CN106960068A - A kind of damping ratios quick calculation method based on pulse excitation response spectrum - Google Patents
A kind of damping ratios quick calculation method based on pulse excitation response spectrum Download PDFInfo
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Abstract
The present invention discloses a kind of damping ratios quick calculation method based on pulse excitation response spectrum, exciting, the pick-up position of structure are determined first, ensure that it had both been located at the node adjacent to Mode Shape, at nodel line, also for each test there is the position obvious responsed under Mode Shape；Signal picker records pick-up point response signal, and is met with a response frequency spectrum as discrete Fourier transform；Corresponding response under resonance (or peak value) frequency and its near by frequency is extracted on this basis, obtains steady-state response amplitude；The relevant parameters such as frequency ratio, response ratio are finally calculated, the identification of structural modal damping ratio is realized.The method can solve following technical problem in the prior art：Traditional half-power method is difficult to be exactly found half power points；Some excitation time-domain signals are difficult to direct measurement, and the frequency response function needed for causing frequency domain method calculating damping ratios can not be obtained sometimes；Response under contact excitation is commonly present the problems such as transient components decay is not thorough, cumbersome.
Description
Technical field
The invention belongs to modal parameters identification field, it is related to a kind of method of testing of Produced by Modal damping ratio,
Impulse response frequency spectrum of the structure in each rank resonance region is particularly related to, its each rank damping ratios are carried out with the reality of inverting
Existing method.
Background technology
Damping parameter is very notable in the response influence of resonance region on structure as an important power performance index.
Engineering structure damping torque is complicated, is usually comprehensively to be determined by internally-damped (material), structural damping and fluid damping
It is fixed, but existing damping test standard (such as GB/T 18258-2000, GB/T 16406-1996) is the material for test specimen mostly
Expect damping measurement, it is difficult to directly apply to respond prediction.Linear vibrational system obeys modal superposition principle, and its sound of something astir is accrued
Calculation has to rely on system mode damping ratio, and some fields are provided by statistical law to the damping ratio, with certain limitation
Property.Therefore, damping ratio also needs to determine by testing, but the fine difference of experimental condition may also can cause measurement result
Huge deviation, probe into reliable and practical damping test method also very urgent.
The modal damping of current special construction recognized by analysis of experiments, traditional parameter identification method can when
Carried out in domain and frequency domain.Conventional frequency domain method includes single-degree-of-freedom diagram method (such as peak picking method, admittance circule method) and more oneself
By degree analytic method (such as all kinds of to fit method), the sparse small damping structure of mode and the intensive big damping knot of mode are respectively suitable for
Structure.Peak picking method has used half-power theoretical, discrete spectral line be difficult to obtain accurate half power points, window damping effect and
Unlike signal processing means, may cause damping calculating error to reach several times even tens times；Admittance circule method computational accuracy by
The limitation of precision is illustrated, and can not be avoided because of the error produced by neighbouring modal superposition.Fitting analytic method often handles multiple degrees of freedom
System, measure-point amount can be increased by generally obtaining the information of close mode, and this behave had both increased amount of calculation or had been also easy to produce morbid state and turned
Matrix is changed, so that affecting parameters accuracy of identification.Parameter identification under many-degrees of freedom system time domain need to use window function to filter signal
Ripple processing, classical window precision when separating low frequency close mode, superposition mode is poor, is particularly at the two ends of frequency response function
And very close to mode.
The global vibration damped coefficient difficulty of test of the labyrinths such as naval vessels is larger, and time domain damped method is only capable of obtaining it
Low order damped coefficient, frequency response curve must measure the clock signal of response and excitation simultaneously again when recognizing, this is in some cases
It is also often unpractical (step excitation of such as large scale structure, autoexcitation), this is damping test and dynamic response forecast band
Difficulty is carried out.
There is contact and contactless two kinds to the exiting form of structured testing.The contact that the effect such as vibrator is produced
Excitation can make structure obtain sustained vibration response, and specification is carried out to the method for testing of different excitation waveforms under vibrator effect
Regulation, but can exist during misoperation free vibration decay not thoroughly, sample data leakage is serious, resonance region data acquisition
The problems such as measuring inadequate, certain error is caused to frequency response function test and parameter identification.In addition, near mesomerism area
When carrying out continuation excitation, if damping is smaller, structure reaches that the steady-state vibration time is longer, it is larger to respond, it is easy to which structure is caused
Damage.
The content of the invention
The purpose of the present invention, is to provide a kind of damping ratios based on pulse excitation response spectrum quickly side of calculating
Method, it can solve technical problem following in the prior art：Traditional half-power method typically is difficult to accurately look for when calculating damping ratio
To half power points；It is difficult to measure by some excitation time-domain signals and is limited, frequency domain method calculates the frequency response letter needed for damping ratios
Number can not be obtained sometimes；And the response under contact excitation is commonly present the problems such as transient components decay is not thorough, cumbersome.
In order to reach above-mentioned purpose, solution of the invention is：
A kind of damping ratios quick calculation method based on pulse excitation response spectrum, comprises the following steps：
Step 1, structure exciting-pick-up point position is determined；
Step 2：Collection pick-up point time domain response signal simultaneously makees frequency domain conversion；
Step 3：Extract stable state resonance response amplitude；
Step 4, damping ratio computing parameter is determined：Frequency ratio and response ratio, calculate damping ratio.
In above-mentioned steps 1, placement sensor in position, to determine structure exciting-pick-up point position, the appropriate position
" node ", " nodel line " place for referring to and being both located at neighbouring mode is put, also for each test there is the position obvious responsed under Mode Shape.
The sensor uses displacement transducer, velocity sensor or acceleration transducer.
In above-mentioned steps 2, response signal of the structure under excited by impact is acquired using dynamic signal acquisition instrument,
Measure pick-up point dynamic response time course curve.
In above-mentioned steps 2, signal is carried out to use discrete Fourier transform during frequency domain conversion, the size N of transform block is 2
Integer power, record time-domain signal duration T=N Δ t, the Δ t of sample frequency 1/, frequency-domain analysis frequency resolution Δ f=1/T
=1/N Δs t；Each sampling point value is xr, r=0,1 ..., N-1, the discrete spectral line under frequency domain is：
Spectral line spacing frequency is Δ f, and fitting discrete spectrum curve is h (k Δs f).
The detailed content of above-mentioned steps 3 is：
It is resonant frequency ω to make frequency corresponding to the m articles spectral linenj, its adjacent the m ± q articles position of spectral line correspondence resonance
The near by frequency of frequencyThen the frequency response spectral line amplitude in test result at jth rank resonant frequency and its near by frequency is：
|hArteries and veins(ωnj) |=| hArteries and veins(m Δs f) |, it is ω corresponding to frequencynjForced vibration under=m Δs f resonant excitation rings
Answer amplitude | xj(t)|；
It is corresponding to frequencyResonant excitation under force and shake
Dynamic response amplitude
Wherein, Δ f is frequency-domain analysis frequency resolution, and m represents the corresponding frequency response spectral line numbering of jth rank resonant frequency, m
± q represents the corresponding frequency response spectral line numbering of jth rank resonant frequency near by frequency.
In above-mentioned steps 4, when damping ratio is smaller, response ratio and frequency ratio are calculated according to following formula：
Wherein, χjResponse amplitude under referring to jth rank resonance response amplitude and being encouraged by jth rank resonant frequency near by frequency
The ratio between, γjRefer to the ratio between jth rank resonant frequency near by frequency and resonant frequency, | hArteries and veins(m Δs f) | represent the resonance that frequency is m Δs f
Frequency response spectral line amplitude under excitation, | hArteries and veins(m ± q) Δ f) | it is the frequency response spectral line under (m ± q) Δ f resonant excitation to represent frequency
Amplitude, Δ f is frequency-domain analysis frequency resolution, and m represents jth rank resonant frequency corresponding frequency response spectral line numbering, and m ± q represents the
The corresponding frequency response spectral line numbering of j rank resonant frequency near by frequencies；
Damping ratios result is obtained according to following formula：
Wherein, ζjRepresent damping ratio.
In above-mentioned steps 4, when damping ratio is larger, response ratio and frequency ratio are calculated according to following formula：
Wherein,Response width under referring to jth rank mode peak response amplitude and being encouraged by response crest frequency near by frequency
The ratio between value,Refer to jth rank peak value of response frequency near by frequency and peak value of response frequency ratio, Δ f is frequency-domain analysis frequency discrimination
Rate,The corresponding frequency response spectral line numbering of jth rank crest frequency is represented,Represent that jth rank crest frequency near by frequency is corresponding
Frequency response spectral line is numbered；
Damping ratios result is obtained according to following formula：
Wherein, ζjRepresent damping ratio.
After such scheme, the present invention directly utilizes the vibratory response progress signal analysis and processing and structure of structure
Damping ratios recognize that exciting, pick-up position first to structure are determined, it is ensured that its be both located at neighbouring mode node,
At nodel line, also to have the position that obvious responses under each first order mode；The response signal of pick-up point is recorded using signal picker,
And it is met with a response frequency spectrum as discrete Fourier transform；Resonance (or peak value) frequency and its neighbouring frequency are extracted on this basis
Response and frequency at rate, obtain steady-state response amplitude；Frequency when response ratio is calculated finally according to theory deduction, phase is completed
The calculating of related parameter, realizes the identification of structural modal damping ratio.
Compared with prior art, the beneficial effects of the invention are as follows：
(1) method that time domain response is obtained from frequency domain, can quick and precisely prediction structure transient state under resonant excitation it is anti-
Answer the steady-state response amplitude of complete attenuation, can also break away from driving frequency transfer the files, the limitation of scope, and avoid resonance excitation
Under to structure cause damage, complete optional frequency under steady-state response extract, in some cases compared with resonant excitation experimental test essence
Degree is high, disturb small, speed fast.In addition, according to the reciprocity of frequency response function, can also be right when energized position is not suitable for excitation
Row energization is entered in pick-up position, and the response of measurement energized position carrys out the response characteristic of equivalent forecast pick-up position, and operation is more clever
It is living；
(2) what is obtained after time domain response progress Fourier transformation is the discrete spectral line under frequency domain, due to by frequency resolution
Limitation, traditional half-power method is often difficult to find half power points to estimate damping ratios just.It is this only to be rung from pulse
Answer discrete spectral line information limited in frequency spectrum to start with come the method for calculating damping ratio, can both avoid measuring the time domain letter of exciting force
Number, dependence to continuous frequency spectrum when solving damping ratio using frequency domain information can be broken away from again, it is simple to operate rapid, and precision compared with
It is high.
Brief description of the drawings
Fig. 1 is the flow chart of the present invention；
Fig. 2 is hull beam model first three the first order mode figure used in the embodiment of the present invention 1；
Fig. 3 is surface ship modal damping coefficient specified in specification；
Fig. 4 is stem numerical computations response spectrum and the stable state resonance time domain response of operating mode 1 in the embodiment of the present invention 1；
Wherein, (a) is numerical computations stem dynamic respond frequency spectrum, and (b) is by ω1jWhen=m Δs f=1.055Hz is encouraged
Stem stable state resonance response, (c) be byStem stable state resonance response during excitation, (d) is
PressStem stable state resonance response during excitation；
Fig. 5 is response spectrum used during each rank damping ratio identification under three kinds of operating modes in embodiment 1；
Wherein, (a) is the response spectrum (to calculate the 1st, 3 rank damping ratios) at the 2nd first order mode " node " place, (b)
It is the response spectrum (to calculate the 2nd rank damping ratios) at the 1st first order mode " node " place.
Fig. 6 is the Slab element bulk testing model structure side view (schematic diagram) used in the embodiment of the present invention 2；
Wherein, structure 1 is upper cover plate, and structure 2 is coverboard test model, and structure 3 is reinforcement, and structure 4 is base；
Fig. 7 is Whole structure model three-dimensional artificial design sketch used in the embodiment of the present invention 2；
Fig. 8 is exciting, pick-up point arrangement schematic diagram in the embodiment of the present invention 2；
Wherein, (a) is plate front impacting point position and numbering, and (b) is back pick-up point (sensor) position and volume
Number；
When Fig. 9 is that Slab element model the first rank damping ratio measurement condition is responded in the embodiment of the present invention 2, frequency-region signal；
Wherein, (a) is according to the domain response of 61# pick-up points is believed during the exciting 58# points of each rank operating mode scheme requirement in Figure 10
Number (interception 0~0.205s), (b) is impulse response frequency spectrum (taking 0~1.0kHz) corresponding with (a).
Figure 10 is Slab element model test with emulating preceding 8 rank model analysis comparing result；
Wherein, bending vibation mode picture is 600mm × 600mm pilot regions, " arrow" it is pulse excitation point, " circle" gathered for response
Point.)
Embodiment
Below with reference to accompanying drawing, technical scheme is described in detail.
As shown in figure 1, the present invention provides a kind of damping ratios based on pulse excitation response spectrum quickly side of calculating
Method, comprises the following steps：
Step 1, structure exciting-pick-up point position is determined
Linear vibrating system structure meets modal superposition principle, and its each rank damping ratios test is all based on actual knot
What structure was obtained.The arrangement of pick-up point sensor should be determined according to the model analysis carried out in advance, i.e., be both located at neighbouring mode
" node ", " nodel line " place, also for there is the position obvious responsed under each test Mode Shape, to reduce the superposition of neighbouring mode
Composition influence.Wherein, displacement, speed or acceleration transducer are applied to measurement demand of this method to response signal.
In necessarily research frequency band, think to be actuated to approximate ideal pulse signal produced by temporary impact during test.
It is excited by impact that experiment can use the forms such as different size of power hammer, collision realize, but the time-domain signal encouraged without measurement.Grind
Study carefully frequency range it is wider when, pulsewidth τ excited by impact is can record, it is determined that effectively excitation cut-off frequency fc=1/ τ.
Step 2：Collection pick-up point time domain response signal simultaneously makees frequency domain conversion
Response signal of the structure under excited by impact is acquired using dynamic signal acquisition instrument, pick-up crawl is measured
State response time course curve.Signal is carried out to use discrete Fourier transform (DFT) during time and frequency zone conversion, because its algorithm is needed
Will, the integer power (being represented with N) for being typically sized to 2 of DFT block, record time-domain signal duration T=N Δs t (unit is s) is adopted
The Δ t of sample frequency 1/, frequency-domain analysis frequency resolution Δ f=1/T=1/N Δs t.
Each sampling point value is xrDiscrete spectral line under (r=0,1 ..., N-1), frequency domain is：
Spectral line frequency is h (k Δs f) at intervals of Δ f, namely frequency-domain analysis frequency resolution, fitting discrete spectrum curve.
Step 3：The extraction of stable state resonance response amplitude
Structure can be obtained to the response characteristic of impact load by the motion analysis of one-dimensional elastic systems.General
Impulsive force is semisinusoidal shape, and time domain impulse pulsewidth is narrower, and its signal band is wider, and limiting case is the δ functions that pulsewidth is 0, its
Fourier transformation is the white spectra without limit for width, i.e.,
(1) when acting on impulsive force to single-degree-of-freedom viscous damping system,
System, which is obtained, to be made free vibration, i.e. impulse response function and is after the initial velocity：
Wherein, p0For impulsive force amplitude, m, c, k are respectively quality, damping and the rigidity of system, ωnInherently freely to shake
Dynamic frequency,To have free decaying vibration frequency, ζ=c/ccWith γ=ω/ωnRespectively damping ratio and frequency
Than.Use hArteries and veins(ω) represents xArteries and veins(t) frequency-domain transform：
Response amplitude-frequency under optional frequency ω is：
(2) when acting on Harmonic Loads to single-degree-of-freedom viscous damping system,
Overall reaction, which can be obtained, is：
Formula (8) right-hand member Section 1 is represented by e-ξωtThe transient response of decay, A is the constant that primary condition is determined；Section 2
For infinitely lasting stable state resonant reactive, with | xIt is humorous(t) | represent its stable state resonance amplitude.It is generally acknowledged that transient response decay is very
Ignored soon, but the reaction is difficult decay in some cases, or even played a leading role in the range of certain time, entering
If this point is ignored during row resonant excitation will influence the accuracy of response test.
Convolution (6), (8), relation between time domain resonant excitation response and frequency-domain impulse exciter response of setting up is：
|hArteries and veins(ω) |=| xIt is humorous(t)| (9)
According to formula (9), impulsive force width (is p with resonance power width0) it is equal when, the amplitude-frequency of impulse response frequency spectrum with it is corresponding humorous
Forced vibration amplitude under vibration frequency ω is equal.Therefore, it can be extracted from impulse response frequency spectrum, power width and pulse force width
Stable state resonance response amplitude after transient response fully decays under equal optional frequency harmonic excitation effect.
It can obtain, the frequency response spectral line amplitude in experimental test result at jth rank resonant frequency and its near by frequency is：
|hArteries and veins(ωnj) |=| hArteries and veins(m Δs f) |, it is ω corresponding to frequencynjForced vibration under=m Δs f resonant excitation rings
Answer amplitude | xj(t)|；
It is corresponding to frequencyResonant excitation under force and shake
Dynamic response amplitude
In formula, frequency corresponding to the m articles spectral line is resonant frequency ωnj, its adjacent the m ± q articles position of spectral line correspondence is altogether
The near by frequency of vibration frequencyM represents jth rank resonant frequency corresponding frequency response spectral line numbering (i.e. the m articles), and m ± q represents the
The corresponding frequency response spectral line numbering (i.e. the m ± q articles) of j rank resonant frequency near by frequencies.
Step 4：The Inversion Calculation of damping ratios
Damping ratio computing formula is deduced with one dimension beam model, two, three dimension system it is equally applicable.It is folded based on mode
Plus it is theoretical, overall response of the system under frequencies omega resonant excitation is：
Exciting force acts on x=x0Place, constant power are p0, by jth rank resonant frequency ωnjDuring excitation, master mode response
Much larger than other rank modal response, i.e. overall responses for (wherein)：
(1) when damping larger, the peak value of response (i.e. mode peak response) of experimental test is greater than frequency resonance response
, that is, survey peak value respective frequencies in response spectrumAnd anti-resonance frequency ωnj, there is relation：
Jth rank peak value of response is：
Jth rank modal response crest frequency near by frequency isOrder PressOverall response is during resonant excitation：
WhenWithVery close to when, jth rank master mode response also be much larger than other rank modal components, for improve calculate essence
Formula (14), can be reduced to being superimposed for master mode and adjacent modal response by degree, if but pick-up-impacting point positioned at adjacent mode
When the vibration shape " node " or " nodel line " position, adjacent modal response component is zero.Now：
It can be obtained by formula (13), (15)：
Order：That is jth rank modal response peak value is with pressingResponse width under frequency excitation
The ratio between value, dimensionless；：
Obtained by formula (16), (17)：
(2) when damping smaller,Formula (13) is approximately reduced to formula (11), and acquired results precision is also subjected to.
It can similarly obtain as stated above：
Now, Represent jth rank resonant frequency ωnjIt is neighbouring
Frequency, χjRepresent jth rank resonance response amplitude with pressingThe ratio between response amplitude under frequency excitation.
The stable state resonance amplitude and spectral line respective frequencies extracted according to step 3 from impulse response frequency spectrum, can be used for
γ is calculated in the stepjWith χj(orWith), i.e.,：
(or)
(or)
Wherein, γjRefer to jth rank resonant frequency near by frequencyWith resonant frequency ωnjThe ratio between, abbreviation frequency ratio； χjRefer to the
J rank resonance response amplitudes are with pressingThe ratio between response amplitude under frequency excitation, abbreviation response ratio；Refer to jth rank peak value of response
Frequency near by frequencyWith peak value of response frequencyThe ratio between, Δ f is frequency-domain analysis frequency resolution,Represent jth rank peak value
Frequency corresponding frequency response spectral line numbering (i.e. theBar),Represent the corresponding frequency response spectrum of jth rank crest frequency near by frequency
Line numbering (i.e. theBar).
Damping ratios result is further obtained according to (18), (19), and damping ratio refers to the ratio between damping and critical damping, ζ=
c/cc；Wherein：
When damping ratio is smaller, formula (19) precision is subjected to；
When damping ratio is larger, peak value of response (i.e. mode peak response amplitude) be more than resonance response, peak value of response frequency with
Resonant frequency has differences, and formula (18) precision is higher.
The present invention will be further described by specific embodiment below.
Embodiment 1：Simulation numerical is tested
In embodiment 1, carried out specifically to extracting steady-state response amplitude, damping ratio Inversion Calculation in impulse response frequency spectrum
Operating instruction and checking.By taking the hull beam model analysis global vibration parameter in field of ship engineering as an example, the damping is pressed to certain ship
Parameter identification is carried out than Inversion Calculation method, model dimension parameter is shown in Table 1.
Certain the shipowner's scale parameter of table 1
Whole ship hull beam model is set up to the ship, is a variable cross-section main hull structure hull girder, while considering full ship
Gross weight and attached Lianshui quality, calculate each section key element.Response analysis is carried out using having MSC.Nastran to limit meta-model,
Apply pulse excitation and resonant excitation (excitation of simulation propeller) both operating modes in hull stern respectively, to contrast pulse
The accuracy for the steady-state response amplitude extracted in exciter response frequency spectrum and the precision for recognizing damping ratio.Hull beam it is vertical first three
The rank global vibration vibration shape is shown in Fig. 2.Dynamic response analyze when, damping according to according in specification on surface ship modal damping coefficient
Regulation, is shown in Fig. 3 (taking low resistance).
Frequency response function is the build-in attribute of Linear Time-Invariant System, is in Fu that arteries and veins rings function (unit impulse response function)
Leaf transformation, it is assumed that single-mode system frequency response function isArteries and veins rings functionIdeal unitary pulse can evoke entirely
The response of frequency range.Pulse response spectrum formula (5) in step 3 and the contrast of frequency response function expression formula are understood：
Frequency response analysis in MSC.Nastran, is that computation structure calculates frequency under Harmonic Loads effect to each
The dynamic response of rate, the mould of plural number response is equal with stable state resonance amplitude amplitude.Therefore, Frequency Response Analysis can obtain structure with equivalent
Impulse response frequency spectrum, simplify the time-domain calculation of impulse response.Calculating parameter is shown in Table in 2, table while giving by calculating work
The steady-state vibration amplitude and actual calculated value error very little extracted in the dynamic respond of ship bow part obtained by condition, contrast response spectrum,
Caused by the relative error of presence is Computer Precision.The stem numerical computations response spectrum and stable state that Fig. 4 gives operating mode 1 are humorous
Shake time domain response, excitation force width takes 1kN.
The numerical computations parameter of table 2 and bow response contrast
The specific implementation for completing hull beam model damping ratio for above-mentioned computation model and parameter illustrates.
Step one, according to the model analysis carried out in advance, first, second and third first order mode middle-range ship stern of hull beam is determined most
Near " node " distance is：51150mm、29700mm、18150mm.Calculate using neighbouring (low) first order mode for studying order
The response spectrum at " node " place, and then three kinds of determination calculates the positions of pick-up point under operating modes, that is, is respectively：2nd first order mode " section
Point ", the 1st first order mode " node ", the 2nd first order mode " node ".
Frequency response analysis in step 2, MSC.Nastran can be counted with the equivalent impulse response frequency spectrum for obtaining structure
Calculation obtains the response spectrum of each pick-up point under three kinds of operating modes in table 2, as shown in Figure 5.
Step 3, extracts the response under the peak response for corresponding to order, near by frequency, note from Fig. 5 response spectrum
Record respective respective frequencies.
Step 4, according to the response and its frequency obtained in step 3, calculates each order frequency ratio, response ratio (γjWith χj),
Table 3 gives hull beam model and calculates obtained damping simulation calculation value, can with being compared by the setting value of code requirement
See, the present invention can identify damping ratio exactly.
The hull beam Damping calculating result of table 3 and identification error
(note：And identification errorCorrespond respectively toDamping simulation calculation value and its identification under frequency excitation
Error)
Embodiment 2：Slab element model test
To verify the validity of the method for the invention, hull partial structurtes composite panel model of element is implemented
Modal test, its structural representation such as Fig. 6.Wherein structure 2 is tested glass epoxy cellular construction, and Fig. 7 is 3D solid experiment
Model.Tool structure material is Q235 steel, and elastic modelling quantity is 210Gpa, and Poisson's ratio is 0.3, and density of material is 7800kg/m3,
Ensure that design frock and each rank resonant frequency of breadboard model of element there are enough rates that staggers by the prior numerical computations that carry out.Institute
The composite panel material used is currently used primarily in the preparation of hull kuppe structural member for the glass epoxy of hand pasting forming,
Its main design parameters is shown in Table 4.
The glass epoxy parameter of table 4
Step one, model analysis is carried out to Slab element test model, modal idenlification employs excitation multiple spot in experiment
Pick-up method (to distinguish the mode repeated root of structure, using tetra- pick-up points of 61#, 64#, 94#, 97#), is struck in test using power hammer
Hit and carry out exciting as pulse excitation source, and using ICP piezoelectric transducers pickup response signal.Swash in uniform 81 of plate front
Encourage a little, the uniform 9 responses pick-up point in the back side, Fig. 8 gives the exciting-pick-up point distribution schematic diagram at plate front and the back side.Sampling
Frequency 5kHz, sampling length is 32748, recorded, and the pulse signal pulsewidth τ that power hammer is produced is 0.7ms or so, can be evoked
Effective excitation frequency range be 0~1.4kHz, the preceding 8 rank resonant frequency of identification is in the frequency range.
Each first order mode and its resonant frequency contrast of experiment and numerical computations are presented in Fig. 10, while in order to pass through control
Position of Vibrating processed realizes the separation of repeated root modal response, and each rank damping ratios test measuring point, both positioned at the " section of neighbouring mode
Point ", " nodel line " place, also to have the position obvious responsed under each test Mode Shape, each rank damping ratio tests exciting, pick-up
Marked in the bending vibation mode picture of position in Fig. 10.
Step 2, required exciting-pick-up location schemes when being tested according to each rank damping ratio determined in step one, is used
Dynamic signal acquisition device obtains the time domain response of the pick-up point under each operating mode to being acquired respectively to each measuring point response signal
Signal.By taking the first rank damping ratio measurement condition as an example, response time-domain signal (0~0.205s of interception) such as Fig. 9 (a) is believed response
Number make time domain conversion, obtain impulse response frequency spectrum (taking 0~1.0kHz), such as Fig. 9 (b).Rest working conditions are tested by the same way
Processing.
Step 3, because breadboard damping is smaller, gained resonance response and peak response difference are little in test, from step
When extracting response amplitude in each operating mode impulse response frequency spectrum data obtained in rapid two, it is believed that resonance response and peak response
It is equal, and by certain rate that staggers while extracting the response of its near by frequency.Related data is shown in Table 5.
The response results extracted are carried out each rank damping ratios according to formula (18) and calculated, respectively obtained by step 4Two damping ratio results are carried out can averagely to reduce calculation error, damping ratio the results are shown in Table 5.
The Slab element model Damping calculating result of table 5
(note：Test response spectral frequencies resolution ax f=0.153Hz, by spectral line interval m=40 values, responds to accelerate
Degree response.)
For the ease of verifying the validity of the inventive method, provided using Jiangsu Dong Hua measuring technologies limited company
DHDAS model analysis softwares, Modal Parameter Identification is carried out to the input and output signal that collects, method therefor is
Polylscf (i.e. steady state picture calculating method), this method is international latest development and the popular model analysis based on transmission function
Method, with good accuracy of identification.The first eight the rank damping ratios for extracting Slab element structure are shown in Table 6, using the result as
The reference value of identification result of the present invention.Each rank damping ratios are carried out to test gained frequency response function using half-power method simultaneously
Calculate, be as a result also given in Table 6.It can be seen that, half-power method recognition result is generally bigger than normal, and Chen Kuifu and Ying Huaiqiao are to this kind of
Error has made theory analysis；The inventive method is closer to (damping ratio worst error with Polylscf result of calculations
4.03%, can receive in engineering), therefore utilize flow of the present invention, even in encourage it is unknown on the premise of, still may be used
To realize the accurate identification of modal parameter.
The actual measurement Slab element model damping parameter recognition result contrast of table 6
The undeclared part being related in the present invention is same as the prior art or is realized using prior art.
The technological thought of above example only to illustrate the invention, it is impossible to which protection scope of the present invention is limited with this, it is every
According to technological thought proposed by the present invention, any change done on the basis of technical scheme each falls within the scope of the present invention
Within.
Claims (7)
1. a kind of damping ratios quick calculation method based on pulse excitation response spectrum, comprises the following steps：
Step 1, structure exciting-pick-up point position is determined；
Step 2：Collection pick-up point time domain response signal simultaneously makees frequency domain conversion；
Step 3：Extract stable state resonance response amplitude；
Step 4, damping ratio computing parameter is determined：Frequency ratio and response ratio, calculate damping ratio,
Characterized in that, the detailed content of the step 3 is：
It is resonant frequency ω to make frequency corresponding to the m articles spectral linenj, its adjacent the m ± q articles position of spectral line correspondence resonant frequency
Near by frequencyThen the frequency response spectral line amplitude in test result at jth rank resonant frequency and its near by frequency is：
|hArteries and veins(ωnj) |=| hArteries and veins(m Δs f) |, it is ω corresponding to frequencynjForced vibration response amplitude under=m Δs f resonant excitation
|xj(t)|；
It is corresponding to frequencyResonant excitation under forced vibration response
Amplitude
Wherein, Δ f is frequency-domain analysis frequency resolution, and m represents the corresponding frequency response spectral line numbering of jth rank resonant frequency, m ± q tables
Show the corresponding frequency response spectral line numbering of jth rank resonant frequency near by frequency.
2. a kind of damping ratios quick calculation method based on pulse excitation response spectrum as claimed in claim 1, it is special
Levy and be：In the step 1, placement sensor in position, to determine structure exciting-pick-up point position, the appropriate location
Refer to " node ", " nodel line " place for being both located at neighbouring mode, also for each test there is the position obvious responsed under Mode Shape.
3. a kind of damping ratios quick calculation method based on pulse excitation response spectrum as claimed in claim 2, it is special
Levy and be：The sensor uses displacement transducer, velocity sensor or acceleration transducer.
4. a kind of damping ratios quick calculation method based on pulse excitation response spectrum as claimed in claim 1, it is special
Levy and be：In the step 2, response signal of the structure under excited by impact is acquired using dynamic signal acquisition instrument, surveyed
Measure pick-up point dynamic response time course curve.
5. a kind of damping ratios quick calculation method based on pulse excitation response spectrum as claimed in claim 4, it is special
Levy and be：In the step 2, signal is carried out to use discrete Fourier transform during frequency domain conversion, the size N of transform block is 2
Integer power, record time-domain signal duration T=N Δ t, the Δ t of sample frequency 1/, frequency-domain analysis frequency resolution Δ f=1/T=1/
NΔt；Each sampling point value is xr, r=0,1 ..., N-1, the discrete spectral line under frequency domain is：
Spectral line spacing frequency is Δ f, and fitting discrete spectrum curve is h (k Δs f).
6. a kind of damping ratios quick calculation method based on pulse excitation response spectrum as claimed in claim 1, it is special
Levy and be：In the step 4, when damping ratio is smaller, response ratio and frequency ratio are calculated according to following formula：
Wherein, χjThe ratio between response amplitude under referring to jth rank resonance response amplitude and being encouraged by jth rank resonant frequency near by frequency,
γjRefer to the ratio between jth rank resonant frequency near by frequency and resonant frequency, | hArteries and veins(m Δs f) | represent frequency under m Δs f resonant excitation
Frequency response spectral line amplitude, | hArteries and veins(m ± q) Δ f) | it is the frequency response spectral line amplitude under (m ± q) Δ f resonant excitation, Δ to represent frequency
F is frequency-domain analysis frequency resolution, and m represents the corresponding frequency response spectral line numbering of jth rank resonant frequency, and m ± q represents that jth rank is resonated
The corresponding frequency response spectral line numbering of frequency near by frequency；
Damping ratios result is obtained according to following formula：
Wherein, ζjRepresent damping ratio.
7. a kind of damping ratios quick calculation method based on pulse excitation response spectrum as claimed in claim 1, it is special
Levy and be：In the step 4, when damping ratio is larger, response ratio and frequency ratio are calculated according to following formula：
Wherein,Refer to jth rank mode peak response amplitude with by the response amplitude under response crest frequency near by frequency excitation it
Than,Refer to jth rank peak value of response frequency near by frequency and peak value of response frequency ratio, Δ f is frequency-domain analysis frequency resolution,
The corresponding frequency response spectral line numbering of jth rank crest frequency is represented,Represent the corresponding frequency response of jth rank crest frequency near by frequency
Spectral line is numbered；
Damping ratios result is obtained according to following formula：
Wherein, ζjRepresent damping ratio.
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