CN106960068B - Rapid modal damping ratio calculation method based on pulse excitation response frequency spectrum - Google Patents
Rapid modal damping ratio calculation method based on pulse excitation response frequency spectrum Download PDFInfo
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Abstract
The invention discloses a method for quickly calculating modal damping ratio based on pulse excitation response frequency spectrum, which comprises the steps of firstly determining the vibration exciting and vibration picking positions of a structure, ensuring that the vibration exciting and vibration picking positions are not only positioned at nodes and nodal lines adjacent to modal vibration modes, but also are positions with obvious response under each tested modal vibration mode; the signal collector records response signals of the vibration pickup points and performs discrete Fourier transform to obtain a response frequency spectrum; extracting the resonance (or peak value) frequency and the corresponding response under the adjacent frequency on the basis to obtain the steady state response amplitude; and finally, calculating related parameters such as a frequency ratio, a response ratio and the like to realize the identification of the structural modal damping ratio. The method can solve the following technical problems in the prior art: the traditional half-power method is difficult to accurately find a half-power point; some excitation time domain signals are difficult to directly measure, so that a frequency response function required by calculating the modal damping ratio by a frequency domain method cannot be obtained sometimes; the problems of incomplete attenuation of transient components, complex operation and the like exist in response under contact excitation.
Description
Technical Field
The invention belongs to the field of structural modal parameter identification, relates to a method for testing a structural vibration modal damping ratio, and particularly relates to a method for inverting each order of modal damping ratio by using an impulse response frequency spectrum of a structure in each order of resonance region.
Background
The damping parameter is an important dynamic performance index, and has obvious influence on the response of the structure in a resonance area. The actual engineering structure damping component is complex, generally determined by the comprehensive of internal damping (material), structural damping and fluid damping, however, the existing damping test standards (such as GB/T18258-. The linear vibration system obeys the mode superposition principle, the dynamic response calculation of the linear vibration system must depend on the mode damping ratio of the system, and the damping ratio is regulated according to the statistical rule in some fields, so that the linear vibration system has certain limitation. Therefore, the damping ratio also needs to be determined through experiments, but small differences of the experimental conditions may cause great deviation of the measurement results, and it is urgent to explore reliable and practical damping test methods.
At present, modal damping of a special structure is identified through experimental analysis, and a traditional parameter identification method can be carried out in a time domain and a frequency domain. Common frequency domain methods include single degree of freedom graphical methods (such as a peak picking method and an admittance circle method) and multiple degree of freedom analytical methods (such as various summation methods), and are respectively suitable for small damping structures with sparse modes and large damping structures with dense modes. The peak value picking method uses a half-power theory, and the discrete spectral lines are difficult to obtain accurate half-power points and window damping influence and different signal processing means, which can cause the damping estimation deviation to be several times or even dozens of times; the calculation accuracy of the admittance circle method is limited by the graphic accuracy, and the error caused by the superposition of adjacent modes cannot be avoided. The fitting analysis method often processes a multi-degree-of-freedom system, generally, the number of measuring points is increased for obtaining information of dense modes, and the measure not only increases the calculation amount, but also easily generates a ill-conditioned transformation matrix, thereby influencing the parameter identification precision. The parameter identification in the time domain of the multi-degree-of-freedom system needs to use a window function to filter and process signals, and the classical window has poor precision when separating low-frequency dense modes and overlapping modes, particularly modes which are positioned at two ends of a frequency response function and are very close to each other.
The test difficulty of the total vibration damping coefficient of complex structures such as naval vessels is high, the time domain attenuation method can only obtain the low-order damping coefficient, and the time sequence signals of response and excitation must be measured simultaneously when a frequency response curve is identified, which is often unrealistic under certain conditions (such as step excitation, self-excitation and the like of large structures), and both the test difficulty and the dynamic response prediction difficulty are brought.
The excitation form for the structure test has two types of contact and non-contact. The contact excitation generated by the vibration exciter and other effects can enable the structure to obtain continuous vibration response, and the test method for different excitation waveforms under the vibration exciter effect is specified, but when the operation is improper, the problems of incomplete free vibration attenuation, serious sample data leakage, insufficient data acquisition amount in a resonance region and the like exist, and certain errors are caused for frequency response function test and parameter identification. In addition, when the structure is continuously excited near the resonance region of the structure, if the damping is small, the structure has long time for reaching steady-state vibration and large response, and the structure is easy to damage.
Disclosure of Invention
The invention aims to provide a method for quickly calculating a modal damping ratio based on an impulse excitation response frequency spectrum, which can solve the following technical problems in the prior art: when the damping ratio is calculated by the traditional half-power method, the half-power point is generally difficult to find accurately; limited by the difficulty in measuring certain excitation time domain signals, a frequency response function required by calculating the modal damping ratio by a frequency domain method cannot be obtained sometimes; and the response under the contact excitation often has the problems of incomplete attenuation of transient components, complex operation and the like.
In order to achieve the above purpose, the solution of the invention is:
a modal damping ratio rapid calculation method based on an impulse excitation response frequency spectrum comprises the following steps:
step 2: collecting a time domain response signal of a vibration pickup point and performing frequency domain conversion;
and step 3: extracting a steady-state resonance response amplitude;
In the step 1, a sensor is arranged at a proper position to determine the position of the structure excitation-vibration pickup position, wherein the proper position refers to the position of the node or the pitch line of the adjacent mode and the position with obvious response under each test mode shape.
The sensor adopts a displacement sensor, a speed sensor or an acceleration sensor.
In the step 2, a dynamic signal acquisition instrument is used for acquiring response signals of the structure under impact excitation, and a dynamic response time history curve of the vibration pickup point is measured.
In the step 2, discrete fourier transform is adopted when performing frequency domain conversion on the signal, the size N of a transform block is an integer power of 2, the time duration T of the time domain signal is recorded as N Δ T, the sampling frequency is 1/Δ T, and the frequency domain analysis frequency resolution Δ f is recorded as 1/T as 1/N Δ T; each sampling point value is xr, r is 0,1, …, N-1, and the discrete spectral lines in the frequency domain are:
the line spacing frequency is Δ f and the fitted discrete spectrum curve is h (k Δ f).
The details of the step 3 are as follows:
let the frequency corresponding to the m-th spectral line be the resonance frequency omeganjThe m + -q adjacent spectral line positions correspond to adjacent frequencies of the resonance frequency
The amplitude of the frequency response spectral line at the j-th order resonance frequency and the adjacent frequency in the test result is:
|hpulse(ωnj)|＝|hPulse(m Δ f) |, corresponding to a frequency ωnjAmplitude | x of forced vibration response under resonance excitation of m Δ fj(t)|；
And delta f is frequency domain analysis frequency resolution, m represents a frequency response line number corresponding to a j-th order resonance frequency, and m +/-q represents a frequency response line number corresponding to a j-th order resonance frequency adjacent frequency.
In the step 4, when the damping ratio is small, the response ratio to the frequency ratio is calculated according to the following formula:
wherein, χjRefers to the ratio of the response amplitude of the j-th order resonance to the response amplitude of the excitation at a frequency adjacent to the j-th order resonance frequency, gammajThe ratio of the adjacent frequency of the j-th order resonance frequency to the resonance frequency, | hPulse(m Δ f) | represents the frequency response line amplitude under resonance excitation with frequency m Δ f, | hPulse(m +/-q) delta f) l represents the frequency response line amplitude under the resonance excitation with the frequency of (m +/-q) delta f, the delta f is the frequency domain analysis frequency resolution, m represents the frequency response line number corresponding to the j-th order resonance frequency, and m +/-q represents the frequency response line number corresponding to the adjacent frequency of the j-th order resonance frequency;
the modal damping ratio results are obtained according to the following formula:
therein, ζjIndicating the damping ratio.
In the step 4, when the damping is relatively large, the response ratio and the frequency ratio are calculated according to the following formula:
wherein the content of the first and second substances,
refers to the ratio of the maximum response amplitude of the j-th order mode to the response amplitude excited by the adjacent frequency of the response peak frequency,
the ratio of the frequency adjacent to the jth order response peak frequency to the response peak frequency, Δ f is the frequency domain analysis frequency resolution,
the number of the frequency response spectral line corresponding to the j-th order peak frequency is shown,
representing the frequency response spectral line number corresponding to the adjacent frequency of the j-th order peak frequency;
the modal damping ratio results are obtained according to the following formula:
therein, ζjIndicating the damping ratio.
After the scheme is adopted, the vibration response of the structure is directly utilized to carry out signal analysis processing and modal damping ratio identification of the structure, and the vibration exciting and vibration pickup positions of the structure are firstly determined to ensure that the vibration exciting and vibration pickup positions are not only positioned at nodes and nodal lines of adjacent modes, but also positioned at positions with obvious response under each order of vibration mode; recording a response signal of a vibration pickup point by using a signal collector, and performing discrete Fourier transform on the response signal to obtain a response frequency spectrum; extracting resonance (or peak value) frequency and response and frequency at adjacent frequency on the basis to obtain steady state response amplitude; and finally, calculating a frequency ratio and a response ratio according to theoretical derivation, completing calculation of related parameters, and realizing identification of the structural modal damping ratio.
Compared with the prior art, the invention has the beneficial effects that:
(1) the method for obtaining the time domain response from the frequency domain can quickly and accurately forecast the steady-state response amplitude of the structure with completely attenuated transient response under the resonance excitation, can also get rid of the limits of excitation frequency gear shifting and range, avoid damage to the structure under the resonance excitation, and finish steady-state response extraction under any frequency, and has higher test precision, less interference and higher speed than a resonance excitation test under certain conditions. In addition, according to the reciprocity of the frequency response function, when the excitation position is not suitable for excitation, the vibration pickup position can be excited, the response of the excitation position is measured to equivalently forecast the response characteristic of the vibration pickup position, and the operation is flexible;
(2) discrete spectral lines in a frequency domain are obtained after Fourier transform is carried out on time domain response, and due to the limitation of frequency resolution, a traditional half-power method is difficult to find a half-power point exactly to estimate the modal damping ratio. The method for calculating the damping ratio only starts from limited discrete spectral line information in the impulse response frequency spectrum, can avoid measuring a time domain signal of the exciting force, can also get rid of dependence on a continuous frequency spectrum when the damping ratio is solved by using frequency domain information, and is simple and rapid to operate and high in precision.
Drawings
FIG. 1 is a flow chart of the present invention;
fig. 2 is a diagram of the front three modes of the hull beam model used in embodiment 1 of the present invention;
FIG. 3 is a surface vessel modal damping coefficient specified in the specification;
FIG. 4 shows a calculated response spectrum and a steady-state resonance time-domain response of a bow value under condition 1 in embodiment 1 of the present invention;
wherein, (a) is used for calculating the displacement response frequency spectrum of the ship bow according to the numerical value, and (b) is used for calculating the displacement response frequency spectrum of the ship bow according to omega1jSteady state resonance response of ship bow when excited at 1.055Hz (m Δ f)
Steady state resonance response of bow when excited, (d) is according to
Steady state resonance response of the bow when excited;
FIG. 5 is a response spectrum for each damping ratio identification in three conditions in example 1;
where (a) is the response spectrum at the 2 nd order mode "node" (used to calculate the 1 st and 3 rd order modal damping ratio) and (b) is the response spectrum at the 1 st order mode "node" (used to calculate the 2 nd order modal damping ratio).
FIG. 6 is a side view (schematic view) showing the structure of a plate unit integral test model used in example 2 of the present invention;
the structure 1 is an upper cover plate, the structure 2 is a shell plate test model, the structure 3 is a reinforcing rib, and the structure 4 is a base;
FIG. 7 is a diagram showing the three-dimensional simulation effect of the overall structure model used in embodiment 2 of the present invention;
FIG. 8 is a schematic diagram of the arrangement of vibration exciting and vibration pickup points in embodiment 2 of the present invention;
wherein, (a) is the position and the number of the excitation point on the front surface of the plate, and (b) is the position and the number of the vibration pickup point (sensor) on the back surface of the plate;
FIG. 9 is a frequency domain signal when the plate unit model responds to the first-order damping ratio test condition in embodiment 2 of the present invention;
wherein, (a) is a domain response signal (0-0.205 s is intercepted) of a 61# vibration pickup point when a 58# point is excited according to the requirement of each stage working condition scheme in the table 5, and (b) is an impulse response frequency spectrum (0-1.0 kHz is taken) corresponding to (a).
FIG. 10 is a comparison of the board cell model test and the pre-simulation 8 th order modal analysis;
wherein the mode shape diagram is a 600mm × 600mm test area, "arrow" is the pulse excitation point, and "circle" is the response collection point.
Detailed Description
The technical scheme of the invention is explained in detail in the following with the accompanying drawings.
As shown in fig. 1, the present invention provides a method for rapidly calculating a modal damping ratio based on an impulse response spectrum, comprising the following steps:
The linear vibration system structure meets the modal superposition principle, and the modal damping ratio test of each order is obtained based on the actual structure. The arrangement of the vibration pickup point sensors should be determined according to the modal analysis performed in advance, that is, the vibration pickup point sensors are located at the nodes and the nodal lines of the adjacent modes, and are also locations with obvious response under each test modal shape, so as to reduce the influence of the superimposed components of the adjacent modes. Wherein, displacement, speed or acceleration sensor is all suitable for the measuring demand of the method to the response signal.
Within a certain frequency band of interest, the excitation produced by the transient impulse is considered to be an approximately ideal pulse signal at the time of testing. The test can realize impact excitation by adopting force hammers with different sizes, collision and the like, but does not need to measure an excited time domain signal. When the frequency range is wider, the pulse width tau of impact excitation can be recorded, and the effective excitation cut-off frequency f can be determinedc＝1/τ。
Step 2: collecting time domain response signal of vibration pickup point and making frequency domain conversion
And acquiring a response signal of the structure under impact excitation by using a dynamic signal acquisition instrument, and measuring a dynamic response time history curve of a vibration pickup point. Discrete Fourier Transform (DFT) is used for time-frequency domain conversion of a signal, and the size of a DFT block is usually an integer power of 2 (represented by N) because of the algorithm requirement, the time domain signal time length T is N Δ T (unit is s), the sampling frequency is 1/Δ T, and the frequency domain analysis frequency resolution Δ f is 1/T is 1/N Δ T.
Each sampling point value is xr(r ═ 0,1, …, N-1), the discrete lines in the frequency domain are:
the spectral line frequency interval is delta f, namely frequency domain analysis frequency resolution, and the fitted discrete spectrum curve is h (k delta f).
And step 3: extraction of steady state resonant response amplitude
The response characteristic of the structure to the impact load can be obtained through the motion analysis of the one-dimensional linear elastic system. The impulse force is semi-sinusoidal, the narrower the impulse width of the time domain impulse, the wider the signal frequency band, and the limit is the function of the impulse width 0, the Fourier transform is the white spectrum with infinite width, i.e. the impulse force is
(1) When an impulse force acts on the single-degree-of-freedom viscous damping system,
the system performs free vibration after obtaining the initial speed, namely the impulse response function is as follows:
wherein p is0The amplitude of the pulse force, m, c and k are respectively the mass, damping and rigidity of the system, omeganIn order to be the natural free-running vibration frequency,
in order to damp the free vibration frequency, ζ is c/ccAnd γ ═ ω/ωnRespectively damping ratio and frequency ratio. By using hPulse(ω) represents xPulse(t) frequency domain transformation:
the response amplitude and frequency at any frequency ω is:
(2) when the single-degree-of-freedom viscous damping system acts on the resonant load,
the overall reaction can be obtained as:
the first term at the right end of the formula (8) is expressed as e-ξωtTransient response of decay, a being a constant determined by the initial conditions; the second term is an infinitely continuous steady state resonance reaction at | xHarmonic wave(t) | denotes its steady-state harmonic amplitude value. Transient response is generally considered to decay rapidly and is ignored, but in some cases, the response is difficult to decay and even plays a dominant role in a certain time range, and the accuracy of response test is influenced if the transient response is ignored when resonance excitation is carried out.
Combining the equations (6) and (8), the relationship between the time domain resonance excitation response and the frequency domain impulse excitation response is established as follows:
|hpulse(ω)|＝|xHarmonic wave(t)| (9)
According to equation (9), when the pulse amplitude is equal to the resonance amplitude (both p0), the amplitude frequency of the impulse response spectrum is equal to the forced vibration amplitude at the corresponding resonance frequency ω. Therefore, the steady-state resonance response amplitude after transient reaction is sufficiently attenuated under the action of simple harmonic excitation of any frequency with the force amplitude equal to the pulse force amplitude can be extracted from the pulse response frequency spectrum.
The amplitude of the frequency response spectral line at the j-th order resonance frequency and the adjacent frequency in the experimental test result can be obtained as follows:
|hpulse(ωnj)＝|＝|hPulse(m Δ f) |, corresponding to a frequency ωnjAmplitude | x of forced vibration response under resonance excitation of m Δ fj(t)|；
Wherein, the frequency corresponding to the m-th spectral line is the resonance frequencyRate omeganjThe m + -q adjacent spectral line positions correspond to adjacent frequencies of the resonance frequency
m represents the frequency response line number corresponding to the j-th order resonance frequency (namely the m-th strip), and m +/-q represents the frequency response line number corresponding to the adjacent frequency of the j-th order resonance frequency (namely the m +/-q-th strip).
And 4, step 4: inversion calculation of modal damping ratio
A damping ratio calculation formula is deduced by using a one-dimensional beam model, and a two-dimensional system and a three-dimensional system are also applicable. Based on the modal superposition theory, the total response of the system under the resonance excitation of the frequency ω is:
the exciting force acting on x ═ x0Constant amplitude of force p0At a resonance frequency ω of order jnjWhen excited, the primary modal response is much larger than the other order modal response, i.e., the total response is (where
)：
(1) When the damping is larger, the response peak value (namely modal maximum response) of the experimental test is larger than the resonance frequency response, namely the peak value in the measured response frequency spectrum corresponds to the frequency
Not the resonance frequency omeganjThere is a relationship:
the j-th order response peak is:
the frequency of the j-th order modal response peak is adjacent to
Order to
Push button
The total response at resonance excitation is:
when in use
And
when the vibration pickup-excitation point is close to the vibration type node or node line of the adjacent mode, the response component of the adjacent mode is zero. At this time:
the following equations (13) and (15) can be obtained:
order:
i.e. j-th order modal response peak and press
The ratio of the response amplitudes under the frequency excitation is dimensionless;
obtaining:
obtained by the formulae (16), (17):
(2) when the damping is small,
the formula (13) is approximately reduced to the formula (11), and the accuracy of the obtained result is also acceptable. The method can be used for obtaining the following products:
at this time, the process of the present invention,
represents the j-th order resonance frequency ωnjAdjacent frequency of χjRepresenting amplitude and pressure of j-th order resonance response
The ratio of the response amplitudes under frequency excitation.
The steady-state harmonic amplitude values and spectral line corresponding frequencies extracted from the impulse response spectrum according to step 3 can be used for calculating gamma in this stepjAnd chij(or
And
) Namely:
Wherein, γjTo the adjacent frequency of the j-th order resonance frequency
With resonant frequency omeganjThe ratio is called frequency ratio for short; chi shapejMean j-th order resonance response amplitude and press
The ratio of the response amplitudes under the frequency excitation, referred to as the response ratio for short;
refers to the frequency adjacent to the jth order response peak frequency
And response peak frequency
In the ratio, Δ f is the frequency domain analysis frequency resolution,
indicating the frequency response line number corresponding to the j-th order peak frequency (i.e. the jth order
A strip),
indicating a frequency neighborhood of the j-th order peakFrequency response line numbering for near frequencies (i.e. the first
A strip).
Further obtaining modal damping ratio results according to (18) and (19), wherein the damping ratio refers to the ratio of damping to critical damping, and zeta is c/cc(ii) a Wherein:
when the damping is smaller, the precision of the formula (19) is acceptable;
when the damping is larger, the response peak value (namely the modal maximum response amplitude) is larger than the resonance response, the response peak value frequency and the resonance frequency have difference, and the precision of the formula (18) is higher.
The present invention will be further illustrated by the following specific examples.
Example 1: simulation numerical test
In example 1, the extraction of the steady-state response amplitude from the impulse response spectrum and the inversion calculation of the damping ratio are specifically explained and verified. Taking a hull beam model in the field of ship engineering as an example for analyzing the total vibration parameters, parameter identification is carried out on a certain ship according to the damping ratio inversion calculation method, and the model scale parameters are shown in table 1.
TABLE 1 Primary Scale parameters of a Ship
A whole ship body beam model is established for the ship, the beam model is an equivalent beam of a variable cross-section main ship body structure, the total weight of the whole ship and the attached ripple water mass are considered, and all section factors are calculated. Nastran is used for carrying out response analysis on the finite element model, and pulse excitation and resonance excitation (simulation propeller excitation) are applied to the stern of the ship body respectively so as to compare the accuracy of steady-state response amplitude extracted from a pulse excitation response frequency spectrum and the accuracy of damping ratio identification. The total vibration mode of the hull beam in the front three vertical directions is shown in figure 2. In dynamic response analysis, damping was as specified in the specification for the surface vessel modal damping coefficient, see figure 3 (with low damping).
The frequency response function is the inherent property of a linear constant system and is the Fourier transform of an impulse response function (unit impulse response function), and the frequency response function of a single-degree-of-freedom system is assumed to be
A pulse function of
An ideal unit pulse may excite the full band response. Comparing the impulse response spectrum expression (5) in the step 3 with the frequency response function expression to obtain:
frequency response analysis in Nastran is to calculate the dynamic response of the structure to each calculated frequency under the action of resonant load, and the mode of complex response is equal to the amplitude of steady-state resonance amplitude. Therefore, the frequency response analysis can equivalently obtain the impulse response frequency spectrum of the structure, and the time domain calculation of the impulse response is simplified. The calculation parameters are shown in a table 2, the displacement response of the bow part of the ship obtained according to the calculation working condition is given in the table, the error between the steady-state vibration amplitude extracted from the comparison response frequency spectrum and the actual calculated value is very small, and the existing relative error is caused by the computer precision. FIG. 4 shows the calculated response frequency spectrum and the steady-state resonance time-domain response of the ship bow under the working condition 1, wherein the amplitude of the exciting force is 1 kN.
TABLE 2 comparison of numerical calculation parameters and bow response
And finishing the concrete implementation description of the damping ratio of the hull beam model according to the calculation model and the parameters.
Step one, according to the modal analysis carried out in advance, determining the distance of a node closest to a stern in a first vibration mode, a second vibration mode and a third vibration mode of a hull beam as follows: 51150mm, 29700mm, 18150 mm. Calculating response frequency spectrum of adjacent (low) order vibration mode node of the researched order, and further determining the positions of vibration pickup points under three calculation conditions, namely: the 2 nd order mode "node", the 1 st order mode "node", and the 2 nd order mode "node".
And step two, the frequency response analysis in MSC. Nastran can equivalently obtain the impulse response frequency spectrum of the structure, and the response frequency spectrum of each vibration pickup point under three working conditions in the table 2 is obtained through calculation, as shown in FIG. 5.
Step three, extracting the maximum response of the corresponding order and the response under the adjacent frequency from the response frequency spectrum of fig. 5, and recording the respective corresponding frequency.
Step four, calculating frequency ratio and response ratio (gamma) of each order according to the response and the frequency thereof obtained in the step threejAnd chij) Table 3 shows the calculated damping simulation value calculated by the hull beam model, and the comparison with the set value according to the specification requirement shows that the damping ratio can be accurately identified by the method.
TABLE 3 Hull Beam damping calculation results and identification errors
(Note:
and recognizing errors
Respectively correspond to
Damping simulation calculation value under frequency excitation and identification error thereof
Example 2: plate unit model test
To verify the effectiveness of the method of the inventionThe modal test of the composite plate unit model of the local structure of the ship body is carried out, and the structure of the model is shown as figure 6. Wherein, the structure 2 is the unit structure of the tested glass fiber reinforced plastic plate, and fig. 7 is a three-dimensional entity test model. The tool structure is made of Q235 steel, the elastic modulus is 210Gpa, the Poisson ratio is 0.3, and the material density is 7800kg/m3And the numerical calculation is carried out in advance to ensure that the resonance frequency of each order of the design tool and the test board unit model has enough staggering rate. The composite material plate is made of a glass steel plate formed by hand pasting and is mainly used for preparing a ship body air guide sleeve structural member at present, and the main design parameters are shown in a table 4.
TABLE 4 FRP parameters
Firstly, performing modal analysis on a plate unit test model, wherein a multipoint excitation multipoint vibration pickup method (four vibration pickup points of 61#, 64#, 94#, and 97# are adopted for distinguishing modal gravity roots of a structure) is adopted for modal identification in the test, a force hammer is adopted for knocking as a pulse excitation source for excitation in the test, and an ICP piezoelectric sensor is adopted for picking up response signals. 81 excitation points are uniformly distributed on the front surface of the board, 9 response vibration pickup points are uniformly distributed on the back surface of the board, and a vibration excitation-vibration pickup point distribution schematic diagram of the front surface and the back surface of the board is given in figure 8. The sampling frequency is 5kHz, the sampling length is 32748, the pulse width tau of a pulse signal generated by the force hammer is about 0.7ms after recording, the effective excitation frequency range capable of being excited is 0-1.4 kHz, and the first 8-order resonance frequency identified by a test is in the frequency range.
The experimental and numerical calculation of each order of mode shape and the comparison of the resonance frequency thereof are shown in fig. 10, and meanwhile, in order to realize the separation of the multiple root modal responses by controlling the excitation position, the test point of each order of modal damping ratio is not only positioned at the node and the pitch line of the adjacent mode, but also is a position with obvious response under each test modal shape, and the excitation and vibration pickup positions of each order of damping ratio test are marked in the mode shape diagram in fig. 10.
And step two, according to the vibration excitation-vibration pickup position scheme determined in the step one and required in the test of each order of damping ratio, collecting the response signals of each measuring point by using a dynamic signal collector to obtain the time domain response signals of the vibration pickup points under each working condition. Taking the first-order damping ratio test condition as an example, a response time domain signal (0-0.205 s is intercepted) is as shown in fig. 9(a), and frequency domain conversion is performed on the response signal to obtain an impulse response frequency spectrum (0-1.0 kHz is taken), as shown in fig. 9 (b). The rest of the working condition tests were processed according to the same method.
And step three, because the damping of the test board is small, the difference between the resonance response obtained in the test and the maximum response is not large, when the response amplitude is extracted from the pulse response frequency spectrum data of each working condition obtained in the step two, the resonance response and the maximum response can be considered to be equal, and the adjacent frequency responses are extracted at the same time according to a certain staggering rate. The relevant data are shown in Table 5.
Step four, calculating modal damping ratio of each order according to the extracted response result and the formula (18) to respectively obtain
Averaging the two damping ratio results reduces the calculation error and the damping ratio results are shown in table 5.
TABLE 5 plate unit model damping calculation results
(note: the frequency resolution of the test response spectrum, Δ f, is 0.153Hz, and the value is taken according to the spectral line interval, m, is 4, and the response is the acceleration response.)
In order to verify the effectiveness of the method, the acquired input and output signals are identified by using DHDAS modal analysis software provided by Jiangsu Donghua test technology GmbH, the method is Polylscf (steady state diagram calculation method), and the method is a latest and popular international transfer function-based modal analysis method and has good identification precision. The first eight-order modal damping ratio of the plate unit structure is extracted and shown in table 6, and the result is used as a reference value of the identification result of the invention. Meanwhile, the half-power method is used to calculate the modal damping ratio of each order of the frequency response function obtained by the test, and the result is also given in table 6. Therefore, the identification result by the half-power method is generally large, and both Chen Qufu and Hui Huai firewood make theoretical analysis on the errors; the method is closer to the calculation result of the Polylscf (the maximum error of the damping ratio is 4.03 percent, and the method can be accepted in engineering), so the accurate identification of the modal parameters can be still realized by utilizing the process of the invention even under the premise of unknown excitation.
TABLE 6 comparison of damping parameter identification results of actual measurement plate unit model
The undescribed parts of the present invention are the same as or implemented using prior art.
The above embodiments are only for illustrating the technical idea of the present invention, and the protection scope of the present invention is not limited thereby, and any modifications made on the basis of the technical scheme according to the technical idea of the present invention fall within the protection scope of the present invention.
Claims (7)
1. A modal damping ratio rapid calculation method based on an impulse excitation response frequency spectrum comprises the following steps:
step 1, determining the position of a structure excitation-vibration pickup point;
step 2: collecting a time domain response signal of a vibration pickup point and performing frequency domain conversion;
and step 3: extracting a steady-state resonance response amplitude;
step 4, determining a damping ratio calculation parameter: frequency ratio and response ratio, calculating damping ratio,
the detailed content of the step 3 is as follows:
let the frequency corresponding to the m-th spectral line be the resonance frequency omeganjThe m + -q adjacent spectral line positions correspond to adjacent frequencies of the resonance frequency
The amplitude of the frequency response spectral line at the j-th order resonance frequency and the adjacent frequency in the test result is:
|hpulse(ωnj)|＝|hPulse(m Δ f) |, corresponding to a frequency ωnjAmplitude | x of forced vibration response under resonance excitation of m Δ fj(t)|；
And delta f is frequency domain analysis frequency resolution, m represents a frequency response line number corresponding to a j-th order resonance frequency, and m +/-q represents a frequency response line number corresponding to a j-th order resonance frequency adjacent frequency.
2. The method for rapidly calculating the modal damping ratio based on the impulse response spectrum as claimed in claim 1, wherein: in the step 1, a sensor is arranged at a proper position to determine the position of the structure excitation-vibration pickup position, wherein the proper position refers to the position of a node or a pitch line of an adjacent mode and is also the position with obvious response under each test mode.
3. The method for rapidly calculating the modal damping ratio based on the impulse response spectrum as claimed in claim 2, wherein: the sensor adopts a displacement sensor, a speed sensor or an acceleration sensor.
4. The method for rapidly calculating the modal damping ratio based on the impulse response spectrum as claimed in claim 1, wherein: in the step 2, a dynamic signal acquisition instrument is used for acquiring response signals of the structure under impact excitation, and a dynamic response time history curve of the vibration pickup point is measured.
5. The method for rapidly calculating the modal damping ratio based on the impulse response spectrum as claimed in claim 4, wherein: in the step 2, discrete fourier transform is adopted when frequency domain conversion is performed on the signal, the size N of a transform block is an integer power of 2, the time duration T of the time domain signal is recorded as N Δ T, the sampling frequency is 1/Δ T, and the frequency domain analysis frequency resolution Δ f is recorded as 1/T as 1/N Δ T; each sampling point value is xrAnd r is 0,1, …, N-1, and the discrete spectral lines in the frequency domain are:
the line spacing frequency is Δ f and the fitted discrete spectrum curve is h (k Δ f).
6. The method for rapidly calculating the modal damping ratio based on the impulse response spectrum as claimed in claim 1, wherein: in the step 4, when the damping ratio is small, the response ratio and the frequency ratio are calculated according to the following formula:
wherein, χjRefers to the ratio of the response amplitude of the j-th order resonance to the response amplitude of the excitation at a frequency adjacent to the j-th order resonance frequency, gammajThe ratio of the adjacent frequency of the j-th order resonance frequency to the resonance frequency, | hPulse(m Δ f) | represents the frequency response line amplitude under resonance excitation with frequency m Δ f, | hPulse(m +/-q) delta f) l represents the frequency response line amplitude under the resonance excitation with the frequency of (m +/-q) delta f, the delta f is the frequency domain analysis frequency resolution, m represents the frequency response line number corresponding to the j-th order resonance frequency, and m +/-q represents the frequency response line number corresponding to the adjacent frequency of the j-th order resonance frequency;
the modal damping ratio results are obtained according to the following formula:
therein, ζjIndicating the damping ratio.
7. The method for rapidly calculating the modal damping ratio based on the impulse response spectrum as claimed in claim 1, wherein: in the step 4, when the damping is large, the response ratio and the frequency ratio are calculated according to the following formula:
wherein the content of the first and second substances,
refers to the ratio of the maximum response amplitude of the j-th order mode to the response amplitude excited by the adjacent frequency of the response peak frequency,
the ratio of the frequency adjacent to the jth order response peak frequency to the response peak frequency, Δ f is the frequency domain analysis frequency resolution,
the number of the frequency response spectral line corresponding to the j-th order peak frequency is shown,
representing the frequency response spectral line number corresponding to the adjacent frequency of the j-th order peak frequency;
the modal damping ratio results are obtained according to the following formula:
therein, ζjIndicating the damping ratio.
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