Svante Finnveden

A super-spectral finite element method for sound transmission in waveguides

A super-spectral finite element method is developed for the study of acoustical wave propagation in nonuniform waveguides. The formulation is based on a finite-element approach using a mixture of high order element shape functions and wave solutions. The numerical method provides solutions to acoustic duct or fluid waveguide environments which may be divided into rectangular sectors. Examples of its use for infinite acoustic waveguides include sound transmission through large ambient density variations and propagation over a geometric stair-step perturbation. Computation of a trapped mode waveform due to a point volume source within a uniform waveguide is also presented.

Wave propagation in sandwich panels with a poroelastic core

Wave propagation in sandwich panels with a poroelastic core, which is modeled by Biots theory, is investigated using the waveguide finite element method. A waveguide poroelastic element is developed based on a displacement-pressure weak form. The dispersion curves of the sandwich panel are first identified as propagating or evanescent waves by varying the damping in the panel, and wave characteristics are analyzed by examining their motions. The energy distributions are calculated to identify the dominant motions. Simplified analytical models are also devised to show the main physics of the corresponding waves. This wave propagation analysis provides insight into the vibro-acoustic behavior of sandwich panels lined with elastic porous materials.

The boundary condition for a free surface with gravity waves formulated as a locally reacting surface impedance

The boundary condition for a free surface with gravity waves formulated as a locally reacting surface impedance

UNIFORM RADIATION CONDITIONS FOR A SOUND PROPAGATION MODEL

In this work, a new set of uniform radiation boundary conditions for a half-space model are derived and applied to a fundamental problem in outdoor sound propagation. This original approach derived here relies upon a high-order family of local radiation boundary conditions related to plane wave reflection coefficients. Validity of the approximation is carried out by examining sound propagation above an impedance ground using a spectral finite element method. This is followed by computational results verified against an analytic solution for sound propagation over hard ground. Finally, the case of sound propagation above a grass-strip surrounded by rigid ground and a rigid-strip in a grassland environment with atmospheric profiles are studied.

Sound propagation over inhomogeneous ground including a sound velocity profile

The atmospheric profile whose sound speed varies linearly with height is simple in concept, but leads to complications when solving for the sound pressure. Its effects are commonly approximated by a similar profile whose squared refractive index is a linear function of height. In this paper, the validity of the approximation has been examined for sound propagation above an impedance ground and a computational approximation is given. The method relies upon a family of radiation boundary conditions for the wave equation derived by truncating a summation function approximation of a corresponding plane wave reflection coefficient representation. It is demonstrated how these boundary conditions can be formulated in terms of a finite element approach. Numerical examples illustrate results with four coefficients included at the upper fictitious boundary conditions for the case of sound propagation above a grass‐strip and sound propagation over the grass‐strip with an atmospheric profile.

Statistical energy analysis of two spring‐coupled oscillators

The response of two spring‐coupled oscillators is investigated to develop our understanding of the weak coupling assumption in the modal approach to statistical energy analysis (SEA). The oscillators have stochastic uncoupled resonance frequencies that are normal distributed. For this case, the SEA coupling power proportionality holds for the ensemble average response, even for single frequency excitation, provided that a suitable definition of modal energy is adopted. It is seen that strength of coupling, from an ensemble point of view, is defined by the nondimensional ‘‘interaction strength.’’ This quantity may, for multi‐modal systems, be interpreted as the ratio of the SEA conductivety to the product of the modal overlaps in each element, in which case the strength of the coupling measure agrees with the one that previously was found to govern the ensemble‐averaged energies in one‐dimensional wave guide systems.

Estimates of dynamic strain and stress in pipes by measured average vibration velocity

A velocity method for estimating dynamic strain and stress in pipe structures is investigated. With this method predicted or measured spatial average vibration velocity and theoretically derived strain factors are used to estimate maximum strain. The nondimensional strain factor is defined as the maximum strain times the ratio of the sound velocity to the spatial rms vibration velocity. Measurements are made confirming that this is a descriptive number. Using a spectral finite‐element method, numerical experiments are made varying the pipe parameters and considering all 16 possible homogeneous boundary conditions. While indicating possible limitations of the method when equipment is mounted on pipes, the experiments verify the theoretical results. The velocity method may become useful in engineering practice for assessments of fatigue life.