CN102930068B - A kind of equivalent-circuit model of structural acoustical coupling - Google Patents

Abstract

A kind of equivalent-circuit model of structural acoustical coupling, be made up of coupling operatic tunes subsystem and coupling elasticity panel subsystem, coupling operatic tunes subsystem is encouraged by Generalized Source and adjustable parallel circuit forms, wherein Generalized Source excitation represents with constant current source parallel with one another, in adjustable parallel circuit, to be resistance be is not coupled the fixed resistance of glottis neoplasms impedance for branch road, the adjustable resistance of another branch road to be resistance be coupled structure modal mobility inverse; Coupling elasticity panel subsystem is encouraged by generalized force and adjustable parallel circuit forms, wherein generalized force excitation represents with the constant pressure source of mutually connecting, the fixed resistance of branch road to be resistance be non-coupled structure modal mobility in adjustable parallel circuit, the adjustable resistance of another branch road to be resistance be coupling glottis neoplasms inverse impedance.Can calculate the natural frequency of coupling plate, chamber system by this model, convenient analytic system coupling mechanism intuitively and the factor affecting degree of coupling, be conducive to analysis and optimal design that project planner carries out structural-acoustic problem.

Description

A kind of equivalent-circuit model of structural acoustical coupling

Technical field

The present invention relates to the equivalent-circuit model of structural acoustical coupling, belong to acoustic engineering technical field.

Background technology

The Acoustic Radiation Problems caused by the vibration of elastic plate class formation is the important subject of associated acoustic engineering field always.Elastic plate closed cavity structure is widely used in Practical Project field, as vehicle, boats and ships, aircraft take cabin etc., the sound radiation of its elastic plate class formation is one of Main Noise Sources in cabin.Along with improving constantly of requiring riding comfort, in cabin, Noise measarement and acoustic design more and more cause the attention of people, and are the keys of carrying out Noise measarement and acoustic design to the research of cabin structure-acoustic coupling characteristic.For this problem, the people such as Kim in 1999 analyze structural-acoustic problem by impedance and admittance method on the basis that forefathers study, but its theoretical model proposed is not directly perceived, the inconvenient factor to system, coupled characteristic and influential system degree of coupling does concrete research.Cavity structure-acoustic coupling system simulation becomes the feedback in control theory and feedforward system to analyze its coupled characteristic by domestic Jin Guoyong etc., but the physical significance of each key element is unclear in model, and cannot by key parameters such as the natural frequencys of elastic plate and the operatic tunes after this analog computation coupling, this limits the application of this model to a certain extent.

Summary of the invention

For said structure-acoustic coupling analytical approach and model Problems existing, the present invention proposes that a kind of convenience is directly perceived, explicit physical meaning, the structural acoustical coupling equivalent-circuit model that has wide range of applications.

For achieving the above object, the equivalent-circuit model of a kind of structural acoustical coupling involved in the present invention, be made up of coupling operatic tunes subsystem and coupling elasticity panel subsystem, coupling operatic tunes subsystem is encouraged by Generalized Source and adjustable parallel circuit forms, wherein Generalized Source excitation represents with constant current source parallel with one another, adjustable parallel circuit is made up of two branch roads, article one, to be resistance be branch road is not coupled the fixed resistance of glottis neoplasms impedance, the adjustable resistance of another branch road to be resistance be coupled structure modal mobility inverse; Coupling elasticity panel subsystem is encouraged by generalized force and adjustable parallel circuit forms, wherein generalized force excitation represents with the constant pressure source of mutually connecting, adjustable parallel circuit is made up of two branch roads,, a fixed resistance for branch road to be resistance be non-coupled structure modal mobility, the adjustable resistance of another branch road to be resistance be coupling glottis neoplasms inverse impedance, in the operatic tunes, pressure response is expressed as the terminal voltage of parallel resistance, and elastic plate modal response is expressed as the total current flowing through parallel resistance.

The glottis neoplasms impedance be not coupled in such scheme is:

$Z_{an}\left(\mathrm{\ω}\right)=\frac{{\mathrm{\ρ}}_0{c}_0^2}{V}\left(\frac{j\mathrm{\ω}}{{\mathrm{\ω}}_n^2-{\mathrm{\ω}}^2+2{\mathrm{j\ω\ω}}_n{\mathrm{\ζ}}_n}\right)=\frac{{\mathrm{\ρ}}_0{c}_0^2}{V}{H}_n\left(\mathrm{\ω}\right)---\left(1\right)$

The structural modal admittance be not coupled is:

$Y_{sm}\left(\mathrm{\ω}\right)=\frac{1}{{\mathrm{\ρS}}_f}\left(\frac{j\mathrm{\ω}}{{\mathrm{\ω}}_m^2-{\mathrm{\ω}}^2+2{\mathrm{j\ξ}}_m{\mathrm{\ω}}_m\mathrm{\ω}}\right)---\left(2\right)$

Wherein ρ, S _fbe respectively surface density and the area of elastic plate, V is enclosure volume; ω _m, ω _nbe respectively the m rank of structure and the operatic tunes, the n-th rank natural frequency, ξ _m, ζ _nbe respectively the m rank of structure harmony pressing mold state, the n-th rank damping factor, c ₀and ρ ₀be respectively velocity of sound when acoustic medium is in equilibrium state and density, H _n(ω) be the glottis neoplasms resonance factor.

The glottis neoplasms impedance of coupling is Z _ca=CZ _ac ^t, the structural modal admittance of coupling is Y _cs=CY _sc ^t, wherein C is coupling coefficient matrix.

The equivalent-circuit model of the structural acoustical coupling that the present invention proposes, not by the restriction of spring plate material character harmony cavity shape, the natural frequency of the rear elastic plate of coupling and the operatic tunes can be calculated by this model, and the influence factor of analytic system coupling mechanism and decision systems degree of coupling intuitively can be facilitated, be conducive to analysis and acoustics optimal design that project planner carries out heterogeneity plate structure enclosure space structural-acoustic problem.

Accompanying drawing explanation

Fig. 1 is the equivalent-circuit model of coupling operatic tunes subsystem.

Fig. 2 is the equivalent-circuit model of coupling elasticity panel subsystem.

Embodiment

Below in conjunction with accompanying drawing and example, the present invention will be further described.

In the arbitrary shape operatic tunes, acoustic pressure and structural modal respond the calculating of available following formula:

P＝(I+Z _aY _cs) ^-1Z _a(q+CY _sf+CY _sp)(3)

V＝(I+Y _sZ _ca) ^-1Y _s(f+p-C ^TZ _aq)(4)

Wherein P, V are respectively the structural modal amplitude of acoustic pressure and elastic plate in chamber; C is coupling coefficient matrix; F is the generalized Modal power acting on sandwich plate; P is structure-sound border surface acoustic pressure; Q is the broad sense strength of sound source in the operatic tunes; I is unit matrix, Z _a, Y _sbe respectively the glottis neoplasms impedance matrix and structural modal admittance matrix that are not coupled.

As can be seen from formula (3) and (4), the operatic tunes, the structural response of coupled system can be divided into two parts: front portion (I+Z _ay _cs) ^-1z _a(I+Y _sz _ca) ^-1y represents the inherent characteristic of the rear operatic tunes of coupling and elastic plate system respectively, also therefore determines the frequency response characteristic of system; Rear portion (q+CY _sf+CY _sp) with (f+p-C ^tz _aq) be respectively the generalized force vector of the Generalized Source vector sum elastic plate of the coupling operatic tunes, they do not determine to be coupled after the inherent characteristic of the operatic tunes and elastic plate system, and only the broad sense of representative system encourages.

The coupled characteristic of system can be analyzed by adjustable parallel circuit.The coupling block diagram of the operatic tunes and elastic plate can be expressed as Fig. 1 and Fig. 2.In figure, each Generalized Source excitation of operatic tunes system represents with constant current source parallel with one another respectively, and their sums form the overall Generalized Source excitation of operatic tunes system; Each generalized force excitation of elastic plate system represents with the constant pressure source of series connection mutually respectively, and their sums form the overall generalized force excitation of elastic plate system; The glottis neoplasms impedance be not coupled and the structural modal admittance be not coupled represent with the resistance of fixed resistance value respectively, and the inverse of the Reciprocals sums coupled structure modal mobility of the glottis neoplasms impedance that is coupled represents with adjustable resistance respectively; In the operatic tunes, pressure response is expressed as the terminal voltage of parallel resistance, and the structural modal response of elastic plate is then expressed as the total current flowing through parallel resistance.

From Fig. 1,2, due to the existence of adjustable resistance branch road in parallel, the natural frequency of system and frequency response will with Y _cs, Z _cachange and change, wherein Y _csdetermine the Generalized Source intensity size that the elastic surface caused by the operatic tunes-structural response acts on the operatic tunes; And Z _cathen determine and respond by structure-operatic tunes the size acting on the generalized force of sandwich plate caused.Parallel resistance value is larger, i.e. Y _cs, Z _caless, then coupling is more weak, and the impact that system inherent characteristic is subject to is less; Otherwise parallel resistance value is less, i.e. Y _cs, Z _calarger, then coupling is stronger, and the impact that system inherent characteristic is subject to is larger.

Next from the influence factor of the degree of coupling of the angle analysis whole system of coupled system structure, physical parameter and coupling terms.Make the impact of adjustable parallel branch on parallel resistance value of system less if systematic parameter changes, i.e. Z _a≈ 0, Y _s≈ 0 or Y _cs≈ 0, Z _ca≈ 0, so that 1/Y _cs→ ∞ or 1/Z _ca→ ∞, makes coupling terms Z _ay _cs≈ 0, Y _sz _ca≈ 0, then adjustable parallel branch can be similar to by open circuit process, and now system is just weakly coupled system.

After coupling, the natural frequency available loop resulting impedance of the operatic tunes and elastic plate system calculates.

The loop resulting impedance of the coupling operatic tunes is:

$Z=\frac{Z_a}{1+Z_a{Y}_{cs}}=\frac{1}{\frac{1}{Z_a}+\frac{1}{1/Y_{cs}}}---\left(5\right)$

When be coupled after the operatic tunes system resonance time, spectrogram parameter amplitude should be tending towards infinite, then loop resulting impedance should level off to infinite, at this moment has:

$\frac{1}{Z_a}=-Y_{cs}---\left(6\right)$

By formula (1) and Y _cs=CY _sc ^tsubstitution formula (6), ignores damping term, then after coupling, the natural frequency of operatic tunes system can be estimated with following formula:

${\mathrm{\ω}}_n^2-{\mathrm{\ω}}^2+\mathrm{\ω}\mathrm{Im}\[\underset{m=1}{\overset{M}{\Σ}}{C}_{n,m}{C}_{n,m}{Y}_{sm}({\mathrm{\ρ}}_0{c}_0^2/V)\]=0---\left(7\right)$

In like manner, when be coupled after elastic plate system resonance time, plate modal amplitudes should be tending towards infinite, and loop resulting impedance levels off to zero, at this moment has:

$\frac{1}{Y_s}=-Z_{ca}---\left(8\right)$

By formula (2) and Z _ca=CZ _ac ^tsubstitution formula (8), ignores damping term, then after coupling, the natural frequency of elastic plate system can be estimated with following formula:

${\mathrm{\ω}}_m^2-{\mathrm{\ω}}^2+\mathrm{\ω}\mathrm{Im}\[\underset{n=1}{\overset{N}{\Σ}}{C}_{n,m}{C}_{n,m}{Z}_{an}/\left({\mathrm{\ρS}}_f\right)\]=0---\left(9\right)$

Utilize this model identical with the result that the paper " the structural-acoustic specificity analysis of elastic plate enclosure " that the people such as Jin Guoyong deliver on " acoustic journal " the 32nd volume the 2nd phase in 2007 draws with (9) to the calculating formula (7) of coupled system natural frequency, illustrate that the model utilizing the present invention to propose can be used for calculating the natural frequency of the rear elastic plate of coupling and the operatic tunes, and the influence factor of analytic system coupling mechanism and decision systems degree of coupling intuitively can be facilitated.

Claims (1)

1. the equivalent-circuit model of a structural acoustical coupling, be made up of coupling operatic tunes subsystem and coupling elasticity panel subsystem, it is characterized in that: coupling operatic tunes subsystem is encouraged by Generalized Source and adjustable parallel circuit forms, wherein Generalized Source excitation represents with constant current source parallel with one another, adjustable parallel circuit is made up of two branch roads, article one, to be resistance be branch road is not coupled the fixed resistance of glottis neoplasms impedance, the adjustable resistance of another branch road to be resistance be coupled structure modal mobility inverse; Coupling elasticity panel subsystem is encouraged by generalized force and adjustable parallel circuit forms, wherein generalized force excitation represents with the constant pressure source of mutually connecting, adjustable parallel circuit is made up of two branch roads,, a fixed resistance for branch road to be resistance be non-coupled structure modal mobility, the adjustable resistance of another branch road to be resistance be coupling glottis neoplasms inverse impedance;

The glottis neoplasms impedance be not coupled is:

$Z_{an}\left(\mathrm{\ω}\right)=\frac{{\mathrm{\ρ}}_0{c}_0^2}{V}\left(\frac{j\mathrm{\ω}}{{\mathrm{\ω}}_n^2-{\mathrm{\ω}}^2+2{\mathrm{j\ω\ω}}_n{\mathrm{\ζ}}_n}\right)=\frac{{\mathrm{\ρ}}_0{c}_0^2}{V}{H}_n\left(\mathrm{\ω}\right)---\left(1\right)$

The structural modal admittance be not coupled is:

$Y_{sm}\left(\mathrm{\ω}\right)=\frac{1}{{\mathrm{\ρS}}_f}\left(\frac{j\mathrm{\ω}}{{\mathrm{\ω}}_m^2-{\mathrm{\ω}}^2+2{\mathrm{j\ξ}}_m{\mathrm{\ω}}_m\mathrm{\ω}}\right)---\left(2\right)$

Wherein: ω _m, ω _nbe respectively the m rank of structure and the operatic tunes, the n-th rank natural frequency, V is operatic tunes volume, S _ffor the area of elastic plate, ρ is the surface density of elastic plate, ξ _m, ζ _nbe respectively the m rank of structure harmony pressing mold state, the n-th rank damping factor, c ₀and ρ ₀be respectively velocity of sound when acoustic medium is in equilibrium state and density, H _n(ω) be the glottis neoplasms resonance factor; The glottis neoplasms impedance of coupling is Z _ca=CZ _ac ^t, the structural modal admittance of coupling is Y _cs=CY _sc ^t, wherein C is coupling coefficient matrix;

When be coupled after the operatic tunes system resonance time: by formula (1) and Y _cs=CY _sc ^tsubstitute into in, ignore damping term, then coupling after operatic tunes system natural frequency can with " ${\mathrm{\ω}}_n^2-{\mathrm{\ω}}^2+\mathrm{\ω}\mathrm{Im}\[\underset{m=1}{\overset{M}{\Σ}}{C}_{n,m}{X}_{n,m}{Y}_{sm}({\mathrm{\ρ}}_0{c}_0^2/V)\]=0$ " estimate.