CN105547619A - Method and system for testing high-order modal frequency and high-order modal damping of thin wall member - Google Patents

Abstract

The invention provides a method and a system for testing high-order modal frequency and high-order modal damping of a thin wall member. The method comprises steps that theoretical modal frequency and modal shape calculation for the thin wall member is carried out, and the high-order modal frequency quantity and corresponding nodes, corresponding to nodel lines, the corresponding to pitch circle position and distribution of the modal shape can be acquired; the constraint boundary condition for testing the high-order modal frequency and the high-order modal damping of the thin wall member are determined; the high-order modal frequency of the thin wall member is tested; the high-order modal damping of the thin wall member is tested. According to the method, a piezoelectric ceramic vibration exciter is employed to realize high frequency excitation for the thin wall member, and a problem that traditional excitation equipment can not effectively excite the high-order modal of the thin wall member is solved. The frequency domain bandwidth method can be utilized to effectively acquire high-order modal damping of same-type structures, and problems of a traditional frequency domain damping test method existing in thin wall structure application can be solved. The method and the system are advantaged in that the test system is easy to establish, the test method is concise, simple and clear, and good repeatability and relatively high test precision are realized.

Description

A kind of thin-wall member high order mode frequency and damping test method and system

Technical field

The invention belongs to vibration test technology field, be specifically related to a kind of thin-wall member high order mode frequency and damping test method and system.

Background technology

Model frequency and damping are the important kinetic parameters of thin-wall member, accurately obtain its model frequency and its damping of identification has important engineering and academic significance.Under the thin-wall member being representative with blade, wheel disc, axle sleeve, thin-wall drum etc. is usually operated at the environment of multi-scenarios method excitation, often be inspired high order mode frequency (more than 6kHz), and the features such as the high order mode of its correspondence also has simultaneously that frequency distribution is intensive, microvibration, local vibration is abundant, stress distribution is complicated, be usually difficult to be obtained by the test of traditional excitation set.For the damping test problem of thin-wall member, current scholar and researchist generally adopt time domain Free-Vibration decay and frequency domain half-power bandwidth method two kinds of methods to obtain.The principle of time domain Free-Vibration decay is simple, but its raw data is the time history of structural vibration response, inevitably includes the impact of ground unrest, and the precision of damping test will be difficult to ensure.The situation that frequency domain half-power bandwidth method is only applicable to that modal distribution is comparatively disperseed, resonance peak waveform is ideal in frequency spectrum, when two resonance peak close together of adjacent order, likely cause the frequency values near half-power point to be difficult to find, and then affect the measuring accuracy of damping.In addition, in the practical studies of thin-wall member vibration-testing, also find that it often exists linear Stiffness feature in complex boundary or coating damping vibration attenuation application, this also can increase the difficulty of damping identification, the application of restriction traditional frequency domain half-power bandwidth method.For these features of thin-wall member, traditional model frequency and damping test method accurately cannot obtain high order mode frequency and the damping of thin-wall member.

Summary of the invention

The object of the present invention is to provide a kind of thin-wall member high order mode frequency and damping test method and system.

Technical scheme of the present invention is:

A kind of thin-wall member high order mode frequency and damping test method, comprise the following steps:

Step 1: carry out model frequency and Mode Shape theory calculate to thin-wall member, obtains the quantity of high order mode frequency and node corresponding to Mode Shape thereof, nodel line, the position of pitch circle and distribution thereof;

Step 2: determine the restrained boundary condition needed for thin-wall member high order mode frequency and damping test;

Step 3: carry out thin-wall member high order mode frequency test;

Step 3.1: the basic parameter needed for high order mode frequency test is set, comprises: the signal type of the sensitivity of piezoelectric actuator, the sensitivity of laser doppler vibrometer, sample frequency, frequency resolution, signal generator;

The signal type of described signal generator is periodicity buzzing pulse excitation signal, and adds the process of hanning window to this signal, and response signal also adds hanning window in the lump.

Step 3.2: be determined by experiment the quantity of the corresponding point of excitation of piezoelectric actuator, position and driving voltage;

Step 3.3: utilize piezoelectric actuator to carry out vibrational excitation to thin-wall member, obtain multiple frequency response function of thin-wall member and multiple coherence function, and by the fiducial interval of lump coherence function determination lump frequency response function, in this fiducial interval, obtain the high order mode frequency of thin-wall member;

Step 4: carry out thin-wall member high order mode damping test;

Step 4.1: the basic parameter needed for high order mode damping test is set, comprises: frequency sweep interval and sweep rate;

Step 4.2: adopt FFT transform method at times, obtains the frequency domain response signal under swept frequency excitation;

Step 4.3: adopt frequency domain bandwidth method to select bandwidth value, identification obtains certain high order mode damping of thin-wall member, and test obtains other high order mode damping successively.

Described step 3.2 is specifically carried out as follows:

Step 3.2.1: with reference to model frequency and Mode Shape the calculated results, tentatively determines the quantity of point of excitation, position and driving voltage on thin-wall member surface;

Step 3.2.2: the driving voltage of drive power supply for piezoelectric ceramics is set to height, in, low three gears, and be carry out experiment under the condition of in point of excitation quantity, namely with reference to the quantity of the high order mode frequency of step 1 acquisition, judge whether the high order mode frequency effectively exciting thin-wall member, if the driving voltage that high tap position is corresponding effectively can not excite the high order mode frequency of thin-wall member, then increase the quantity of point of excitation or change the position of point of excitation, until the high order mode number of frequencies of testing acquisition is by experiment more than or equal in step 1 quantity obtaining high order mode frequency, determine the quantity of the corresponding point of excitation of piezoelectric actuator, position and driving voltage.

Described step 3.3 is specifically carried out as follows:

Step 3.3.1: test obtains multiple frequency response function of thin-wall member and multiple coherence function, obtain the time domain waveform of pumping signal and the time domain waveform of response signal respectively, and obtain further one or more pumping signal relative to the frequency response function of response signal and coherence function;

Step 3.3.2: carry out summation for each pumping signal respectively relative to the frequency response function of response signal and coherence function and be averaged, calculate lump frequency response function and lump coherence function;

Step 3.3.3: by the fiducial interval of lump coherence function determination lump frequency response function, if the coefficient of coherence of lump coherence function within the scope of certain sample frequency is more than or equal to 0.8, then this sample frequency scope is the fiducial interval of lump frequency response function;

Step 3.3.4: in the fiducial interval of lump frequency response function, obtains the high order mode frequency of thin-wall member by modal idenlification.

Described step 4.2 is specifically carried out as follows:

Step 4.2.1: data prediction: DC component and smoothing processing are gone to the original swept-frequency signal obtained;

Step 4.2.2: time division section: whole time domain response is divided into some time section, is converted to original swept-frequency signal the time domain response signal in some time section;

Step 4.2.3: time-frequency conversion: FFT conversion is carried out to the time domain response signal of each time period, and carry out windowing, filtering process, transfer the time domain response signal of each section to frequency domain response signal;

Step 4.2.4: draw frequency response curve figure: in whole frequency sweep interval, using the frequency after the FFT of each time period conversion as x-axis, the frequency domain response peak value of different time sections, as y-axis, after interpolation smoothing process, draws out the frequency response curve figure of original swept-frequency signal.

The identification formula of the high order mode damping of described thin-wall member is as follows:

$\mathrm{\ξ}=\frac{{\mathrm{\ω}}_2-{\mathrm{\ω}}_1}{2{\mathrm{\ω}}_n\sqrt{1/r^2-1}}$

Wherein, ω _n, ξ is respectively high order mode frequency and high order mode damping ratio, ω ₁, ω ₂be respectively ω _nthe Frequency point of the right and left, r is bandwidth value.

The thin-wall member high order mode frequency that described method adopts and damping test system, comprising:

Produce the signal generator of low voltage excitation signal;

Low voltage excitation signal is converted to the hyperchannel drive power supply for piezoelectric ceramics of high voltage pumping signal;

According to the piezoelectric actuator that high voltage pumping signal encourages thin-wall member;

The laser doppler vibrometer of test thin-wall member response signal;

Gather the data acquisition equipment of exciting force signal and response signal;

Basic parameter needed for high order mode frequency and damping test is set, the computing machine of high order mode damping that the high order mode frequency obtaining thin-wall member in the fiducial interval of lump coherence function determination lump frequency response function, identification obtain thin-wall member;

The input end of the output terminal connecting multi-channel drive power supply for piezoelectric ceramics of signal generator, the output terminal of hyperchannel drive power supply for piezoelectric ceramics connects the input end of piezoelectric actuator, piezoelectric actuator is attached to thin-wall member surface, the input end of the output terminal connection data collecting device of laser doppler vibrometer, the output terminal of data acquisition equipment connects the input end of computing machine.

Beneficial effect:

The inventive method solves thin-wall member high order mode frequency and damping test problem by the test macro built, and this device and method has following technical advantage:

(1) adopt piezoelectric actuator to carry out high frequency pumping to thin-wall member, solve the problem that traditional excitation set effectively cannot encourage thin-wall member high order mode.

(2) the high order mode frequency test step adopted can obtain to degree of precision the high order mode frequency of thin-wall member.

(3) utilize frequency domain bandwidth method effectively can obtain this class formation high order mode damping, solve traditional frequency domain damping test method Problems existing in thin-wall construction application.

(4) test macro adopted is easy to build, and method of testing step is succinctly clear and definite, and favorable repeatability, measuring accuracy is higher.

Accompanying drawing explanation

Fig. 1 is thin-wall member high order mode frequency and the damping test system architecture diagram of the specific embodiment of the invention;

Fig. 2 is frequency response function and the coherence function of the thin-wall member obtained by Piezoelectric Ceramics Excitation of the specific embodiment of the invention;

Fig. 3 is the frequency domain response figure of the 3rd rank swept-frequency signal of Thin-Wall Cylindrical Shells 3 response point of the specific embodiment of the invention;

Fig. 4 is the test Thin-Wall Cylindrical Shells schematic diagram of the specific embodiment of the invention, wherein, and 1-vibration measuring point, 2-annulus pressing plate, 3-M8 bolt, 4-pedestal, 5-piezoelectric actuator, 6-thin wall cylindrical hull structure component;

Fig. 5 is the test of Thin-Wall Cylindrical Shells high frequency model frequency and damping identification process flow diagram under the Piezoelectric Ceramics Excitation of the specific embodiment of the invention.

Embodiment

Below in conjunction with accompanying drawing, the specific embodiment of the present invention is elaborated.

The thin-wall member high order mode frequency that present embodiment adopts and damping test system, as shown in Figure 1, comprising:

Produce the signal generator of low voltage excitation signal;

Low voltage excitation signal is converted to the hyperchannel drive power supply for piezoelectric ceramics of high voltage pumping signal;

According to the piezoelectric actuator that high voltage pumping signal encourages thin-wall member;

The laser doppler vibrometer of test thin-wall member response signal;

Gather the data acquisition equipment of exciting force signal and response signal;

Basic parameter needed for high order mode frequency and damping test is set, the computing machine of high order mode damping that the high order mode frequency obtaining thin-wall member in the fiducial interval of lump coherence function determination lump frequency response function, identification obtain thin-wall member;

The input end of the output terminal connecting multi-channel drive power supply for piezoelectric ceramics of signal generator, the output terminal of hyperchannel drive power supply for piezoelectric ceramics connects the input end of piezoelectric actuator, piezoelectric actuator is attached to thin-wall member surface, the input end of the output terminal connection data collecting device of laser doppler vibrometer, the output terminal of data acquisition equipment connects the input end of computing machine.

Signal generator is used for sending sine, frequency sweep, random, the periodically multiple analog signal such as buzzing pulse.In present embodiment using the signal source of LMSSCADAS acquisition controller as signal generator.LMSSCADAS acquisition controller comprises 16 data acquisition channels and 2 standard signal sources, so possess the function of data acquisition and signal generator simultaneously, can send sine, frequency sweep, random, the periodically multiple analog signal such as buzzing pulse.

Drive power supply for piezoelectric ceramics is used for providing high stability, high-resolution voltage for piezoelectric actuator, in present embodiment, driving power is designed to the form that hyperchannel drives, to avoid single channel actuation in the problem that may there is excitation energy deficiency towards the shell structure of large-size.The Rhvd3c110v driving power matched possesses the function simultaneously driving three piezoelectric actuators, is connected with the output terminal of signal generator by BNC connector.Analogue stimulus signal can be amplified 24 times, and by arranging bias voltage, piezoelectric ceramics is operated within the scope of positive voltage.Its voltage output resolution ratio 5mV, peak power output 100W, can pass through LCD display Real-Time Monitoring output voltage amount.

The thin-wall member of present embodiment is thin wall cylindrical hull structure component, piezoelectric actuator is for being pasted onto the surface of thin-wall member and carrying out vibrational excitation to it, in order to avoid bringing thin wall cylindrical shell structure too large additional mass impact, the piezoelectric actuator that physical dimension is less should be matched.Meanwhile, in order to possess larger excitation amplitude, the stacked thickness of potsherd should be large as far as possible.Through actual test Contrast on effect, piezoelectric actuator matches the P-885.10 of German PI Corp., its physical dimension 5 × 5 × 9mm, electric capacity 0.6uf, only heavy 2g.Can bear the bias voltage of 2.5V to 100V, under 25kHz excitation, maximum displacement vibratory response, close to 0.65um, can realize vibrational excitation in 0.1k ~ 20kHz frequency range, effectively can meet the high frequency pumping demand of thin-wall member at more than 6kHz.

Vibration response signal for obtaining the vibration response signal of thin-wall member, and is sent to data collection and analysis instrument by laser doppler vibrometer.The laser doppler vibrometer that present embodiment is selected is PolytecPDV-100, and vibration velocity minimum resolution is 0.02 μm/s, operating distance 0.15m ~ 30m, frequency range 1Hz ~ 22KHZ.

Data acquisition equipment is 16 passage LMSSCADASMobileFront-End, the response signal that exciting force signal and laser doppler vibrometer test for gathering piezoelectric actuator obtain, and is sent to computing machine.

Computing machine stores test data, show with timely, frequency-domain analysis, and what present embodiment was selected is DELLM6400 high-performance notebook computer.

In present embodiment, tested object is thin wall cylindrical hull structure component 6 as shown in Figure 4, and its quality is 1070g, and its dimensional parameters is in table 1, and concrete material parameter is in table 2.Utilize annulus pressing plate 2 to be fixed on fixture by its mounting edge by 8 M8 bolts 3 and simulate clamped-boundary condition freely, M8 bolt on fixture is then tightened on pedestal 4 by torque spanner with the moment of Uniform provisions, piezoelectric actuator 5 is pasted onto the surface of thin wall cylindrical hull structure component 6, and at vibration measuring point 1, place gathers response signal by laser doppler vibrometer.

The dimensional parameters of table 1 thin wall cylindrical hull structure component

The material parameter of table 2 thin wall cylindrical hull structure component

The thin-wall member high order mode frequency of present embodiment and damping test method, as shown in Figure 5, comprise the following steps:

Step 1: carry out model frequency and Mode Shape theory calculate to thin wall cylindrical hull structure component, obtains the quantity of high order mode frequency and node corresponding to Mode Shape thereof, nodel line, the position of pitch circle and distribution thereof;

Select the lower-frequency limit f of thin wall cylindrical hull structure component high order mode frequency _l, when model frequency is more than or equal to this lower-frequency limit f _ltime, be high order mode frequency, when model frequency is less than this lower-frequency limit f _ltime, be lower mode frequency (selection of lower frequency limit).Simultaneously, respectively in lower mode frequency and high order mode frequency range, by to resolve or Finite Element Method carries out to the model frequency of thin wall cylindrical hull structure component the quantity that theory calculate tentatively obtains high order mode frequency, and grasp node corresponding to its Mode Shape, nodel line, the position of pitch circle and distribution thereof.

Step 2: determine the restrained boundary condition needed for thin-wall member high order mode frequency and damping test;

During free state test, elastic string need be adopted to be hung by tested thin-wall member; The test of constraint state, need by fixture, thin-wall member effectively to be clamped, determined the maximum moment value of M8 bolt by torque spanner, and guarantee effectively to clamp tested housing (for 12.9 grade bolts that fixture adopts, finally determining that screw-down torque value is 40Nm).Ensureing its model frequency and damping parameter when testing, interference and the impact of boundary condition can not be subject to, there is repeatability and consistance preferably.

Step 3: carry out thin-wall member high order mode frequency test;

Step 3.1: the basic parameter needed for high order mode frequency test is set, comprises: the signal type of the sensitivity of piezoelectric actuator, the sensitivity of laser doppler vibrometer, sample frequency, frequency resolution, signal generator;

The sensitivity of the sensitivity and laser doppler vibrometer that arrange piezoelectric actuator is respectively 11.4mV/Pa and 40000mV/ (m/s).

With reference to the test frequency range of Finite element analysis results determination high frequency model frequency, and sample frequency used when determining to test according to Shannon theorem.

The signal type of signal generator is periodicity buzzing pulse excitation signal, and adds the process of hanning window to this signal, and response signal also adds hanning window in the lump, to reduce the impact of lobe error.

Step 3.2: be determined by experiment the quantity of the corresponding point of excitation of piezoelectric actuator, position and driving voltage;

Step 3.2.1: with reference to model frequency and Mode Shape the calculated results, tentatively determines the quantity of point of excitation, position and driving voltage on thin-wall member surface;

Due to laser doppler vibrometer belong to accurate, expensive instrument, the quantity of usual vibration measurement with laser point is only defined as one, and laser doppler vibrometer is arranged in the larger position of thin-wall member vibratory response; Then, a piezoelectric actuator is arranged in the root position of housing.

Step 3.2.2: the driving voltage of drive power supply for piezoelectric ceramics is set to height, in, low three gears, and be carry out experiment under the condition of in point of excitation quantity, namely with reference to the quantity of the high order mode frequency of step 1 acquisition, judge whether the high order mode frequency effectively exciting thin-wall member, if the driving voltage that high tap position is corresponding effectively can not excite the high order mode frequency of thin-wall member, then increase the quantity of point of excitation or change the position of point of excitation, until the high order mode number of frequencies of testing acquisition is by experiment more than or equal in step 1 quantity obtaining high order mode frequency, determine the quantity of the corresponding point of excitation of piezoelectric actuator, position and driving voltage.

Step 3.3: utilize piezoelectric actuator to carry out vibrational excitation to thin-wall member, obtain multiple frequency response function of thin-wall member and multiple coherence function, and by the fiducial interval of lump coherence function determination lump frequency response function, in this fiducial interval, obtain the high order mode frequency of thin-wall member;

Step 3.3.1: signal generator sends simulating signal and amplified by drive power supply for piezoelectric ceramics, piezoelectric actuator is driven to carry out vibrational excitation to thin-wall member, data acquisition equipment gathers the vibration response signal that laser doppler vibrometer obtains, computing machine obtains multiple frequency response function of thin-wall member and multiple coherence function, obtain the time domain waveform of pumping signal and the time domain waveform of response signal respectively, and obtain further one or more pumping signal relative to the frequency response function of response signal and coherence function, as shown in Figure 2;

Step 3.3.2: carry out summation for each pumping signal respectively relative to the frequency response function of response signal and coherence function and be averaged, calculate lump frequency response function and lump coherence function;

Step 3.3.3: by the fiducial interval of lump coherence function determination lump frequency response function, if the coefficient of coherence of lump coherence function within the scope of certain sample frequency is more than or equal to 0.8, then this sample frequency scope is the fiducial interval of lump frequency response function;

Step 3.3.4: in the fiducial interval of lump frequency response function, by modal identification methods such as single-degree-of-freedom Peak Intensity Method, modal idenlification obtains the high order mode frequency f of thin-wall member _n.

Model frequency within the scope of the Thin-Wall Cylindrical Shells 0 ~ 12kHz obtained under piezoelectric actuator excitation is in table 3.

Model frequency within the scope of the Thin-Wall Cylindrical Shells 0 ~ 12kHz obtained under table 3 Piezoelectric Ceramics Excitation

Step 4: carry out thin-wall member high order mode damping test;

Step 4.1: the basic parameter needed for high order mode damping test is set, comprises: frequency sweep interval and sweep rate;

Start frequency according to frequency sweep interval criteria determination frequency sweep and terminate frequency.This frequency sweep interval criteria can be described as:

First, the beginning frequency f in this frequency sweep interval must be ensured ₁with end frequency f ₂with certain rank model frequency f of thin wall cylindrical hull structure component _n, and forward and backward rank model frequency f _n-1, f _n+1demand fulfillment formula (1), meanwhile, determines to start frequency f according to formula (2) ₁with end frequency f ₂concrete numerical value.

f _n-1＜f ₁≤f _n≤f ₂＜f _n+1(1)

f ₁＝(0.8～0.85)f _n(2)

f ₂＝(1.15～1.2)f _n

Determine to test certain sweep rate needed for high order mode damping: because too fast sweep velocity likely comprises the impact of transient oscillation, cause the final damping results obtained to occur error.Therefore, before carrying out sweep check, the frequency resultant that the spectrum curve maximal value of the vibration response signal obtained under needing first to compare several sweep rates is corresponding, if said frequencies result corresponding to certain several speed parameter closely, then one of them can be selected as test sweep rate used.

Step 4.2: adopt FFT transform method at times, obtains the frequency domain response signal under swept frequency excitation, as shown in Figure 3;

Step 4.2.1: data prediction: go DC component and smoothing processing to the original swept-frequency signal obtained, rejects the burr in time-domain signal, and reduce the impact of disturbing factor, the original swept-frequency signal that test is obtained is as far as possible close to its actual value;

Step 4.2.2: time division section: whole time domain response is divided into some time section, is converted to original swept-frequency signal the time domain response signal in some time section; Time period divides more, then the precision of the frequency response curve of follow-up acquisition is higher.

Step 4.2.3: time-frequency conversion: FFT conversion is carried out to the time domain response signal of each time period, and carry out windowing, filtering process, transfer the time domain response signal of each section to frequency domain response signal;

Step 4.2.4: draw frequency response curve figure: in whole frequency sweep interval, using the frequency after the FFT of each time period conversion as x-axis, the frequency domain response peak value of different time sections, as y-axis, after interpolation smoothing process, draws out the frequency response curve figure of original swept-frequency signal.

Step 4.3: adopt frequency domain bandwidth method to select bandwidth value, identification obtains certain high order mode damping of thin-wall member, and test obtains other high order mode damping successively.

Suppose the motion of tested thin-wall member under the excitation of certain piezoelectric actuator to be x (t), m, c, k be the quality of system, damping and rigidity, excitation types is harmonic excitation, and excitation amplitude is F ₀, excitation frequency is ω, then its equation of motion can be expressed as:

$m\stackrel{\·\·}{x}+c\stackrel{\·}{x}+kx=F_{0}sin\mathrm{\ω}t---\left(3\right)$

Its steady-state response amplitude is

$X=\frac{F_0/k}{\sqrt{{\[1-{(\mathrm{\ω}/{\mathrm{\ω}}_n)}^2\]}^2+{\[2\mathrm{\ξ}(\mathrm{\ω}/{\mathrm{\ω}}_n)\]}^2}}---\left(4\right)$

In formula, ω _n, ξ is respectively certain rank model frequency and damping ratios.

If λ=ω/ω _nfor frequency ratio, formula (4) is dissolved and can be obtained

$\mathrm{\β}=\frac{Xk}{F_0}=\frac{1}{\sqrt{{\[1-{(\mathrm{\ω}/{\mathrm{\ω}}_n)}^2\]}^2+{\[2\mathrm{\ξ}(\mathrm{\ω}/{\mathrm{\ω}}_n)\]}^2}}---\left(5\right)$

${\mathrm{\β}}_{max}=\frac{1}{2\mathrm{\ξ}}---\left(6\right)$

At ω _ntwo Frequency point ω are got in left and right ₁, ω ₂, and ensure ω ₁, ω ₂corresponding dimensionless amplitude is equal, i.e. β ₁=β ₂, β ₁, β ₂with dimensionless amplitude maximum β _maxratio be r (0 < r < 1), i.e. β ₁=β ₂=r β _max, then have

$\frac{r}{2\mathrm{\&xi;}}=\frac{1}{\sqrt{{(1-{\mathrm{\&lambda;}}^2)}^2+{\left(2\mathrm{\&xi;}\mathrm{\&lambda;}\right)}^2}}---\left(7\right)$

Can obtain further

${\mathrm{\&lambda;}}^2=\frac{(2r^2-4r^2{\mathrm{\&xi;}}^2)\&PlusMinus;4r\mathrm{\&xi;}\sqrt{1+r^2{\mathrm{\&xi;}}^2-r^2}}{2r^2}---\left(8\right)$

As ξ < < 1, ξ can be ignored ², then can be by further for formula (6) abbreviation

${\mathrm{\&lambda;}}^2\&ap;\frac{2r^2\&PlusMinus;4r\mathrm{\&xi;}\sqrt{1-r^2}}{2r^2}=\frac{2r^2\&PlusMinus;4r^2\mathrm{\&xi;}\sqrt{1/r^2-1}}{2r^2}---\left(9\right)$

Two corresponding solutions are respectively

${\mathrm{\&omega;}}_2^2=\frac{{\mathrm{\&omega;}}_n^2(2r^2+4r^2\mathrm{\&xi;}\sqrt{1/r^2-1})}{2r^2}---\left(10\right)$

${\mathrm{\&omega;}}_1^2=\frac{{\mathrm{\&omega;}}_n^2(2r^2-4r^2\mathrm{\&xi;}\sqrt{1/r^2-1})}{2r^2}---\left(11\right)$

Two separate square to subtract each other

${\mathrm{\&omega;}}_2^2-{\mathrm{\&omega;}}_1^2=\frac{{\mathrm{\&omega;}}_n^{2}8r^2\mathrm{\&xi;}\sqrt{1/r^2-1}}{2r^2}---\left(12\right)$

Can obtain formula (12) abbreviation

$2\mathrm{\&xi;}=\frac{2({\mathrm{\&omega;}}_2^2-{\mathrm{\&omega;}}_1^2)r^2}{4r^2{\mathrm{\&omega;}}_n^2\sqrt{1/r^2-1}}=\frac{({\mathrm{\&omega;}}_2^2-{\mathrm{\&omega;}}_1^2)}{2{\mathrm{\&omega;}}_n^2\sqrt{1/r^2-1}}---\left(13\right)$

Two summed square of separating obtain carry it into formula (13), the identification formula that can obtain the high order mode damping of thin-wall member is

$\mathrm{\&xi;}=\frac{{\mathrm{\&omega;}}_2-{\mathrm{\&omega;}}_1}{2{\mathrm{\&omega;}}_n\sqrt{1/r^2-1}}---\left(14\right)$

Wherein, ω _n, ξ is respectively high order mode frequency and high order mode damping ratio, ω ₁, ω ₂be respectively ω _nthe Frequency point of the right and left, r is bandwidth value.

Formula (14) is the principle formula of certain the high order mode damping adopting frequency domain bandwidth method identification thin-wall member, can according to this formula, and after selected rational bandwidth value r, identification obtains certain high-order damping of thin-wall member.Because each rank mode of the thin wall cylindrical hull structure component in present embodiment is not very dense, therefore the r value of frequency domain bandwidth method is set as be half-power bandwidth method test and obtain its modal damping.But the interval of some high frequency natural frequency of thin-wall member is often comparatively near, setting the frequency values near half-power point may be can not find, then need the new bandwidth value r of setting to carry out identification damping.Adopt the principle formula (12) of certain high order mode damping of frequency domain bandwidth method identification thin-wall member to obtain the high order mode damping of Thin-Wall Cylindrical Shells successively, the high order mode damping ratio of the Thin-Wall Cylindrical Shells that test obtains is in table 4.

Table 4 tests the front 8 rank model frequencies of thin wall cylindrical hull structure component, damping ratio and the variance that obtain

Specific embodiment described in present embodiment is only to the enforcement of art solutions of the present invention explanation for example.Patent person of ordinary skill in the field of the present invention can make an amendment described specific embodiment or supplements or adopt similar mode to substitute, but can't depart from technical scheme of the present invention or surmount the scope that appended claims defines.

Claims (7)

1. thin-wall member high order mode frequency and a damping test method, is characterized in that, comprise the following steps:

Step 1: carry out model frequency and Mode Shape theory calculate to thin-wall member, obtains the quantity of high order mode frequency and node corresponding to Mode Shape thereof, nodel line, the position of pitch circle and distribution thereof;

Step 2: determine the restrained boundary condition needed for thin-wall member high order mode frequency and damping test;

Step 3: carry out thin-wall member high order mode frequency test;

Step 3.1: the basic parameter needed for high order mode frequency test is set, comprises: the signal type of the sensitivity of piezoelectric actuator, the sensitivity of laser doppler vibrometer, sample frequency, frequency resolution, signal generator;

Step 3.2: be determined by experiment the quantity of the corresponding point of excitation of piezoelectric actuator, position and driving voltage;

Step 3.3: utilize piezoelectric actuator to carry out vibrational excitation to thin-wall member, obtain multiple frequency response function of thin-wall member and multiple coherence function, and by the fiducial interval of lump coherence function determination lump frequency response function, in this fiducial interval, obtain the high order mode frequency of thin-wall member;

Step 4: carry out thin-wall member high order mode damping test;

Step 4.1: the basic parameter needed for high order mode damping test is set, comprises: frequency sweep interval and sweep rate;

Step 4.2: adopt FFT transform method at times, obtains the frequency domain response signal under swept frequency excitation;

Step 4.3: adopt frequency domain bandwidth method to select bandwidth value, identification obtains certain high order mode damping of thin-wall member, and test obtains other high order mode damping successively.

2. thin-wall member high order mode frequency according to claim 1 and damping test method, it is characterized in that, the signal type of described signal generator is periodicity buzzing pulse excitation signal, and adds the process of hanning window to this signal, and response signal also adds hanning window in the lump.

3. thin-wall member high order mode frequency according to claim 1 and damping test method, is characterized in that, described step 3.2 is specifically carried out as follows:

Step 3.2.1: with reference to model frequency and Mode Shape the calculated results, tentatively determines the quantity of point of excitation, position and driving voltage on thin-wall member surface;

Step 3.2.2: the driving voltage of drive power supply for piezoelectric ceramics is set to height, in, low three gears, and be carry out experiment under the condition of in point of excitation quantity, namely with reference to the quantity of the high order mode frequency of step 1 acquisition, judge whether the high order mode frequency effectively exciting thin-wall member, if the driving voltage that high tap position is corresponding effectively can not excite the high order mode frequency of thin-wall member, then increase the quantity of point of excitation or change the position of point of excitation, until the high order mode number of frequencies of testing acquisition is by experiment more than or equal in step 1 quantity obtaining high order mode frequency, determine the quantity of the corresponding point of excitation of piezoelectric actuator, position and driving voltage.

4. thin-wall member high order mode frequency according to claim 1 and damping test method, is characterized in that, described step 3.3 is specifically carried out as follows:

Step 3.3.1: test obtains multiple frequency response function of thin-wall member and multiple coherence function, obtain the time domain waveform of pumping signal and the time domain waveform of response signal respectively, and obtain further one or more pumping signal relative to the frequency response function of response signal and coherence function;

Step 3.3.2: carry out summation for each pumping signal respectively relative to the frequency response function of response signal and coherence function and be averaged, calculate lump frequency response function and lump coherence function;

Step 3.3.3: by the fiducial interval of lump coherence function determination lump frequency response function, if the coefficient of coherence of lump coherence function within the scope of certain sample frequency is more than or equal to 0.8, then this sample frequency scope is the fiducial interval of lump frequency response function;

Step 3.3.4: in the fiducial interval of lump frequency response function, obtains the high order mode frequency of thin-wall member by modal idenlification.

5. thin-wall member high order mode frequency according to claim 1 and damping test method, is characterized in that, described step 4.2 is specifically carried out as follows:

Step 4.2.1: data prediction: DC component and smoothing processing are gone to the original swept-frequency signal obtained;

Step 4.2.2: time division section: whole time domain response is divided into some time section, is converted to original swept-frequency signal the time domain response signal in some time section;

Step 4.2.3: time-frequency conversion: FFT conversion is carried out to the time domain response signal of each time period, and carry out windowing, filtering process, transfer the time domain response signal of each section to frequency domain response signal;

Step 4.2.4: draw frequency response curve figure: in whole frequency sweep interval, using the frequency after the FFT of each time period conversion as x-axis, the frequency domain response peak value of different time sections, as y-axis, after interpolation smoothing process, draws out the frequency response curve figure of original swept-frequency signal.

6. thin-wall member high order mode frequency according to claim 1 and damping test method, is characterized in that, the identification formula of the high order mode damping of described thin-wall member is as follows:

$\mathrm{\&xi;}=\frac{{\mathrm{\&omega;}}_2-{\mathrm{\&omega;}}_1}{2{\mathrm{\&omega;}}_n\sqrt{1/r^2-1}}$

Wherein, ω _n, ξ is respectively high order mode frequency and high order mode damping ratio, ω ₁, ω ₂be respectively ω _nthe Frequency point of the right and left, r is bandwidth value.

7. the thin-wall member high order mode frequency that adopts of the method for claim 1 and damping test system, is characterized in that, comprising:

Produce the signal generator of low voltage excitation signal;

Low voltage excitation signal is converted to the hyperchannel drive power supply for piezoelectric ceramics of high voltage pumping signal;

According to the piezoelectric actuator that high voltage pumping signal encourages thin-wall member;

The laser doppler vibrometer of test thin-wall member response signal;

Gather the data acquisition equipment of exciting force signal and response signal;

Basic parameter needed for high order mode frequency and damping test is set, the computing machine of high order mode damping that the high order mode frequency obtaining thin-wall member in the fiducial interval of lump coherence function determination lump frequency response function, identification obtain thin-wall member;

The input end of the output terminal connecting multi-channel drive power supply for piezoelectric ceramics of signal generator, the output terminal of hyperchannel drive power supply for piezoelectric ceramics connects the input end of piezoelectric actuator, piezoelectric actuator is attached to thin-wall member surface, the input end of the output terminal connection data collecting device of laser doppler vibrometer, the output terminal of data acquisition equipment connects the input end of computing machine.