CN102510548B - Output adjustment method for sound energy obtained by sound wave interaction in nonlinear medium - Google Patents

Abstract

The invention provides an output adjustment method for sound energy obtained by sound wave interaction in a nonlinear medium. The output adjustment method comprises the following steps of: (a) performing nonlinear interaction on a pump wave with the frequency of w3 and a weak signal wave with the frequency of omega1, and generating a resonance wave with the frequency of omega2; (b) respectively calculating amplitude values B1(x), B2(x) and B3(x) of the three waves at the displacement x after interaction according to the frequencies omega3, omega1 and omega2 of the pump wave, the weak signal wave and the resonance wave; and (c) adjusting the output energy of the three waves according to the change characteristics of the amplitude values B1(x), B2(x) and B3(x) of the pump wave, the weak signal wave and the resonance wave. According to the output adjustment method, the energy of the generated sound wave is changed according to a pulse rule on the basis of a basic theory of interaction of sound waves in optics and hydroacoustics; therefore, the output energy of each wave can be adjusted according to actual requirements.

Description

The output adjusting method of acoustic energy after sound wave interaction in nonlinear dielectric

Technical field

The present invention relates to sound wave nonlinear interaction field, relate in particular to the interactional output adjusting method of nonlinear parameter between sound wave.

Background technology

Since begin proposing to utilize the nonlinear interaction formation parametric array concept of sound and sound from nineteen sixty Vista Wei Er JP, the development of nonlinear acoustics is more and more faster, applies more and more extensivelyr, and its research and application obtained to a lot of new progresses.The nonlinear interaction of underwater acoustic wave can be thought to have formed variable element reflector or variable element receiver in interaction zone.The concept of variable element interaction process is born in the study of radio, while its essence is electric capacity in certain oscillating circuit or the variation of inductance generating period, just can make ultra-weak electronic signal occur amplifying or weakening.Between sound wave, occur in the process of nonlinear interaction, the parametric interaction problem is occupied extremely important status.In the process of acoustic wave energy transmission, what play the role of a nucleus is to induce diffusion process, makes weak signal ripple and pump wave interaction produce each order harmonics simultaneously, show as the unsteadiness of applicator quantum splitting, the vibration of ripple, the transfer of spectrum energy etc., but observe law of conservation of energy in interaction process.The interactional condition of nonlinear parameter occurs being medium between sound wave, to have one of strong non-linear or interactional sound wave be high-power sound wave, can exciting media non-linear, this sound wave can low-frequency sound wave can be also low-frequency sound wave.Existing a lot of scholar's research the parametric interaction problem of sound wave, Fenlon utilizes fourier progression expanding method, has provided the form of expression of each frequency content after a plurality of large amplitude simple harmonic quantity sound wave interactions.The Fenlon theory take in prior art as basis, studied the inhibition of good amplitude wave to sound wave in the air dielectric, the also research to the scale-up problem of smooth sea relevant for good amplitude wave.Utilize in addition two hyperacoustic nonlinear interaction theories in spectral factorization method research aqueous medium, the variation of low frequency wave energy has been discussed.Do not generate ω after interacting about the sound wave variable element ₂after new sound field three row magnitudes of acoustic waves with the variation characteristic of distance and frequency, acoustic wave energy the energy transfer process with propagation distance and frequency change.

Summary of the invention

The object of the present invention is to provide in a kind of nonlinear dielectric of the output energy that can regulate according to actual needs each train wave the output adjusting method of acoustic energy after sound wave interaction.

The object of the present invention is achieved like this:

Comprise the following steps:

(a) frequency is ω ₃pump ripple and frequency be ω ₁weak signal ripple generation nonlinear interaction, the generation frequency is ω ₂resonance wave;

(b) according to described pump ripple, weak signal ripple and resonance wave frequency ω ₃, ω ₁and ω ₂, calculate respectively the amplitude B at three train wave displacement x places afterwards that interacts ₁(x), B ₂and B (x) ₃(x);

(c) according to the pump wave amplitude B obtained ₃(x), weak signal wave amplitude B ₁and resonance wave amplitude B (x) ₂(x) Variation Features is realized the output energy adjustment to three train waves.

The present invention can also comprise:

1, described resonance wave is and frequency resonance wave or difference frequency resonance wave, i.e. ω ₂=ω ₁+ ω ₃perhaps ω ₂=ω ₃-ω ₁.

2, the amplitude B at described calculating three train wave displacement x places ₁(x), B ₂and B (x) ₃(x) method is:

Step (b1) is interactional Burgers (Burgers) equation in nonlinear dielectric according to pump ripple and weak signal ripple, calculates and obtains at the sound wave vibration velocity v of displacement x place (x);

The sound wave vibration velocity v (x) that step (b2) obtains according to step (b1), calculating obtains the wave amplitude equation after three row sound wave interactions;

Three train waves after step (b3) is interacted by wave amplitude equation calculating acquisition are at the amplitude B at displacement x place ₁(x), B ₂and B (x) ₃(x).

3, described Burgers (Burgers) equation is:

$\frac{\&PartialD;v}{\&PartialD;x}-\frac{\mathrm{\&beta;}}{{\mathrm{<figure-callout\; id="0"\; label="c"\; filenames="HDA0000099677340000011.png,HDA0000099677340000021.png"\; state="\{\{state\}\}">c</figure-callout>}}_0^2}v\frac{\&PartialD;v}{\&PartialD;\mathrm{\&tau;}}=\frac{b}{2{\mathrm{<figure-callout\; id="0"\; label="c"\; filenames="HDA0000099677340000011.png,HDA0000099677340000021.png"\; state="\{\{state\}\}">c</figure-callout>}}_0^2{\mathrm{\&rho;}}_0}\frac{{\&PartialD;}^{2}v}{{\&PartialD;\mathrm{\&tau;}}^2}$

Wherein, v is sound wave vibration velocity, β=1+B/2A, and the nonlinear parameter that B/A is medium, be the ratio of quadratic term coefficient and linear coefficient in the state equation taylor series expansion, it is the basic parameter of nonlinear acoustics, c ₀for the static velocity of sound, ρ ₀for the density of nonlinear dielectric, τ=t-x/c ₀for time delay, x is measuring distance.B is the medium coefficient of viscosity,

ζ is for cutting the coefficient of viscosity, and η is bulk viscosity,

for temperature conductivity coefficient, c _v, c _pfor electric capacity specific heat and voltage specific heat;

The sine wave that sound source sends at the x=0 place, calculate acquisition and be expressed as at the sound wave vibration velocity v of displacement x place (x):

$v(x,t)=\underset{n=\mathrm{1,2,3}}{\mathrm{\&Sigma;}}{A}_n\left(x\right)\exp \left(i{\mathrm{\&omega;}}_n(t-\frac{x}{c_0})\right)+c$

Wherein, A ₁(x), A ₂(x), A ₃(x) be the complex amplitude of three row sound waves, c is constant.

4, nonlinear dielectric is water.

5, the wave amplitude equation after three row sound wave interactions:

$\left\{\begin{array}{c}\frac{d{A}_1\left(x\right)}{\mathrm{dx}}+{\mathrm{\&delta;}}_1{A}_1\left(x\right)=j\frac{A_2^{*}\left(x\right)A_3\left(x\right)e^{\mathrm{j\&Delta;kx}}\mathrm{\&beta;}{\mathrm{\&omega;}}_1}{{\mathrm{<figure-callout\; id="0"\; label="c"\; filenames="HDA0000099677340000011.png,HDA0000099677340000021.png"\; state="\{\{state\}\}">c</figure-callout>}}_0^2}\\ \frac{d{A}_2\left(x\right)}{\mathrm{dx}}+{\mathrm{\&delta;}}_2{A}_2\left(x\right)=j\frac{A_1^{*}\left(x\right)A_3\left(x\right)e^{\mathrm{j\&Delta;kx}}\mathrm{\&beta;}{\mathrm{\&omega;}}_2}{{\mathrm{<figure-callout\; id="0"\; label="c"\; filenames="HDA0000099677340000011.png,HDA0000099677340000021.png"\; state="\{\{state\}\}">c</figure-callout>}}_0^2}\\ \frac{d{A}_3\left(x\right)}{\mathrm{dx}}+{\mathrm{\&delta;}}_3{A}_3\left(x\right)=j\frac{A_1\left(x\right)A_2\left(x\right)e^{-\mathrm{j\&Delta;kx}}\mathrm{\&beta;}{\mathrm{\&omega;}}_3}{{\mathrm{<figure-callout\; id="0"\; label="c"\; filenames="HDA0000099677340000011.png,HDA0000099677340000021.png"\; state="\{\{state\}\}">c</figure-callout>}}_0^2}\end{array}\right.$

Wherein, k ₁=ω ₁/ c ₀, k ₂=ω ₂/ c ₀, k ₃=ω ₃/ c ₀, Δ k=k ₃-k ₁-k ₂for the phase mismatch factor.If Δ k=0, three ripples are phase matched, are equivalent to three phonon conservations of momentum,

for dissipation factor.

6, when the resonance wave produced be and during the frequency resonance wave, i.e. ω ₂=ω ₁+ ω ₃the time, the form that is real amplitude and phase place by the Complex Amplitude of three train waves:

Wherein, B ₁(x), B ₂(x), B ₃(x) and

,

,

for frequencies omega ₁, ω ₂, ω ₃real number amplitude and the phase constant of sound wave;

Dissipation factor δ _i=0 (i=1,2), the pump intensity of wave does not change initial condition B because generate resonance wave ₂(0)=0,

the time, trying to achieve the rear frequency of sound wave that interacts is ω ₁, ω ₂amplitude be

$\left\{\begin{array}{c}{B}_1\left(x\right)=B_1\left(0\right)\cos \left(\frac{\mathrm{x\&beta;}{B}_3\left(0\right)\sqrt{{\mathrm{\&omega;}}_1{\mathrm{\&omega;}}_2}}{{\mathrm{<figure-callout\; id="0"\; label="c"\; filenames="HDA0000099677340000011.png,HDA0000099677340000021.png"\; state="\{\{state\}\}">c</figure-callout>}}_0^2}\right)\\ B_2\left(x\right)=\sqrt{\frac{{\mathrm{\&omega;}}_2}{{\mathrm{\&omega;}}_1}}{B}_1\left(0\right)\sin \left(\frac{\mathrm{x\&beta;}{B}_3\left(0\right)\sqrt{{\mathrm{\&omega;}}_1{\mathrm{\&omega;}}_2}}{{\mathrm{<figure-callout\; id="0"\; label="c"\; filenames="HDA0000099677340000011.png,HDA0000099677340000021.png"\; state="\{\{state\}\}">c</figure-callout>}}_0^2}\right)\end{array}\right...$

7, when the resonance wave produced is the difference frequency resonance wave, i.e. ω ₂=ω ₃-ω ₁the time, the form that is real amplitude and phase place by the Complex Amplitude of three train waves:

Wherein, B ₁(x), B ₂(x), B ₃(x) and

,

, for frequencies omega ₁, ω ₂, ω ₃real number amplitude and the phase constant of sound wave;

Dissipation factor δ _i=0, i=1,2,3, initial condition B ₂(0)=0,

the time, the amplitude of trying to achieve the rear three row sound waves that interact is:

$\left\{\begin{array}{c}{B}_1\left(x\right)=\frac{B_3\left(0\right)\sqrt{{\mathrm{\&omega;}}_1/{\mathrm{\&omega;}}_3}}{k}\mathrm{dn}(\mathrm{\&kappa;}+\frac{\mathrm{\&beta;}{B}_3\left(0\right)x\sqrt{{\mathrm{\&omega;}}_1{\mathrm{\&omega;}}_3}}{\mathrm{<figure-callout\; id="0"\; label="k\; c"\; filenames="HDA0000099677340000011.png,HDA0000099677340000021.png"\; state="\{\{state\}\}">k</figure-callout>}{c}_{}^{}{}_0^2})\\ B_2\left(x\right)=\sqrt{{\mathrm{\&omega;}}_2/{\mathrm{\&omega;}}_3}{B}_3\left(0\right)\mathrm{cn}(\mathrm{\&kappa;}+\frac{\mathrm{\&beta;}{B}_3\left(0\right)x\sqrt{{\mathrm{\&omega;}}_1{\mathrm{\&omega;}}_3}}{\mathrm{<figure-callout\; id="0"\; label="k\; c"\; filenames="HDA0000099677340000011.png,HDA0000099677340000021.png"\; state="\{\{state\}\}">k</figure-callout>}{c}_{}^{}{}_0^2})\\ B_3\left(x\right)=B_3\left(0\right)\mathrm{sn}(\mathrm{\&kappa;}+\frac{\mathrm{\&beta;}{B}_3\left(0\right)x\sqrt{{\mathrm{\&omega;}}_1{\mathrm{\&omega;}}_3}}{\mathrm{<figure-callout\; id="0"\; label="k\; c"\; filenames="HDA0000099677340000011.png,HDA0000099677340000021.png"\; state="\{\{state\}\}">k</figure-callout>}{c}_{}^{}{}_0^2})\end{array}\right.$

Y=sn (u, k) is the Jacobi elliptic function, cn (u)=(1-sn ²) ^1/2, dn (u)=(1-k ²sn ²) ^1/2;

Wherein, $\mathrm{\&kappa;}=\underset{0}{\overset{1}{\&Integral;}}\sqrt{(1-y^2)(1-k^2{y}^2)}\mathrm{dy},$ k∈(0，1)。

8, according to pump wave amplitude B after interacting ₃(x), weak signal wave amplitude B ₁and resonance wave amplitude B (x) ₂(x), with the Variation Features of propagation distance, regulate the output energy of weak signal ripple or resonance wave.

9, according to weak signal wave amplitude B after interacting ₁and resonance wave amplitude B (x) ₂(x) with pump ripple frequencies omega ₃variation Features, regulate the output energy of weak signal ripple or resonance wave;

Perhaps, according to weak signal wave amplitude B after interacting ₁) and resonance wave amplitude B (x) ₂(x) with weak signal ripple frequencies omega ₁variation Features, regulate the output energy of weak signal ripple or resonance wave;

Perhaps, according to weak signal wave amplitude B after interacting ₁and resonance wave amplitude B (x) ₂(x) with pump wave amplitude B ₃(0) Variation Features, the output energy of adjusting weak signal ripple or resonance wave.

Method of the present invention, in conjunction with the basic principle of sound wave interaction in optics and marine acoustics, consider the dissipation effect that high-power sound wave is propagated in nonlinear dielectric, sound wave ω in aqueous medium ₁and ω ₃the second order nonlinear effect that (weak signal ripple and pump ripple) causes because of nonlinear interaction, generate and frequency sound wave ω ₂or difference frequency sound wave ω ₂, utilized runge kutta method (Runger-Kutta) numerical analysis the sound wave variable element generate ω after interacting ₂resonance wave after three row magnitudes of acoustic waves with the variation characteristic of distance and frequency, acoustic wave energy the energy transfer process with propagation distance and frequency change, determine that the energy changing that generates sound wave presents the pulsation rule, can regulate the output energy of each train wave according to actual needs.

The accompanying drawing explanation

Fig. 1 is that magnitudes of acoustic waves is with the propagation distance change curve;

Fig. 2 is that acoustic wave energy is with the propagation distance change curve;

Fig. 3 is that acoustic wave energy is with pump ripple frequency variation curve;

Fig. 4 is weak signal wave amplitude (ω ₁ripple) with pump wave amplitude and frequency variation curve;

Fig. 5 is weak signal wave energy (ω ₁ripple) with pump wave amplitude and frequency variation curve;

Fig. 6 is that magnitudes of acoustic waves is with the propagation distance change curve; Wherein

(a) be pump ripple frequencies omega ₃during for 2kHz, weak signal wave amplitude (ω ₁ripple), resonance wave amplitude (ω ₂ripple), pump wave amplitude (ω ₃ripple) with the propagation distance change curve;

(b) be pump ripple frequencies omega ₃during for 5kHz, weak signal wave amplitude (ω ₁ripple), resonance wave amplitude (ω ₂ripple), pump wave amplitude (ω ₃ripple) with the propagation distance change curve;

(c) pump ripple frequencies omega ₃during for 10kHz, weak signal wave amplitude (ω ₁ripple), resonance wave amplitude (ω ₂ripple), pump wave amplitude (ω ₃ripple) with the propagation distance change curve;

Fig. 7 is different pump ripple frequencies omega ₃the time, resonance wave energy (ω ₂ripple) with the propagation distance change curve;

Fig. 8 is different pump wave amplitude (ω ₃ripple) time, weak signal wave energy (ω ₁ripple) with the propagation distance change curve.

The flow chart that Fig. 9 is the interactional output adjusting method of nonlinear parameter between sound wave.

Embodiment

Below in conjunction with drawings and Examples, technical scheme of the present invention is described in detail.

The present invention be take Burgers (Burgers) equation as basis, draw the expression formula of the amplitude of each sound field after weak signal ripple and pump wave interaction, utilize the emulation of Runger-Kutta method to obtain the amplitude of each sound field or the energy change curve with propagation distance, the rear energy transfer process of the non-linear variable element interaction of sound wave that obtains directly perceived, utilize described transfer, realize the output energy adjustment to three train waves.

The variable element interaction phenomenon of sound wave is explained with the quantum mechanics language, can regard high frequency pump ripple as

phonon splits into two low frequencies

phonon, or split into the more process of low frequency phonon.The essence of three-wave interaction is the non-linear variable element of sound wave to have occurred interact.In aqueous medium, as pump ripple ω ₃with weak signal sound wave ω ₁nonlinear interaction occurs generate ω ₂the time, realize Best Coupling (sound wave resonance), must observe following law of conservation of energy and the law of conservation of momentum

In formula, for composing bright gram constant, k ₁, k ₂, k ₃for the sound wave wave number.When meeting formula (1), can only consider ω ₁, ω ₂, ω ₃the coupling of this three row frequency wave, and can not consider any coupling of this three row frequency wave and all other frequency waves fully.Sound wave is the acoustic energy conservation in the nonlinear interaction process, when acoustic wave energy generation transfer meets formula (1), and energy exchange maximum between sound wave.

In desirable nonlinear dielectric, when the sound reynolds number Re>>(Re=ρ 1 time ₀c ₀v/b ω), weak signal ripple and pump ripple interaction process in nonlinear dielectric can be write as general Burgers equation form

$\frac{\&PartialD;v}{\&PartialD;x}-\frac{\mathrm{\&beta;}}{{\mathrm{<figure-callout\; id="0"\; label="c"\; filenames="HDA0000099677340000011.png,HDA0000099677340000021.png"\; state="\{\{state\}\}">c</figure-callout>}}_0^2}v\frac{\&PartialD;v}{\&PartialD;\mathrm{\&tau;}}=\frac{b}{2{\mathrm{<figure-callout\; id="0"\; label="c"\; filenames="HDA0000099677340000011.png,HDA0000099677340000021.png"\; state="\{\{state\}\}">c</figure-callout>}}_0^2{\mathrm{\&rho;}}_0}\frac{{\&PartialD;}^{2}v}{{\&PartialD;\mathrm{\&tau;}}^2}---\left(2\right)$

In formula, v is underwater acoustic wave vibration velocity, β=1+B/2A, and the nonlinear parameter that B/A is medium, be the ratio of quadratic term coefficient and linear coefficient in the state equation taylor series expansion, it is the basic parameter of nonlinear acoustics, c ₀for the static velocity of sound, ρ ₀for the density of aqueous medium, τ=t-x/c ₀for time delay, x is propagation distance.B is the medium coefficient of viscosity, ζ is for cutting the coefficient of viscosity, and η is bulk viscosity, for temperature conductivity coefficient, c _v, c _pfor electric capacity specific heat and voltage specific heat.

Suppose that sound source is in x=0 place emission sinusoidal signal, the form that provides displacement x place sound wave solution according to the Burgers equation is

$v(x,t)=\underset{n=\mathrm{1,2,3}}{\mathrm{\&Sigma;}}{A}_n\left(x\right)\exp \left(i{\mathrm{\&omega;}}_n(t-\frac{x}{c_0})\right)+c---\left(3\right)$

In formula, A ₁(x), A ₂(x), A ₃(x) be the complex amplitude of sound wave, c is constant.

Consider the dissipation effect that high-power sound wave is propagated in nonlinear dielectric, now acoustic energy is non-vanishing to the derivative of displacement x, and after the interaction that obtains three row sound waves in formula (3) of deriving, the wave amplitude equation is

$\left\{\begin{array}{c}\frac{d{A}_1\left(x\right)}{\mathrm{dx}}+{\mathrm{\&delta;}}_1{A}_1\left(x\right)=\mathrm{<figure-callout\; id="2"\; label="j\; A"\; filenames="HDA0000099677340000031.png,HDA0000099677340000041.png"\; state="\{\{state\}\}">j</figure-callout>}\frac{A_{}^{}}{}\frac{{}_2^{*}\left(x\right)A_3\left(x\right)e^{\mathrm{j\&Delta;kx}}{\mathrm{\&beta;\&omega;}}_1}{{\mathrm{<figure-callout\; id="0"\; label="c"\; filenames="HDA0000099677340000011.png,HDA0000099677340000021.png"\; state="\{\{state\}\}">c</figure-callout>}}_0^2}\\ \frac{d{A}_2\left(x\right)}{\mathrm{dx}}+{\mathrm{\&delta;}}_2{A}_2\left(x\right)=\mathrm{<figure-callout\; id="1"\; label="j\; A"\; filenames="HDA0000099677340000022.png"\; state="\{\{state\}\}">j</figure-callout>}\frac{A_{}^{}}{}\frac{{}_1^{*}\left(x\right)A_3\left(x\right)e^{\mathrm{j\&Delta;kx}}{\mathrm{\&beta;\&omega;}}_2}{{\mathrm{<figure-callout\; id="0"\; label="c"\; filenames="HDA0000099677340000011.png,HDA0000099677340000021.png"\; state="\{\{state\}\}">c</figure-callout>}}_0^2}\\ \frac{d{A}_3\left(x\right)}{\mathrm{dx}}+{\mathrm{\&delta;}}_3{A}_3\left(x\right)=j\frac{A_1\left(x\right)A_2\left(x\right)e^{-\mathrm{j\&Delta;kx}}{\mathrm{\&beta;\&omega;}}_3}{{\mathrm{<figure-callout\; id="0"\; label="c"\; filenames="HDA0000099677340000011.png,HDA0000099677340000021.png"\; state="\{\{state\}\}">c</figure-callout>}}_0^2}\end{array}\right.---\left(4\right)$

In formula, k ₁=ω ₁/ c ₀, k ₂=ω ₂/ c ₀, k ₃=ω ₃/ c ₀, Δ k=k ₃-k ₁-k ₂for the phase mismatch factor.If Δ k=0, three ripples are phase matched, are equivalent to three phonon conservations of momentum.

for dissipation factor.

Formula (4) is the Non-Self-Governing form, more convenient in order to make to solve on this equation mathematics, and numerical computations also is convenient to process, and makes simple conversion A ' ₃≡ A ₃e ^{j Δ kx}and turn to autonomous form

$\left\{\begin{array}{c}\frac{1}{j{k}_1}(\frac{d{A}_1\left(x\right)}{\mathrm{dx}}+{\mathrm{\&delta;}}_1)A_1\left(x\right)=\frac{\mathrm{\&beta;}}{c_0}{\mathrm{<figure-callout\; id="2"\; label="A"\; filenames="HDA0000099677340000031.png,HDA0000099677340000041.png"\; state="\{\{state\}\}">A</figure-callout>}}_2^{*}\left(x\right)A_3^{\&prime;}\left(x\right)\\ \frac{1}{j{k}_2}(\frac{d{A}_2\left(x\right)}{\mathrm{dx}}+{\mathrm{\&delta;}}_2)A_2\left(x\right)=\frac{\mathrm{\&beta;}}{c_0}{\mathrm{<figure-callout\; id="1"\; label="A"\; filenames="HDA0000099677340000022.png"\; state="\{\{state\}\}">A</figure-callout>}}_1^{*}\left(x\right)A_3^{\&prime;}\left(x\right)\\ \frac{1}{j{k}_3}(\frac{d{A}_3\left(x\right)}{\mathrm{dx}}+{\mathrm{\&delta;}}_3)A_3^{\&prime;}\left(x\right)=\frac{\mathrm{\&Delta;k}}{k_3}{A}_3^{\&prime;}\left(x\right)+\frac{\mathrm{\&beta;}}{c_0}{A}_1\left(x\right)A_2\left(x\right)\end{array}---\left(5\right)\right.$

Formula (5) is form common in the three-wave interaction problem.

Conservation of momentum during three ripple Best Coupling, get Δ k=0; As the dissipation effect (δ that ignores sound wave ₁=δ ₂=δ ₃=0), three formulas of formula (4) are multiplied by successively

when x gets arbitrary value, formula (4) becomes after integral operation

$\left\{\begin{array}{c}\frac{|A_1\left(x\right){|}^2}{{\mathrm{\&omega;}}_1}-\frac{|A_2\left(x\right){|}^2}{{\mathrm{\&omega;}}_2}=\mathrm{const}\\ \frac{|A_1\left(x\right){|}^2}{{\mathrm{\&omega;}}_1}+\frac{|A_3\left(x\right){|}^2}{{\mathrm{\&omega;}}_3}=\mathrm{const}\\ \frac{|A_2\left(x\right){|}^2}{{\mathrm{\&omega;}}_2}+\frac{|A_3\left(x\right){|}^2}{{\mathrm{\&omega;}}_3}=\mathrm{const}\end{array}\right.---\left(6\right)$

Every two equations in formula (6) subtract each other all can obtain another equation, is not independently each other.Be multiplied by ω by second of formula (6) ₁, the 3rd is multiplied by ω ₂, and utilize ω ₂=ω ₁+ ω ₃can obtain law of conservation of energy after conversion

$\frac{d\left[\right|A_1\left(x\right){|}^2+|A_2\left(x\right){|}^2+|A_3\left(x\right){|}^2]}{\mathrm{dx}}=0---\left(7\right)$

Formula (7) shows, if total acoustic energy at coordinate x place is

above formula (7) is dE/dx=0 namely, illustrates that in the process of three row frequency sound wave interactions, its gross energy is constant.In other words, the energy value of sound wave just exchanges between each frequency sound wave, and medium does not participate in, and only plays instrumentality, and this is interactional characteristics of all parameters just also.

Formula (6) can further be written as

$\frac{d}{\mathrm{dx}}\left(\frac{E_1\left(x\right)}{{\mathrm{\&omega;}}_1}\right)=\frac{d}{\mathrm{dx}}\left(\frac{E_2\left(x\right)}{{\mathrm{\&omega;}}_2}\right)=-\frac{d}{\mathrm{dx}}\left(\frac{E_3\left(x\right)}{{\mathrm{\&omega;}}_3}\right)---\left(8\right)$

In formula, E ₁(x), E ₂(x), E ₃(x) be the acoustic energy value of sound wave at distance sound source x place.Between formula (8) and nonlinear optics derivation light wave, interactional Manley-Rowe form class seemingly, also can use for reference the interactional meaning of light wave in optics and analyzed and process thus by the nonlinear interaction form of underwater acoustic wave and meaning.According to the Manley-Rowe theorem, formula (6) differential is obtained

$\left\{\begin{array}{c}\frac{d|A_1\left(x\right){|}^2}{{\mathrm{\&omega;}}_1}=\frac{d|A_2\left(x\right){|}^2}{{\mathrm{\&omega;}}_2}\\ \frac{d|A_1\left(x\right){|}^2}{{\mathrm{\&omega;}}_1}=-\frac{d|A_3\left(x\right){|}^2}{{\mathrm{\&omega;}}_3}\\ \frac{d|A_2\left(x\right){|}^2}{{\mathrm{\&omega;}}_2}=-\frac{d|A_3\left(x\right){|}^2}{{\mathrm{\&omega;}}_3}\end{array}\right.---\left(9\right)$

Utilize the physical definition of sound energy flux density, the expression formula that obtains the phonon average flux is

formula (9) is rewritten as

dN ₁=dN ₂，dN ₁=-dN ₃，dN ₂=-dN ₃ (10)

According to formula (10), the acoustic energy transfer relationship of nonlinear interaction between sound wave is carried out to qualitative analysis.Formula (10) shows in the sound wave interaction process, and frequency is ω ₃phonon of the every minimizing of sound wave, frequency is ω ₁and ω ₂sound wave all to increase a phonon, this that is to say powerful sound wave ω in accordance with the acoustic energy law of conservation ₃incide in nonlinear dielectric, making the incident frequency is ω ₁weak sound wave to convert frequency to through difference frequency be ω ₃-ω ₁=ω ₂(or ω ₃+ ω ₁=ω ₂) sound wave, this process is the process of sound wave decay, i.e. dN ₁, dN ₂increment for just, and dN ₃increment for negative.Can estimate thus the action effect of nonlinear interaction according to formula (9) and formula (10).

The complex amplitude form of expression of three row sound waves is

In formula, B ₁(x), B ₂(x), B ₃(x) and for frequencies omega ₁, ω ₂, ω ₃real number amplitude and the phase constant of sound wave.

Below show in two kinds of situation that nonlinear interaction produces the resonance wave amplitude

1 and sound wave frequently

Starting not have frequency in sound field is ω ₂sound wave, this component is to be ω by frequency ₂=ω ₁+ ω ₃sound wave coupling form.If the pump intensity of wave can not have larger change because of generating sound wave, the pump wave field can be approximately to a constant field, i.e. dB ₃(x)/dx=0, have the formula (4) of formula (11) substitution three ripple couplings

In formula,

at dissipative approximation, be 0 o'clock, the first two equation of formula (12) can also be expressed as

Wushu (13) generation is to the 3rd equation of formula (12), and after integral operation is

In formula (14), as initial condition B ₂(0)=0 o'clock, make formula (14) both members equate, have

now

below discuss and get

so formula (13) can further be written as

$\left\{\begin{array}{c}\frac{d{B}_1\left(x\right)}{\mathrm{dx}}+{\mathrm{\&delta;}}_1{B}_1\left(x\right)+\frac{B_3\left(x\right)B_2\left(x\right)\mathrm{\&beta;}{\mathrm{\&omega;}}_1}{{\mathrm{<figure-callout\; id="0"\; label="c"\; filenames="HDA0000099677340000011.png,HDA0000099677340000021.png"\; state="\{\{state\}\}">c</figure-callout>}}_0^2}=0\\ \frac{d{B}_2\left(x\right)}{\mathrm{dx}}+{\mathrm{\&delta;}}_2{B}_2\left(x\right)+\frac{B_3\left(x\right)B_1\left(x\right)\mathrm{\&beta;}{\mathrm{\&omega;}}_2}{{\mathrm{<figure-callout\; id="0"\; label="c"\; filenames="HDA0000099677340000011.png,HDA0000099677340000021.png"\; state="\{\{state\}\}">c</figure-callout>}}_0^2}=0\\ {\mathrm{\&omega;}}_1\frac{B_2\left(x\right)}{B_1\left(x\right)}=-{\mathrm{\&omega;}}_2\frac{B_1\left(x\right)}{B_2\left(x\right)}\end{array}\right.---\left(15\right)$

Because formula (15) is linear, its solution can be write as the form of following formula

B ₁=C ₁exp(lx)，B ₂=C ₂exp(lx) (16)

For asking the particular solution of formula (15), by formula (16) substitution formula (15), making the determinant of equation after substitution is zero,

$(l+{\mathrm{\&delta;}}_1)(l+{\mathrm{\&delta;}}_2)-\frac{\mathrm{\&beta;}{\mathrm{\&omega;}}_1{\mathrm{\&omega;}}_2{B}_3\left(x\right)}{{\mathrm{<figure-callout\; id="0"\; label="c"\; filenames="HDA0000099677340000011.png,HDA0000099677340000021.png"\; state="\{\{state\}\}">c</figure-callout>}}_0^2}=0---\left(17\right)$

Formula (17) can be determined two value l of l ₁, l ₂, the solution of formula (15) can be rewritten into again thus

$\left[\begin{array}{c}{B}_1\\ {\mathrm{<figure-callout\; id="2"\; label="B"\; filenames="HDA0000099677340000031.png,HDA0000099677340000041.png"\; state="\{\{state\}\}">B</figure-callout>}}_2\end{array}\right]=\left[\begin{array}{cc}{C}_{11}& C_{12}\\ C_{21}& C_{22}\end{array}\right]\left[\begin{array}{c}{e}^{l_{1}x}\\ e^{l_{2}x}\end{array}\right]---\left(18\right)$

Wherein, C _{i, j}undetermined constant, by the boundary condition at x=0 place

$\begin{array}{c}{B}_1(x=0)=B_1\left(0\right)\\ B_2(x=0)=0\\ B_3(x=0)=B_3\left(0\right)\end{array}---\left(19\right)$

Determine.

Because formula (15) only can be used mathematical method or Numerical Methods Solve, for trying to achieve its analysis result, can suppose δ when pumping source is stronger _i=0 (i=1,2), the rear frequency of sound wave that obtains thus interacting is ω ₁, ω ₂the amplitude analytic solutions

$\left\{\begin{array}{c}{B}_1\left(x\right)=B_1\left(0\right)\cos \left(\frac{\mathrm{x\&beta;}{B}_3\left(x\right)\sqrt{{\mathrm{\&omega;}}_1{\mathrm{\&omega;}}_2}}{{\mathrm{<figure-callout\; id="0"\; label="c"\; filenames="HDA0000099677340000011.png,HDA0000099677340000021.png"\; state="\{\{state\}\}">c</figure-callout>}}_0^2}\right)\\ B_2\left(x\right)=\sqrt{\frac{{\mathrm{\&omega;}}_2}{{\mathrm{\&omega;}}_1}}{B}_1\left(0\right)\sin \left(\frac{\mathrm{x\&beta;}{B}_3\left(x\right)\sqrt{{\mathrm{\&omega;}}_1{\mathrm{\&omega;}}_2}}{{\mathrm{<figure-callout\; id="0"\; label="c"\; filenames="HDA0000099677340000011.png,HDA0000099677340000021.png"\; state="\{\{state\}\}">c</figure-callout>}}_0^2}\right)\end{array}\right.---\left(20\right)$

Found out B by formula (20) ₂(x) amplitude is weak signal strength B in sound field ₁(0) determine.

2, difference frequency sound wave

Starting not have frequency in sound field is ω ₂sound wave, this component is to be ω by frequency ₂=ω ₃-ω ₁sound wave coupling form.When considering pump ripple ω ₃during energy changing in the nonlinear interaction process, according to three ripple coupled wave equation formulas (4), obtain following ACOUSTIC WAVE EQUATION

Ordinary circumstance following formula (21) only can be used mathematical method or Numerical Methods Solve, for trying to achieve its analysis result, at the dissipation factor δ of three ripples _i=0, i=1,2,3 o'clock, utilize the x=0 place, initial condition formula (19) reaches similar with the solution of formula (12), every two equations combination of formula (21) obtains after integral and calculating

$\left\{\begin{array}{c}{\mathrm{<figure-callout\; id="1"\; label="B"\; filenames="HDA0000099677340000022.png"\; state="\{\{state\}\}">B</figure-callout>}}_1^2\left(x\right)={\mathrm{<figure-callout\; id="1"\; label="B"\; filenames="HDA0000099677340000022.png"\; state="\{\{state\}\}">B</figure-callout>}}_1^2\left(0\right)+{\mathrm{<figure-callout\; id="2"\; label="B"\; filenames="HDA0000099677340000031.png,HDA0000099677340000041.png"\; state="\{\{state\}\}">B</figure-callout>}}_2^2\left(x\right)\frac{{\mathrm{\&omega;}}_1}{{\mathrm{\&omega;}}_2}\\ {\mathrm{<figure-callout\; id="2"\; label="B"\; filenames="HDA0000099677340000031.png,HDA0000099677340000041.png"\; state="\{\{state\}\}">B</figure-callout>}}_2^2\left(x\right)=[B_3^2\left(0\right)-B_3^2\left(x\right)]\frac{{\mathrm{\&omega;}}_2}{{\mathrm{\&omega;}}_3}\\ B_3^2\left(x\right)=B_3^2\left(0\right)+[{\mathrm{<figure-callout\; id="1"\; label="B"\; filenames="HDA0000099677340000022.png"\; state="\{\{state\}\}">B</figure-callout>}}_1^2\left(0\right)-{\mathrm{<figure-callout\; id="1"\; label="B"\; filenames="HDA0000099677340000022.png"\; state="\{\{state\}\}">B</figure-callout>}}_1^2\left(x\right)]\frac{{\mathrm{\&omega;}}_3}{{\mathrm{\&omega;}}_1}\end{array}\right.---\left(22\right)$

The form that formula (22) substitution formula (23) obtains variables separation is

$\frac{{\mathrm{dB}}_2\left(x\right)}{\mathrm{dx}}=-\frac{\mathrm{\&beta;}\sqrt{{\mathrm{\&omega;}}_1{\mathrm{\&omega;}}_3[w^2-{\mathrm{<figure-callout\; id="2"\; label="B"\; filenames="HDA0000099677340000031.png,HDA0000099677340000041.png"\; state="\{\{state\}\}">B</figure-callout>}}_2^2\left(x\right)][v^2-{\mathrm{<figure-callout\; id="2"\; label="B"\; filenames="HDA0000099677340000031.png,HDA0000099677340000041.png"\; state="\{\{state\}\}">B</figure-callout>}}_2^2\left(x\right)]}}{{\mathrm{<figure-callout\; id="0"\; label="c"\; filenames="HDA0000099677340000011.png,HDA0000099677340000021.png"\; state="\{\{state\}\}">c</figure-callout>}}_0^2}---\left(23\right)$

In formula, ${\mathrm{<figure-callout\; id="2"\; label="w"\; filenames="HDA0000099677340000031.png,HDA0000099677340000041.png"\; state="\{\{state\}\}">w</figure-callout>}}^2=\frac{{\mathrm{\&omega;}}_2{B}_3^2\left(0\right)}{{\mathrm{\&omega;}}_3},$ ${\mathrm{<figure-callout\; id="2"\; label="v"\; filenames="HDA0000099677340000031.png,HDA0000099677340000041.png"\; state="\{\{state\}\}">v</figure-callout>}}^2=\frac{{\mathrm{\&omega;}}_2{\mathrm{<figure-callout\; id="1"\; label="B"\; filenames="HDA0000099677340000022.png"\; state="\{\{state\}\}">B</figure-callout>}}_1^2\left(0\right)}{{\mathrm{\&omega;}}_1}.$ For asking the solution of formula (23), introduce $w^2-{\mathrm{<figure-callout\; id="2"\; label="B"\; filenames="HDA0000099677340000031.png,HDA0000099677340000041.png"\; state="\{\{state\}\}">B</figure-callout>}}_2^2\left(x\right)=w^2{\mathrm{<figure-callout\; id="2"\; label="y"\; filenames="HDA0000099677340000031.png,HDA0000099677340000041.png"\; state="\{\{state\}\}">y</figure-callout>}}^2,$ ${\mathrm{<figure-callout\; id="2"\; label="k"\; filenames="HDA0000099677340000031.png,HDA0000099677340000041.png"\; state="\{\{state\}\}">k</figure-callout>}}^2=\frac{w^2}{{\mathrm{<figure-callout\; id="2"\; label="v"\; filenames="HDA0000099677340000031.png,HDA0000099677340000041.png"\; state="\{\{state\}\}">v</figure-callout>}}^2+{\mathrm{<figure-callout\; id="2"\; label="w"\; filenames="HDA0000099677340000031.png,HDA0000099677340000041.png"\; state="\{\{state\}\}">w</figure-callout>}}^2}$ After conversion, obtain

$\underset{0}{\overset{\sqrt{1-{\mathrm{<figure-callout\; id="2"\; label="B"\; filenames="HDA0000099677340000031.png,HDA0000099677340000041.png"\; state="\{\{state\}\}">B</figure-callout>}}_2^2\left(x\right)/{\mathrm{<figure-callout\; id="2"\; label="w"\; filenames="HDA0000099677340000031.png,HDA0000099677340000041.png"\; state="\{\{state\}\}">w</figure-callout>}}^2}}{\&Integral;}}\frac{1}{(1-y^2)(1-k^2{y}^2)}\mathrm{dy}-\mathrm{\&kappa;}=\frac{\mathrm{\&beta;x}\sqrt{{\mathrm{\&omega;}}_1{\mathrm{\&omega;}}_3({\mathrm{<figure-callout\; id="2"\; label="w"\; filenames="HDA0000099677340000031.png,HDA0000099677340000041.png"\; state="\{\{state\}\}">w</figure-callout>}}^2+v^2)}}{{\mathrm{<figure-callout\; id="0"\; label="c"\; filenames="HDA0000099677340000011.png,HDA0000099677340000021.png"\; state="\{\{state\}\}">c</figure-callout>}}_0^2}---\left(24\right)$

The left-hand component of formula (24) contains the single order ellptic integral, utilizes ellptic integral

$\mathrm{\&kappa;}(y,k)={\&Integral;}_0^y\frac{1}{\sqrt{(1-t^2)(1-k^2{t}^2)}}\mathrm{dt}---\left(25\right)$

After variable t=sin θ replacement, obtain

$\mathrm{\&kappa;}(y,k)={\&Integral;}_0^{\mathrm{\&psi;}}\frac{1}{\sqrt{(1-{\mathrm{<figure-callout\; id="2"\; label="k"\; filenames="HDA0000099677340000031.png,HDA0000099677340000041.png"\; state="\{\{state\}\}">k</figure-callout>}}^2{\mathrm{<figure-callout\; id="2"\; label="sin"\; filenames="HDA0000099677340000031.png,HDA0000099677340000041.png"\; state="\{\{state\}\}">sin</figure-callout>}}^2\mathrm{\&theta;})}}\mathrm{d\&theta;}---\left(26\right)$

In formula, k ∈ (0,1), ψ=arcsiny, κ (y thus, k) also can be write as κ (ψ, k) form, the inverse function y=sn (u of title u=κ (y, k), k) be the Jacobi elliptic function, two kinds of forms of other of elliptic function can be write cn (u)=(1-sn ²) ^1/2, dn (u)=(1-k ²sn ²) ^1/2.

When y=1 (ψ=pi/2), the result of integration type (25) is complete elliptic integral of the first kind, and its value is designated as κ, and the expression-form of κ is: $\mathrm{\&kappa;}=\underset{0}{\overset{1}{\&Integral;}}\sqrt{(1-y^2)(1-k^2{y}^2)}\mathrm{dy}.$

According to the ellptic integral of the Jacobian transform (24) of the complete elliptic function of the first kind, after interacting, the ripple solution of three row sound waves can be write as the following formula form

$\left\{\begin{array}{c}{B}_1\left(x\right)=\frac{B_3\left(0\right)\sqrt{{\mathrm{\&omega;}}_1/{\mathrm{\&omega;}}_3}}{k}\mathrm{dn}(\mathrm{\&kappa;}+\frac{\mathrm{\&beta;}{B}_3\left(0\right)x\sqrt{{\mathrm{\&omega;}}_1{\mathrm{\&omega;}}_3}}{\mathrm{<figure-callout\; id="0"\; label="k\; c"\; filenames="HDA0000099677340000011.png,HDA0000099677340000021.png"\; state="\{\{state\}\}">k</figure-callout>}{c}_{}^{}{}_0^2})\\ B_2\left(x\right)=\sqrt{{\mathrm{\&omega;}}_2/{\mathrm{\&omega;}}_3}{B}_3\left(0\right)\mathrm{cn}(\mathrm{\&kappa;}+\frac{\mathrm{\&beta;}{B}_3\left(0\right)x\sqrt{{\mathrm{\&omega;}}_1{\mathrm{\&omega;}}_3}}{\mathrm{<figure-callout\; id="0"\; label="k\; c"\; filenames="HDA0000099677340000011.png,HDA0000099677340000021.png"\; state="\{\{state\}\}">k</figure-callout>}{c}_{}^{}{}_0^2})\\ B_3\left(x\right)=B_3\left(0\right)\mathrm{sn}(\mathrm{\&kappa;}+\frac{\mathrm{\&beta;}{B}_3\left(0\right)x\sqrt{{\mathrm{\&omega;}}_1{\mathrm{\&omega;}}_3}}{\mathrm{<figure-callout\; id="0"\; label="k\; c"\; filenames="HDA0000099677340000011.png,HDA0000099677340000021.png"\; state="\{\{state\}\}">k</figure-callout>}{c}_{}^{}{}_0^2})\end{array}\right.---\left(27\right)$

Formula (27) provides after three-wave interaction and variable

the sound wave amplitude form of expression of the elliptic function form of substantial connection is arranged, there is the obvious periodic feature of elliptic function.

In formula (20)

and in formula (27)

all mean the sound wave phase place, and phase place and propagation distance x are proportional, and the sound wave amplitude is the function of measuring distance.Found out B by formula (27) ₂(x) maximum stronger pumping source intensity B in sound field ₃(0) determine.

Below utilize the emulation of Runger-Kutta method to carry out emulation to amplitude or the energy of each sound field of obtaining, obtain the amplitude of each sound field or the energy change curve with propagation distance, wherein ω ₁weak signal ripple initial magnitude is 1, and frequency is 1kHz, and the non-linear variable element of aqueous medium is 3.6.

(1) in the situation that do not consider that the pumping source acoustic energy changes, and has carried out following simulation analysis according to solution (20).A: measuring distance x is 78.5 meters of 1, and the pumping source initial magnitude is 10, and frequency is 80000rad/s; With the variable in distance curve as shown in Figure 1, energy with the variable in distance curve as shown in Figure 2 for amplitude.B: measuring distance is 78.5 meters, and the pumping source initial magnitude is taken as 10, and frequency is 1000rad/s～80000rad/s, and energy with the pumping source frequency variation curve as shown in Figure 3; When the pumping source amplitude is 1 100, the weak signal wave amplitude with pumping source amplitude and frequency variation curve as shown in Figure 4; ω ₁the energy difference with pumping source amplitude and frequency variation curve as shown in Figure 5 before and after the ripple nonlinear interaction.

(2) while considering the pumping source energy changing, utilize the Runger-Kutta method to sound wave interaction after acoustic signature carry out numerical analysis.Parameter: while getting 10 ℃, the coefficient of viscosity of aqueous medium is b=1.308 * 10 ^-3pa.s, Dissipation Parameters

a: the pumping source initial magnitude is 10, and frequency is 2kHz, 5kHz, 10kHz, obtain sound wave interaction after amplitude with the measuring distance change curve as shown in Figure 6, generate ω ₂wave energy with the variable in distance curve as shown in Figure 7.B: the pumping source frequency is taken as 2kHz, and amplitude is taken as 5,10,20, generates ω ₁wave energy with the variable in distance curve as shown in Figure 8.

B in each figure ₁, B ₂, B ₃represent that respectively the rear frequency of sound wave variable element interaction is ω ₁, ω ₂and ω ₃the amplitude of sound wave.DE ₁represent ω ₁energy difference before wave interaction after energy and interaction, dE ₂after interacting, representative generates ω ₂the energy value of ripple.

Weak signal ripple ω in Fig. 1 ₁with pump ripple ω ₃by with frequency ω ₃+ ω ₁=ω ₂generate ω ₂ripple, sound wave is the acoustic energy conservation in the process that nonlinear interaction occurs, and the acoustic wave energy generated mainly comes from weak signal ripple ω ₁so the weak signal ripple is transferred to newly-generated sound wave ω to energy again ₂process in the energy of weak signal ripple will reduce.See newly-generated sound wave ω from expression formula (20) ₂amplitude presents periodic variation, generates thus and frequency ω ₂sound field can not unrestrictedly increase, the power entrained when weak signal is evacuated, ω ₂power increase process gradually in, there will be saturated phenomenon, ω ₂ripple can be passed to ω to energy back again ₁, as can be seen from Figure 1 waveform presents the variation of pulsation trend.Fig. 2～5 simulation results see that the energy of weak signal ripple all can reduce as long as between sound wave, nonlinear interaction has occurred, and difference is greater than zero all the time, and maximum decrease can reach thirties dB, and amplitude changes and energy changing all presents the cycle pulsation.By (a) (b) (c) figure contrast discovery of Fig. 6, initial sound wave ω ₂acoustic pressure be zero, weak signal sound wave ω ₁with pump ripple ω ₃nonlinear interaction ω occurs ₃-ω ₁=ω ₂be transferred to sound wave ω ₂, sound wave ω thus ₂amplitude start from scratch gradually and to increase, want to make weak signal ω ₁magnitudes of acoustic waves obtains maximum amplification in certain segment distance need to meet ω ₃=2 ω ₁.Work as ω ₃=2 ω ₁the time, added damping parameter, find out that from figure damping parameter can change the range attenuation rate of sound wave, on the not impact of propagation law of sound wave, frequency is higher, decays larger.Fig. 7 shows the increase with the pumping source frequency, ω ₂acoustic wave energy reduces; During twice that it is signal frequency that Fig. 8 shows in the pumping source frequency, along with the increase of pumping source frequency, the amplification quantity of weak signal increases.Increase or reduce trend and still present the variation of pulsation rule.

By simulation result, can find out:

(1) between sound wave the interactional process of non-linear variable element occurs in, generate new frequency content and shift with energy.

(2) in the non-linear variable element interaction process of sound wave, generate and frequently during sound wave, and the energy of ripple mainly comes from the weak signal ripple frequently, due to the conservation of energy in interaction process, institute so that the weak signal ripple certain section propagation distance self-energy, reduce.

(3) when the non-linear variable element interaction process of sound wave generates the difference frequency sound wave, the energy of difference frequency ripple mainly comes from pumping source, when meeting between applicator Best Coupling and being two frequencys multiplication, the weak signal wave energy will farthest be amplified in certain section propagation distance.

(4) between sound wave in when, non-linear variable element occurring interacting, energy shifts to have periodically, thereby causes the energy value periodically-varied of weak signal ripple, has long-term modularity.

Therefore, after non-linear variable element interaction occurs between sound wave, can realize that the weak signal wave energy presents the trend variation of pulsation, by selecting applicable parameter, can realize the output energy adjustment of three train waves, make the output energy reduce or amplify.

The present invention also can have other various embodiments; in the situation that do not deviate from spirit of the present invention and essence thereof; those of ordinary skill in the art are when making according to the present invention various corresponding changes and distortion, and these change and be out of shape the protection range that all should belong to the appended claim of the present invention accordingly.

Claims (4)

1. the output adjusting method of acoustic energy after sound wave interaction in a nonlinear dielectric is characterized in that comprising the following steps:

(a) frequency is ω ₃pump ripple and frequency be ω ₁weak signal ripple generation nonlinear interaction, the generation frequency is ω ₂resonance wave;

(b) according to described pump ripple, weak signal ripple and resonance wave frequency ω ₃, ω ₁and ω ₂, calculate respectively the amplitude B at three train wave displacement x places afterwards that interacts ₁(x), B ₂and B (x) ₃(x);

The amplitude B at described calculating three train wave displacement x places ₁(x), B ₂and B (x) ₃(x) method is:

Step (b1) is interactional Burgers equation in nonlinear dielectric according to pump ripple and weak signal ripple, calculates and obtains at the sound wave vibration velocity v of displacement x place (x);

The sound wave vibration velocity v (x) that step (b2) obtains according to step (b1), calculating obtains the wave amplitude equation after three row sound wave interactions;

Three train waves after step (b3) is interacted by wave amplitude equation calculating acquisition are at the amplitude B at displacement x place ₁(x), B ₂and B (x) ₃(x);

Described Burgers equation is:

Wherein, v is sound wave vibration velocity, β=1+B/2A, and the nonlinear parameter that B/A is medium, be the ratio of quadratic term coefficient and linear coefficient in the state equation taylor series expansion, it is the basic parameter of nonlinear acoustics, c ₀for the static velocity of sound, ρ ₀for the density of nonlinear dielectric, τ=t-x/c ₀for time delay, x is measuring distance, and b is the medium coefficient of viscosity,

ζ is for cutting the coefficient of viscosity, and η is bulk viscosity,

for temperature conductivity coefficient, c _v, c _pfor electric capacity specific heat and voltage specific heat;

The sine wave that sound source sends at the x=0 place, calculate acquisition and be expressed as at the sound wave vibration velocity v of displacement x place (x):

Wherein, A ₁(x), A ₂(x), A ₃(x) be the complex amplitude of three row sound waves, c is constant;

Wave amplitude equation after three row sound wave interactions:

Wherein, k ₁=ω ₁/ c ₀, k ₂=ω ₂/ c ₀, k ₃=ω ₃/ c ₀, Δ k=k ₃-k ₁-k ₂for the phase mismatch factor; If Δ k=0, three ripples are phase matched, are equivalent to three phonon conservations of momentum, for dissipation factor;

When the resonance wave produced be and during the frequency resonance wave, i.e. ω ₂=ω ₁+ ω ₃the time, the form that is real amplitude and phase place by the Complex Amplitude of three train waves:

Wherein, B ₁(x), B ₂(x), B ₃(x) and for frequencies omega ₁, ω ₂, ω ₃real number amplitude and the phase constant of sound wave;

Dissipation factor δ _i=0 (i=1,2), the pump intensity of wave does not change initial condition B because generate resonance wave ₂(0)=0,

the time, trying to achieve the rear frequency of sound wave that interacts is ω ₁, ω ₂amplitude be

(c) according to the pump wave amplitude B obtained ₃(x), weak signal wave amplitude B ₁and resonance wave amplitude B (x) ₂(x) Variation Features is realized the output energy adjustment to three train waves.

2. the output adjusting method of acoustic energy after sound wave interaction in nonlinear dielectric according to claim 1 is characterized in that: described resonance wave for and resonance wave or difference frequency resonance wave, i.e. ω frequently ₂=ω ₁+ ω ₃perhaps ω ₂=ω ₃-ω ₁.

3. the output adjusting method of acoustic energy after sound wave interaction in nonlinear dielectric according to claim 2 is characterized in that: when the resonance wave produced is the difference frequency resonance wave, i.e. and ω ₂=ω ₃-ω ₁the time, the form that is real amplitude and phase place by the Complex Amplitude of three train waves:

Wherein, B ₁(x), B ₂(x), B ₃(x) and

for frequencies omega ₁, ω ₂, ω ₃real number amplitude and the phase constant of sound wave;

Dissipation factor δ _i=0, i=1,2,3, initial condition B ₂(0)=0,

the time, the amplitude of trying to achieve the rear three row sound waves that interact is:

Y=sn (u, k) is the Jacobi elliptic function, cn (u)=(1 one sn ²) ^1/2, dn (u)=(1-k ²sn ²) ^1/2;

Wherein,

4. the output adjusting method of acoustic energy after sound wave interaction in nonlinear dielectric according to claim 1, is characterized in that the described pump wave amplitude B according to obtaining ₃(x), weak signal wave amplitude B ₁and resonance wave amplitude B (x) ₂(x) Variation Features realizes that the output energy adjustment to three train waves is one of following:

(1) according to the pump wave amplitude B obtained ₃(x), weak signal wave amplitude B ₁and resonance wave amplitude B (x) ₂(x) Variation Features is realized the output energy adjustment to three train waves, regulates the output energy of weak signal ripple or resonance wave;

(2) according to weak signal wave amplitude B after interacting ₁and resonance wave amplitude B (x) ₂(x) with pump ripple frequencies omega ₃variation Features, regulate the output energy of weak signal ripple or resonance wave;

(3) according to weak signal wave amplitude B after interacting ₁) and resonance wave amplitude B (x) ₂(x) with weak signal ripple frequencies omega ₁variation Features, regulate the output energy of weak signal ripple or resonance wave;

(4) according to weak signal wave amplitude B after interacting ₁and resonance wave amplitude B (x) ₂(x) with pump wave amplitude B ₃(0) Variation Features, the output energy of adjusting weak signal ripple or resonance wave.

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