CN107941485A - A kind of ship typical structure internal loss factor method for rapidly testing - Google Patents
A kind of ship typical structure internal loss factor method for rapidly testing Download PDFInfo
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- CN107941485A CN107941485A CN201711079820.4A CN201711079820A CN107941485A CN 107941485 A CN107941485 A CN 107941485A CN 201711079820 A CN201711079820 A CN 201711079820A CN 107941485 A CN107941485 A CN 107941485A
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- G—PHYSICS
- G01—MEASURING; TESTING
- G01M—TESTING STATIC OR DYNAMIC BALANCE OF MACHINES OR STRUCTURES; TESTING OF STRUCTURES OR APPARATUS, NOT OTHERWISE PROVIDED FOR
- G01M13/00—Testing of machine parts
Abstract
The present invention provides a kind of ship typical structure internal loss factor method for rapidly testing, first according to Ship Structure feature, deck, bulkhead, inner bottom plating, side plate are chosen as component to be measured, and component to be measured is done into lifting processing, select 9 groups of acceleration transducers and be averagely arranged on component to be measured, enabling signal Acquisition Instrument, channel parameters are set, channel balance is reset, the input of transient state load is applied in energized position using hammering method, is obtained respectively after signal attenuation to be collected is steady and goes through signal when storing the acceleration of each group sensor.Based on Hilbert transformation theories, when acceleration that will be collected go through deamplification converted, parsed, process of fitting treatment, obtain the internal loss factor that geodesic structure is treated under once encouraging.It is final to obtain the average internal loss factor for treating geodesic structure by converting energized position and repetitive operation.Accuracy of the present invention is good, easy to operation, cost is low, ancillary equipment is few and degree of controllability is high, has good economy and wide application prospect.
Description
Technical field
The present invention relates to a kind of test method, more particularly to a kind of quick side of test of ship typical structure internal loss factor
Method.
Background technology
Internal loss factor is to weigh system damping characteristic and determine the important parameter of its vibrational energy dissipation capabilities, determines knot
Structure, which damps the most frequently used and most reliable approach, to be determined by measuring;At present, such as half-power method, mode circle fitting process are all
Produced with model analysis and parameter identification technology, measurement result is the single-frequency internal loss factor i.e. mode internal loss of structure
The factor.Usually there are steady state energy stream method and transient state decay for measuring the be averaged method of internal loss factor of frequency band.But stable state
Energy stream method needs accurate calculating input power, this undoubtedly makes troubles to measurement internal loss factor, and error also can be very big.
Ship is solved the problems, such as when the vibration and noise of labyrinth, relatively effective method is statistic energy analysis method
(SEA).The viewpoint of this approach application energy, ignores the detail of structure, unified solution vibration and noise problem, but
It is that precondition in this way is to obtain three parameters, wherein just including internal loss factor.Due to structural complexity
Raising causes to be increasingly difficult to using theoretical calculation, and precision is also not high enough, so reliable method is experimental method --- transient state
Damped method.The frequency band that transient state decay is suitable for quick estimation structure harmony volume is averaged internal loss factor, and need not measure defeated
Enter power, its statistical error is relatively small.According to the fading characteristics of free vibration signal, met with a response using Hilbert conversion
The envelope line function of signal, realizes that frequency range of the structure in any frequency range is averaged the measurement of internal loss factor.Using
Hilbert, which is converted, can easily determine the enveloping outer enclosure of response signal, and clearly reflection signal amplitude is with becoming of decaying of time
Gesture, so as to provide a conveniently approach for the frequency range internal loss factor that is averaged of measurement structure.
Found by the literature search to the prior art, in recent years, similar on Structure's Internal Loss Factor measurement is special
Sharp document, which rarely has, to be delivered, and the open source information related with patent of the present invention mainly includes:1st, the measurement side of aircraft internal loss factor
Method (the patent No.:CN105987953A);2nd, a kind of method (patent No. of material internal loss factor measurement:CN103983691A);
3rd, damping material internal loss factor measuring method and the measuring device (patent No. based on impulse response method:CN103698404A);
Patent 1 is a kind of measuring method of aircraft internal loss factor, including:Aircraft bay section is freely hung, in institute
State and M test point is determined on aircraft, wherein M is the integer more than or equal to 1;The aircraft bay section is tapped, measurement is each
The vibratory response of test point;Decayed the reverberation time according to the vibration of each test point of the Calculation of Vibration Response;Shaken according to described
The dynamic decay reverberation time calculates internal loss factor;Excitation sound source is set outside the aircraft bay section, controls the excitation sound source
Output and measure the acoustic attenuation reverberation time, according to acoustic attenuation reverberation time calculating sound space internal loss factor;Patent 2 is public
A kind of method of material internal loss factor measurement has been opened, has belonged to material damping feature measurement field.This method includes standby two pieces together
The metallic plate of size same material;One layer of detected materials are laid on one piece of metallic plate wherein and form composite damping board;Measurement obtains
The bending velocity of wave propagation of composite damping board and metallic plate under different pulse signal frequencies;Calculate the Young of damping layer and metal layer
Modular ratio e;Measurement obtains composite damping board Structure's Internal Loss Factor p;The material internal loss factor of damping layer is finally calculated
It is several.3 invention of patent is related to a kind of damping material internal loss factor measuring method and measuring device based on impulse response method, measurement
Method comprises the following steps:1) signal emission module sends pumping signal to the test specimen on damping platform;2) signal acquisition mould
Block gathers test specimen vibration velocity signal and sends it to signal processing module;3) the received vibration speed of signal processing module docking
Degree signal obtains the impulse response and frequency response function of test specimen, and damping material internal loss factor after being handled, and by result
It is sent to display module, storage and report generation module;4) display module shows impulse response and frequency response function curve, damping material
Expect internal loss factor;5) storage and report generation module storage measurement data and damping material internal loss factor result of calculation,
And generate test report;6) off-line analysis module can call stored data to be analysed in depth.
In summary, it has been disclosed that the patent and the present invention delivered there is no related application special there are larger difference
Profit, the present invention are described a kind of ship typical structure internal loss factor test method, special for the damping of ship typical structure
Property measurement reference is provided, and accuracy of the present invention is good, easy to operation, cost is low, ancillary equipment is few and degree of controllability
It is high, there is good economy and wide application prospect.
The content of the invention
It is a kind of energy the purpose of the invention is to provide a kind of ship typical structure internal loss factor method for rapidly testing
Enough quick Validity Test methods for obtaining ship typical structure damping characteristic.
The object of the present invention is achieved like this:
Step 1:According to Ship Structure feature, deck, bulkhead, inner bottom plating or side plate are chosen as component to be measured, and will
Component to be measured does lifting processing, selects 9 groups of acceleration transducers and is averagely arranged on component to be measured, determines acceleration sensing
Connected between device, ICP accelerometer signals conditioner and signal sampler correct;
Step 2:Enabling signal Acquisition Instrument, sets channel parameters, and channel balance is reset, applied using hammering method in energized position
Add transient state load to input, obtained respectively after signal attenuation to be collected is steady and decay letter is gone through when storing the acceleration of each group sensor
Number;
Step 3:Based on Hilbert transformation theories, when acceleration that will be collected go through deamplification converted, parsed,
Process of fitting treatment, obtains the internal loss factor that geodesic structure is treated under once encouraging;
Step 4:Energized position is constant, repeating said steps 2-3, obtains treating geodesic structure under single energized position repeatedly encourages
Average internal loss factor;
Step 5:Change energized position, repeating said steps 2-4, obtains treating geodesic structure under multiple energized positions repeatedly encourage
Average internal loss factor.
Present invention additionally comprises some such architectural features:
1. the position of energized position and acceleration transducer is chosen at the allusion quotation of structure grillage geometric center to be measured, 1/4 and 1/8
At type position, energized position should be able to evoke the former rank mode for treating geodesic structure, the letter that the arrangement of acceleration transducer should collect
Number it can reflect the Vibration Condition for treating geodesic structure entirety.
2. step 3 is specially to 5:
(1) curve is gone through during the component vibration acceleration to be measured that will be collected, is decayed through automatic or manual selected parts formant bent
Line, it should be ensured that comprising from formant to the stable complete procedure curve of signal attenuation.
(2) go through signal when becoming by Hilbert and change commanders vibration acceleration to be handled, obtain component vibration acceleration to be measured
When go through the analytic signal of signal, its calculation formula is as follows:
In formula:* --- convolution symbol;H [x (t)] --- Hilbert transformation for mula;X (t) --- adding after transient state excitation
Signal is gone through during speed;--- Hilbert conversion after acceleration when go through signal;U (t) --- acceleration analytic signal;
(3) obtained acceleration analytic signal is handled, obtains the envelope of acceleration responsive signal, then response is believed
Number envelope carry out logarithmic transformation, obtain its attenuation curve, its calculation formula is as follows:
In formula:The envelope of A (t) --- response signal;--- the attenuation curve of acceleration responsive signal;
(4) to attenuation curveOnce linear fitting is carried out, and obtains the absolute value of attenuation curve slope, it is as to be measured
The structural damping η of structure, the damping ratio of structure to be measured is obtained by itself divided by circular frequency ω2 times of damping ratio are quilt
The ζ of the internal loss factor ξ of test structure=2;
(5) (1)-(4) are repeated, obtain treating the average internal loss factor of geodesic structure under multiple energized positions repeatedly encourageFor:
In formula:ξij--- i-th bit puts Structure's Internal Loss Factor during jth time excitation;ξi--- after i-th bit puts j excitation
The average internal loss factor of structure;--- the average internal loss factor of structure after n position excitation.
Compared with prior art, the beneficial effects of the invention are as follows:Problem to be solved by this invention is:Weigh ship typical case
Structural system damping characteristic, determines ship typical structure vibrational energy dissipation capabilities, solves the vibration of ship labyrinth with making an uproar
Acoustic control problem.Accuracy of the present invention is good, easy to operation, cost is low, ancillary equipment is few and degree of controllability is high, has good
Economy and wide application prospect.
Present invention can apply to the quick test of ship typical structure internal loss factor, is rationally determined to swash according to structure size
Encourage position, acceleration transducer quantity and installation position, the position of exciting force and acceleration transducer is generally chosen at knot to be measured
At the exemplary positions such as structure grillage geometric center, 1/4 and 1/8, the position of exciting force guarantees to evoke the former rank moulds for treating geodesic structure
State, the arrangement of acceleration transducer is it is ensured that the signal collected can reflect the Vibration Condition for treating geodesic structure entirety.According to sampling
Frequency, the sensitivity of acceleration transducer and range determine sampling time length, and general control was at 8-10 seconds, signal to be collected
The storage of signal is carried out after decay is steady.
1) curve is gone through when using automatic or manual selected parts acceleration, then three-dimensional acceleration solution is obtained after being converted to Hilbert
The envelope for analysing signal carries out linear fit, finally obtains the internal loss factor for treating geodesic structure, this method is fast with speed, accuracy
The advantages of good, because signal reaction is gone through during acceleration is the build-in attribute of vibrational system.
2) measurement process is easy, ancillary equipment is few and degree of controllability is high, the degree of automation is higher, measurement process is intuitively visual
Change, the state it can be seen that formant is gone through on curve in vibration acceleration, by observing the attenuation curve of formant, tester
Member can directly conclude the reasonability of test process, can avoid the occurrence of unreasonable test result.
Brief description of the drawings
The ship typical structure internal loss factor method for rapidly testing FB(flow block) of Fig. 1 present invention;
The measurement system diagram of ship typical members internal loss factor in Fig. 2 the embodiment of the present invention;
The layout drawing of excitation point and measuring point in Fig. 3 the embodiment of the present invention;
In Fig. 4 the embodiment of the present invention curve is gone through during acceleration;
Acceleration decay matched curve in Fig. 5 the embodiment of the present invention;
Fig. 6 is ship typical structure internal loss factor table in the embodiment of the present invention.
Embodiment
The present invention is described in further detail with embodiment below in conjunction with the accompanying drawings.
With reference to Fig. 1 to Fig. 6, step of the invention is as follows:
Step 1:According to Ship Structure feature, selection specification is 1500 × 1000mm2Deck, bulkhead, inner bottom plating,
The typical structures such as side plate do lifting processing as component to be measured, and by component to be measured, and 9 groups of acceleration transducers of selection are simultaneously average
It is arranged on component to be measured, determines that acceleration transducer, ICP accelerometer signals conditioner and signal sampler connect between the two
Connect correct;
Step 2:Enabling signal Acquisition Instrument, sets channel parameters, and channel balance is reset, applied using hammering method in energized position
Add transient state load to input, obtained respectively after signal attenuation to be collected is steady and go through signal when storing the acceleration of each group sensor.
Step 3:Based on Hilbert transformation theories, when acceleration that will be collected go through deamplification converted, parsed,
The series of processes such as fitting, obtain the internal loss factor that geodesic structure is treated under once encouraging.
Step 4:Energized position is constant, repeating said steps 2-3, obtains treating geodesic structure under single energized position repeatedly encourages
Average internal loss factor.
Step 5:Change energized position, repeating said steps 2-4, obtains treating geodesic structure under multiple energized positions repeatedly encourage
Average internal loss factor.
It is typical that the position of energized position and acceleration transducer is chosen at structure grillage geometric center to be measured, 1/4 and 1/8 etc.
At position, the position of exciting force guarantees to evoke the former rank mode for treating geodesic structure, and the arrangement of acceleration transducer is it is ensured that adopt
The signal collected can reflect the Vibration Condition for treating geodesic structure entirety.According to sample frequency, the sensitivity of acceleration transducer and amount
Journey determines sampling time length, and for general control at 8-10 seconds, signal attenuation to be collected steadily carried out the storage of signal afterwards.
In step 3 to step 5, the series of processes such as converted, parsed, is fitted to going through signal during the acceleration of collection
Afterwards, obtain treating the average internal loss factor of geodesic structure under multiple energized positions repeatedly encourage, detailed process is as follows:
1) curve is gone through during the component vibration acceleration to be measured that will be collected, is decayed through automatic or manual selected parts formant bent
Line, it should be ensured that comprising from formant to the stable complete procedure curve of signal attenuation.
2) go through signal when becoming by Hilbert and change commanders vibration acceleration to be handled, obtain component vibration acceleration to be measured
When go through the analytic signal of signal, its calculation formula is as follows:
In formula:* --- convolution symbol;
H [x (t)] --- Hilbert transformation for mula;
X (t) --- transient state excitation after acceleration when go through signal;
--- Hilbert conversion after acceleration when go through signal;
U (t) --- acceleration analytic signal;
3) above-mentioned acceleration analytic signal is handled, obtains the envelope of acceleration responsive signal, then response is believed
Number envelope carry out logarithmic transformation, obtain its attenuation curve, its calculation formula is as follows:
In formula:The envelope of A (t) --- response signal;
--- the attenuation curve of acceleration responsive signal;
4) to attenuation curveOnce linear fitting is carried out, and obtains the absolute value of attenuation curve slope, is knot to be measured
The structural damping η of structure, the damping ratio of structure to be measured is obtained by itself divided by circular frequency2 times of damping ratio are tested
The ζ of the internal loss factor ξ of structure=2.
5) repetitive process 1) -5) operation, you can obtain multiple energized positions repeatedly treat under excitation geodesic structure it is average in
Fissipation factorCalculation formula is as follows:
In formula:ξij--- i-th bit puts Structure's Internal Loss Factor during jth time excitation;
ξi--- i-th bit puts the average internal loss factor of structure after j excitation;
--- the average internal loss factor of structure after n position excitation.
One embodiment of the present of invention is given below (it is component to be measured to choose ship deck region steel plate structure):
Step 1:Exemplified by choosing ship deck region steel plate structure in the present embodiment, the specific size of steel plate for 1500 ×
1000×12mm3, its perforate of light plate top two top corner regions setting for lifting, is used cooperatively steel plate structure with shackle
Lifting.
Step 2:9 acceleration transducers and 4 excitation point positions, 9 measuring points are set in the side of steel plate structure to be measured
It is evenly arranged on framed plate structure to be measured, 4 energized positions are arranged in the central area of framed plate structure to be measured, as shown in Figure 2.
Determine to connect between acceleration transducer, ICP accelerometer signals conditioner and signal sampler three correctly, test system is such as
Shown in attached drawing 3.
Step 3:Enabling signal Acquisition Instrument, sets channel parameters, and channel balance is reset.Using hammering method in any excitation
Position stores each channel signal, obtains each group and add respectively to one transient state excitation of geodesic structure is treated after signal attenuation to be collected is steady
Velocity sensor when go through signal.Signal is gone through during the acceleration collected as shown in Figure 4.
Step 4:Curve is gone through during the component vibration acceleration to be measured that will be collected, is declined through automatic or manual selected parts formant
Subtract curve, it should be ensured that comprising from formant to the stable complete procedure curve of signal attenuation.Then to being gone through during the acceleration of selected parts
Signal carries out dissection process, obtains the internal loss factor that geodesic structure is treated under once encouraging.Acceleration decay matched curve such as attached drawing 5
It is shown.
Step 5:Energized position is constant, repeating said steps three and step 4, obtains under the multiple excitation of an energized position
Treat the average internal loss factor of geodesic structure.
Step 6:Changing energized position, repeat the above steps three -- step 5, obtains multiple energized positions repeatedly under excitation
Treat the average internal loss factor of geodesic structure.Ship typical structure internal loss factor is as shown in Figure 6.
Accuracy of the present invention is good, easy to operation, cost is low, ancillary equipment is few and degree of controllability is high, can weigh ship
Oceangoing ship typical structure system damping characteristic, determines ship typical structure vibrational energy dissipation capabilities, solves shaking for ship labyrinth
Dynamic and noise abatement problem.With good economy and wide application prospect.
To sum up, it is an object of the invention to provide a kind of ship typical structure internal loss factor method for rapidly testing, it is walked
Suddenly it is:First according to Ship Structure feature, selection specification is 1500 × 1000mm2Deck, bulkhead, inner bottom plating, topside
The typical structures such as plate do lifting processing as component to be measured, and by component to be measured, select 9 groups of acceleration transducers and the arrangement that is averaged
In on component to be measured, determining that acceleration transducer, ICP accelerometer signals conditioner and signal sampler connect just between the two
Really;Enabling signal Acquisition Instrument, sets channel parameters, and channel balance is reset, and applies transient state load in energized position using hammering method
Input, obtains and goes through signal when storing the acceleration of each group sensor respectively after signal attenuation to be collected is steady.Based on Hilbert
Transformation theory, when acceleration that will be collected, go through deamplification and the series of processes such as are converted, parsed, is fitted, once swashed
Encourage down the internal loss factor for treating geodesic structure.By converting energized position, aforesaid operations are repeated, final obtain treats being averaged for geodesic structure
Internal loss factor.Accuracy of the present invention is good, easy to operation, cost is low, ancillary equipment is few and degree of controllability is high, has good
Economy and wide application prospect.
Claims (3)
- A kind of 1. ship typical structure internal loss factor method for rapidly testing, it is characterised in that:Step is as follows:Step 1:According to Ship Structure feature, deck, bulkhead, inner bottom plating or side plate are chosen as component to be measured, and will be to be measured Component does lifting processing, selects 9 groups of acceleration transducers and is averagely arranged on component to be measured, determines acceleration transducer, ICP Connected between accelerometer signal conditioner and signal sampler correct;Step 2:Enabling signal Acquisition Instrument, sets channel parameters, and channel balance is reset, and applies wink in energized position using hammering method State load inputs, and is obtained respectively after signal attenuation to be collected is steady and goes through deamplification when storing the acceleration of each group sensor;Step 3:Based on Hilbert transformation theories, when acceleration that will be collected, goes through deamplification and is converted, parsed, be fitted Processing, obtains the internal loss factor that geodesic structure is treated under once encouraging;Step 4:Energized position is constant, repeating said steps 2-3, obtains treating the flat of geodesic structure under single energized position repeatedly encourages Equal internal loss factor;Step 5:Change energized position, repeating said steps 2-4, obtains treating the flat of geodesic structure under multiple energized positions repeatedly encourage Equal internal loss factor.
- A kind of 2. ship typical structure internal loss factor method for rapidly testing according to claim 1, it is characterised in that:Swash The position for encouraging position and acceleration transducer is chosen at the exemplary position of structure grillage geometric center to be measured, 1/4 and 1/8, is swashed The former rank mode for treating geodesic structure should be able to be evoked by encouraging position, and the signal that the arrangement of acceleration transducer should collect can reflect to be measured The Vibration Condition of structure entirety.
- 3. a kind of ship typical structure internal loss factor method for rapidly testing according to claim 1 or 2, its feature exist In:Step 3 is specially to 5:(1) curve is gone through during the component vibration acceleration to be measured that will be collected, should through automatic or manual selected parts formant attenuation curve Ensure to include from formant to the stable complete procedure curve of signal attenuation.(2) go through signal when becoming by Hilbert and change commanders vibration acceleration to be handled, gone through when obtaining component vibration acceleration to be measured The analytic signal of signal, its calculation formula are as follows:<mrow> <mover> <mi>x</mi> <mo>^</mo> </mover> <mrow> <mo>(</mo> <mi>t</mi> <mo>)</mo> </mrow> <mo>=</mo> <mi>H</mi> <mo>&lsqb;</mo> <mi>x</mi> <mrow> <mo>(</mo> <mi>t</mi> <mo>)</mo> </mrow> <mo>&rsqb;</mo> <mo>=</mo> <mi>x</mi> <mrow> <mo>(</mo> <mi>t</mi> <mo>)</mo> </mrow> <mo>*</mo> <mfrac> <mn>1</mn> <mrow> <mi>&pi;</mi> <mi>t</mi> </mrow> </mfrac> <mo>=</mo> <mo>-</mo> <mfrac> <mn>1</mn> <mi>&pi;</mi> </mfrac> <msubsup> <mo>&Integral;</mo> <mrow> <mo>-</mo> <mi>&infin;</mi> </mrow> <mrow> <mo>+</mo> <mi>&infin;</mi> </mrow> </msubsup> <mfrac> <mrow> <mi>x</mi> <mrow> <mo>(</mo> <mi>&tau;</mi> <mo>)</mo> </mrow> </mrow> <mrow> <mi>t</mi> <mo>-</mo> <mi>&tau;</mi> </mrow> </mfrac> <mi>d</mi> <mi>&tau;</mi> </mrow><mrow> <mi>u</mi> <mrow> <mo>(</mo> <mi>t</mi> <mo>)</mo> </mrow> <mo>=</mo> <mi>x</mi> <mrow> <mo>(</mo> <mi>t</mi> <mo>)</mo> </mrow> <mo>+</mo> <mi>j</mi> <mover> <mi>x</mi> <mo>^</mo> </mover> <mrow> <mo>(</mo> <mi>t</mi> <mo>)</mo> </mrow> </mrow>In formula:* --- convolution symbol;H [x (t)] --- Hilbert transformation for mula;X (t) --- the acceleration after transient state excitation When go through signal;--- Hilbert conversion after acceleration when go through signal;U (t) --- acceleration analytic signal;(3) obtained acceleration analytic signal is handled, obtains the envelope of acceleration responsive signal, then to response signal Envelope carries out logarithmic transformation, obtains its attenuation curve, its calculation formula is as follows:<mrow> <mi>A</mi> <mrow> <mo>(</mo> <mi>t</mi> <mo>)</mo> </mrow> <mo>=</mo> <msqrt> <mrow> <mi>x</mi> <msup> <mrow> <mo>(</mo> <mi>t</mi> <mo>)</mo> </mrow> <mn>2</mn> </msup> <mo>+</mo> <mover> <mi>x</mi> <mo>^</mo> </mover> <msup> <mrow> <mo>(</mo> <mi>t</mi> <mo>)</mo> </mrow> <mn>2</mn> </msup> </mrow> </msqrt> </mrow><mrow> <mover> <mrow> <mi>A</mi> <mrow> <mo>(</mo> <mi>t</mi> <mo>)</mo> </mrow> </mrow> <mo>^</mo> </mover> <mo>=</mo> <mi>l</mi> <mi>n</mi> <mrow> <mo>(</mo> <mi>A</mi> <mo>(</mo> <mi>t</mi> <mo>)</mo> <mo>)</mo> </mrow> </mrow>In formula:The envelope of A (t) --- response signal;--- the attenuation curve of acceleration responsive signal;(4) to attenuation curveOnce linear fitting is carried out, and obtains the absolute value of attenuation curve slope, as treats geodesic structure Structural damping η, itself divided by circular frequency ω are obtained into the damping ratio of structure to be measured2 times of damping ratio are tested The ζ of the internal loss factor ξ of structure=2;(5) (1)-(4) are repeated, obtain treating the average internal loss factor of geodesic structure under multiple energized positions repeatedly encourageFor:<mrow> <msub> <mi>&xi;</mi> <mi>i</mi> </msub> <mo>=</mo> <mfrac> <mn>1</mn> <mi>j</mi> </mfrac> <mrow> <mo>(</mo> <msub> <mi>&xi;</mi> <mrow> <mi>i</mi> <mn>1</mn> </mrow> </msub> <mo>+</mo> <msub> <mi>&xi;</mi> <mrow> <mi>i</mi> <mn>2</mn> </mrow> </msub> <mo>+</mo> <msub> <mi>&xi;</mi> <mrow> <mi>i</mi> <mn>3</mn> </mrow> </msub> <mo>+</mo> <mo>...</mo> <mo>+</mo> <msub> <mi>&xi;</mi> <mrow> <mi>i</mi> <mi>j</mi> </mrow> </msub> <mo>)</mo> </mrow> </mrow><mrow> <mover> <mi>&xi;</mi> <mo>&OverBar;</mo> </mover> <mo>=</mo> <mfrac> <mn>1</mn> <mi>n</mi> </mfrac> <mrow> <mo>(</mo> <msub> <mi>&xi;</mi> <mn>1</mn> </msub> <mo>+</mo> <msub> <mi>&xi;</mi> <mn>2</mn> </msub> <mo>+</mo> <msub> <mi>&xi;</mi> <mn>3</mn> </msub> <mo>+</mo> <mo>...</mo> <mo>+</mo> <msub> <mi>&xi;</mi> <mi>n</mi> </msub> <mo>)</mo> </mrow> </mrow>In formula:ξij--- i-th bit puts Structure's Internal Loss Factor during jth time excitation;ξi--- i-th bit puts structure after j excitation Average internal loss factor;--- the average internal loss factor of structure after n position excitation.
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CN110954340A (en) * | 2019-12-11 | 2020-04-03 | 中国汽车工程研究院股份有限公司 | Test method for obtaining coupling loss factor of complex structure by using transient excitation |
CN115586251A (en) * | 2022-09-01 | 2023-01-10 | 哈尔滨工程大学 | Ship typical structure connection coupling loss factor testing method |
CN115586251B (en) * | 2022-09-01 | 2023-06-02 | 哈尔滨工程大学 | Ship typical structure connection coupling loss factor testing method |
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