Abstract: Earphones and headphones, which are compact electro-acoustic transducers, tend to have a lot of acoustic absorption materials and porous materials known as dampers, which often have a large number of extremely small holes and narrow slits to inhibit the resonance of the vibrating system, because the air viscosity significantly affects the acoustic characteristics in such acoustic paths. In order to perform simulations using the finite element method (FEM), it is necessary to be aware of material characteristics such as the impedance and propagation constants of sound absorbing materials and porous materials. The transfer function is widely known as a measurement method for an acoustic tube with such physical properties, but literature describing the measurements at the upper limits of the audible range is yet to be found. The acoustic tube, which is a measurement instrument, must be made narrow, and the distance between the two sets of microphones must be shortened in order to take measurements of acoustic characteristics at higher frequencies. When such a tube is made narrow, however, the characteristic impedance has been observed to become lower than the impedance of air. This paper considers the cause of this phenomenon to be the effect of the air viscosity and describes an FEM analysis of an acoustic tube considering air viscosity to compare to the theoretical formula by including the effect of air viscosity in the theoretical formula for an acoustic tube.
Abstract: Headphones and earphones have many extremely small
holes or narrow slits; they use sound-absorbing or porous material (i.e.,
dampers) to suppress vibratory system resonance. The air viscosity in
these acoustic paths greatly affects the acoustic properties. Simulation
analyses such as the finite element method (FEM) therefore require
knowledge of the material properties of sound-absorbing or porous
materials, such as the characteristic impedance and propagation
constant. The transfer function method using acoustic tubes is a widely
known measuring method, but there is no literature on taking
measurements up to the audible range. To measure the acoustic
properties at high-range frequencies, the acoustic tubes that form the
measuring device need to be narrowed, and the distance between the
two microphones needs to be reduced. However, when the tubes are
narrowed, the characteristic impedance drops below the air impedance.
In this study, we considered the effect of air viscosity in an acoustical
tube, introduced a theoretical formula for this effect in the form of
complex density and complex sonic velocity, and verified the
theoretical formula. We also conducted an experiment and observed
the effect from air viscosity in the actual measurements.
Abstract: A numerical method is proposed to calculate damping
properties for sound-proof structures involving elastic body,
viscoelastic body, and porous media. For elastic and viscoelastic body
displacement is modeled using conventional finite elements including
complex modulus of elasticity. Both effective density and bulk
modulus have complex quantities to represent damped sound fields in
the porous media. Particle displacement in the porous media is
discretised using finite element method. Displacement vectors as
common unknown variables are solved under coupled condition
between elastic body, viscoelastic body and porous media. Further,
explicit expressions of modal loss factor for the mixed structures are
derived using asymptotic method. Eigenvalue analysis and frequency
responded were calculated for automotive test panel laminated
viscoelastic and porous structures using this technique, the results
almost agreed with the experimental results.
Abstract: Sound pathways in the enclosures of small earphones
are very narrow. In such narrow pathways, the speed of sound
propagation and the phase of sound waves change because of the air
viscosity. We have developed a new finite element method that
includes the effects of damping due to air viscosity for modeling the
sound pathway. This method is developed as an extension of the
existing finite element method for porous sound-absorbing materials.
The numerical calculation results using the proposed finite element
method are validated against the existing calculation methods.
Abstract: In very narrow pathways, the speed of sound propagation and the phase of sound waves change due to the air viscosity. We have developed a new finite element method (FEM) that includes the effects of air viscosity for modeling a narrow sound pathway. This method is developed as an extension of the existing FEM for porous sound-absorbing materials. The numerical calculation results for several three-dimensional slit models using the proposed FEM are validated against existing calculation methods.
Abstract: This paper describes dynamic analysis using proposed
fast finite element method for a shock absorbing structure including a
sponge. The structure is supported by nonlinear concentrated springs.
The restoring force of the spring has cubic nonlinearity and linear
hysteresis damping. To calculate damping properties for the structures
including elastic body and porous body, displacement vectors as
common unknown variable are solved under coupled condition. Under
small amplitude, we apply asymptotic method to complex eigenvalue
problem of this system to obtain modal parameters. And then
expressions of modal loss factor are derived approximately. This
approach was proposed by one of the authors previously. We call this
method as Modal Strain and Kinetic Energy Method (MSKE method).
Further, using the modal loss factors, the discretized equations in
physical coordinate are transformed into the nonlinear ordinary
coupled equations using normal coordinate corresponding to linear
natural modes. This transformation yields computation efficiency. As
a numerical example of a shock absorbing structures, we adopt double
skins with a sponge. The double skins are supported by nonlinear
concentrated springs. We clarify influences of amplitude of the input
force on nonlinear and chaotic responses.