Under NVH and Weight Constraints Using RSM

One of the important challenges in the auto industry is to reduce the mass of the vehicle while meeting structural performance requirements for Crashworthiness, Noise, Vibration and Harshness (NVH) etc. In this paper, a multidisciplinary optimization (MDO) of a car back-bonnet is investigated by using the Response Surface Method (RSM). Firstly, a car body is fully surface modeled in CATIA and meshed in HYPERMESH software. Then, modal analysis of the finite element model is performed by NASTRAN software to find natural frequencies. Frequency map of that component is extracted and compared with a reference map to detect defects. Design of Experiments (DOE) methodologies is used for a screening of the design space and for the generation of approximation models using RSM techniques. Therefore, to optimize the model, improvement of the NVH behavior and minimization of the weight are imposed.

Generating Near-THz Surface Acoustic Waves Using Picosecond Ultrasonics

We present here a technique to generate high frequency SAW in non-piezoelectric substrate with nanostructure grating of period less than 100 nm fabricated on it. A short pulse laser (with rise time less than 100fs) incident on this structure creates a periodic thermal stress due to the differential absorption in the substrate and the grating. We show that this stress sets up a surface acoustic wave on the substrate that can be detected optically. Modeling the generation process and analysis of SAW spectrum reveals the critical parameters to be controlled for obtaining SAW of high frequency. We show that the grating period less than 50 nm, a laser pulse of rise time less than 100fs and substrate properties like high optical absorption and high Rayleigh velocity are necessary for generating surface acoustic waves in near-THz range. This work provides quantitative guidelines on the design of near THz phononics.

Nonlinear Dynamic of Cantilever Functionally Graded Plates Under the Thermalmechanical Loads

An analysis on nonlinear dynamic of a cantilevered functionally graded materials (FGM) plate which subjected to the transverse excitation in the uniform thermal environment is presented for the first time. Materials properties of the constituents are graded in the thickness direction according to a power-law distribution and assumed to be temperature dependent. In the framework of the Third-order shear deformation plate theory, the nonlinear governing equations of motion for the functionally graded materials plate are derived by using the Hamilton’s principle. For cantilever rectangular plate, the first two vibration mode shapes that satisfy the boundary conditions is given. The Galerkin’s method is utilized to discretize the governing equations of motion to a two-degree-of-freedom nonlinear system under combined thermal and external excitations. By using the numerical method, the two-degree-of-freedom nonlinear system is analyzed to find the nonlinear responses of the cantilever FGMs plate. The influences of the thermal environments on the nonlinear dynamic response of the cantilevered FGM plate are discussed in detail through a parametric study.

Decision-Making Under Model Uncertainty of Damaged Aircraft Systems

When in-flight failures occur, rapid and precise decision-making under imprecise information is required in order to regain and maintain control of the aircraft. To achieve planned aircraft trajectory and complete landing safely, the uncertainties in vehicle parameters of the damaged aircraft need to be learned and incorporated at the level of motion planning. Uncertainty is a very important concern in recovery of damaged aircraft since it can cause false diagnosis and prognosis that may lead to further performance degradation and mission failure. The mathematical and statistical approaches to analyzing uncertainty are first presented. The damaged aircraft is simulated via a simplified kinematics model. The different sources and perspectives of uncertainties under a damage assessment process and post-failure trajectory planning are presented and classified. The decision-making process for an emergency motion planning to landing site is developed via the Dempster-Shafer evidence theory. The objective of the trajectory planning is to arrive at a target position while maximizing the safety of the aircraft under uncertain conditions. Simulations are presented for an emergency motion planning and landing that takes into account aircraft dynamics, path complexity, distance to landing site, runway characteristics, and subjective human decision.

Badge-Type Noise Dosimeters Used in the Mining Industry

Currently, a number of manufacturers have developed and made commercially available badge-type (cordless) noise dosimeters. Previous studies conducted by the Mine Safety and Health Administration (MSHA) revealed that microphone size and placement/orientation significantly influence measurement error. The badge-type design houses the microphone within a significantly larger casing than does the traditional corded-type dosimeter. This presents concern that badge-type designs may significantly inhibit measurement accuracy. The purpose of this study is to evaluate the casing of various badge-type dosimeters in order to discern conditions and assess the extent to which the badge-type design contributes toward measurement error in comparison with the traditionally used corded dosimeter. For this, a series of laboratory measurements were conducted employing various commercially available badge-type casings and corded counterparts. Corresponding results are summarized and extended to conclusions regarding the effect of microphone casing design, badge-type versus corded, on measurement accuracy for personal noise dosimetry.

Preliminary NVH Characterization of Metal Foam-Polymer Interpenetrating Phase Composites

The damping and basic dynamic properties of a novel type of multifunctional hybrid material known as Metal Foam-Polymer Composite are investigated. This material is obtained by injection molding a thermoplastic polymer through an open cell Aluminum Foam, in essence creating two contiguous morphologies; an Aluminum Foam interconnected “skeleton” with the open pores filled with a similarly interconnected polymer substructure. This coexistence of both materials allows each to contribute its salient properties (e.g. the plastics contributing surface toughness and the metal foams contributing thermal stability). Basic damping testing results are presented for various Aluminum Foam porosities and pore sizes as well as for three types of polymers. A basic mathematical model of the damping is also presented. The integrity of the interface between the Aluminum Foam and the Polymer is discussed in terms of its effect on the overall material damping.

An Experimental Investigation on the Bridge Effect in Sound Produced by Setar

This study aims to evaluate the amount of energy transfers through the bridge in Setar, a Persian long-necked lute. Stringed musical instruments are among the most complicated acoustical systems. When the string is plucked, its vibration distributes into the entire vibrating system (i.e. body, string, air enclosure) and produces sound. The resultant sound consists of three parts: the first is the string’s direct sound; the second is that part of sound-box vibration being excited by string’s direct sound, and the third is the part of sound-box vibration being excited by string force passing through bridge. The last part believed to have the major share and the others have minor effect. For this research, a specific fixture has been made and a precise plucking machine is installed to hold and pluck the instrument uniformly. Also, a novel approach is utilized to evaluate the share of each abovementioned part in the output near-field sound produced by Setar.