CN1851436A - Big-span roof and super high-rise building structure wind vibration response detecting and computing method - Google Patents

Abstract

The invention relates to testing method used in wide span house cover and super tall building structure wind induced oscillation response. The feature is that it directly adopts the mold analyzing method to use the response of physical coordination and mode coordination under the random air driving bearing final function. The calculating result has the same accuracy as the method of CQC. But the calculating speed is much faster than CQC method, and the request for memory is also lowered. It is especially suited for realizing on middle class PC.

Description

The detection computations method of wide span house cap and super-high building structure wind vibration response

Technical field:

The present invention relates to the structures under wind analysis field of wide span house cap and super-high building structure, be specifically related to the synchronous wind pressure measurement of wind-tunnel of BUILDINGS MODELS and calculate the wind-induced vibration response of this class formation and the equivalent static wind load of structure.

Background technology:

Wide span house cap and super-high building structure are subjected to the effect of RANDOM WIND load stably, be to calculate response on its optional position in theory, before the present invention, the exact method that is adopted is complete quadratic form combination (CQC) method, and the accurate Calculation of wind induced structural vibration response analysis is further to calculate the key of the equivalent static wind load that can be used for structural design.Yet, because large-scale engineering structure all has very large degree of freedom, directly adopt the CQC method to have the big and huge problem in committed memory space of calculated amount and influenced its engineering adaptability, these problems are particularly evident in the wind vibration response of multipoint random excitation in calculating wide span house cap structure, the result that it finally causes is that counting yield is low, data analysis is long computing time, and, often be difficult to satisfy the needs of structural design in case after the structural parameters adjustment, calculate again the computing time of spending same again.Therefore, guaranteeing under the constant condition of computational accuracy, is seeking and a kind ofly not only saved internal memory but also efficient method fast quick and optimal design has very significant meaning undoubtedly for the engineering windproof of this class formation.

Summary of the invention:

Technical matters to be solved by this invention is two key issues in the detection computations of wide span house cap and high-rise building wind vibration response and equivalent static wind load: CQC method calculated amount is too big and occupy the too big problem of storage space.

The present invention solves the problems of the technologies described above by following technical scheme, it is characterized in that it may further comprise the steps:

1) utilizes high-speed synchronous pressure instrumentataion blast to the BUILDINGS MODELS surface in wind-tunnel to carry out the high-speed data sampling, and carry out mould/number conversion (A/D conversion), obtain N _pThe discrete blast time-histories data sample vector { P of the digitizing of * 1 dimension _T(t) }, t=i Δ t wherein, Δ t is a sampling interval, i=1,2 ... N, j=1,2 ... Np; N is a sample points, and T=N Δ t is the sampling time, and Np is synchronous pressure measurement measuring point number, and the result of sampling is stored in the computing machine; { P in essence _T(t) } be equivalent to the truncated sample sequence of actual blast time-histories { p (t) }, that is:

2) calculate the Fourier transform of this truncated function vector:

$\left\{P(f,T)\right\}={\∫}_{-\∞}^{+\∞}\left\{p_T\left(t\right)\right\}{e}^{-i2\mathrm{\πft}}\mathrm{dt}$

3) can get the modal coordinate of structure under the effect of above truncated function vector and the Fourier transform of displacement of joint response with modal analysis method:

{Q(f，T)}＝[h _p(f)] ^*[Φ] ^T[R]{P(f，T)}

{Y(f，T)}＝[Φ]]{Q(f，T)}

Wherein: [h _p(ω)] be the frequency response function matrix under the modal coordinate, [Φ] is vibration shape matrix, and [R] is load oriental matrix or expansion load allocation matrix, and Q, Y represent the Fourier transform of the truncated function of modal coordinate q (t) and displacement of joint y (t) respectively; Can distinguish the estimation of the power spectral density function of compute mode response and displacement of joint response by above result:

$\left[S_{q_T{q}_T}\left(f\right)\right]=\frac{1}{T}{\left\{Q(f,T)\right\}}^{*}{\left\{Q(f,T)\right\}}^T$

$\left[S_{y_T{y}_T}\left(f\right)\right]=\frac{1}{T}{\left\{Y(f,T)\right\}}^{*}{\left\{T(f,T)\right\}}^T$

4) adopt the overlapping sampling mode can obtain the truncated sample function of different time sections, repetitive process 2) 3) [S to being calculated _QTqTAnd [S (f)] _YTyT(f)] carry out arithmetic mean to improve the precision that spectrum is estimated, finally obtain the power spectral density function of modal response and displacement of joint response:

$\left[S_{\mathrm{qq}}\left(f\right)\right]=\stackrel{\‾}{\⟨{[S}_{q_T{q}_T}\left(f\right)]\⟩}$

$\left[S_{\mathrm{yy}}\left(f\right)\right]=\stackrel{\‾}{\⟨\left[S_{y_T{y}_T}\left(f\right)\right]\⟩}$

The covariance matrix of corresponding modal response is:

$\left[C_{\mathrm{qq}}\right]={\∫}_0^{\∞}\left[S_{\mathrm{qq}}\left(f\right)\right]\mathrm{df}$

And the covariance matrix of displacement of joint response is:

$\left[C_{\mathrm{yy}}\right]=\left[\mathrm{\Φ}\right]\left[C_{\mathrm{qq}}\right]{\left[\mathrm{\Φ}\right]}^T$

More than two matrixes are keys of further calculating equivalent static wind load.

The present invention has following technique effect:

1, avoided the power spectrum density matrix  S of direct calculating random load excitation _Pp(f)  can save taking of calculator memory widely.

In the wind vibration response that adopts with the synchronous pressure measurement data computation of the multiple spot of wind tunnel test structure, the power spectrum density matrix of excitation is converted to the power spectral density function matrix of measuring point blast usually.Because the power spectrum density that needs to calculate on the different frequency value is calculated [S _Pp(f)] be actually a three-dimensional complex matrix, its length depends on the measuring point number of test and the sample length of The data, the synchronous pressure measurement of general wide span house cap structure needs 400 more than the measuring point usually, suppose that the spectral line number that final power spectral density is calculated was 1024 (depending on the sample length of data sampling and the segments in the analysis of spectrum), the needed amount of ram of above like this measuring point blast desired power spectral density matrix just is: 16 * 400 * 400 * 1024/1024 ³=2.44GB byte, this also is difficult to realize on general top-grade computer or workstation, and the needed internal memory of blast time-histories function Fourier transform of depositing same length only is the 6.25MB byte.

Even taking of a large amount of internal memories makes high performance workstation all can't adopt the CQC method to calculate, the inventive method then makes the wind vibration analysis problem of labyrinth to carry out on middle-grade microcomputer.

2, in fact, just because of avoiding directly to three-dimensional power spectrum density matrix  S _PpThe power spectrum density that the computing simplification of (f) containing in the computing of  and this process makes follow-up modal response and displacement of joint respond is calculated required amount of calculation, and also the CQC method more than traditional is few.

Two key issues in more than having solved large and complex structure especially the detection computations of wide span house cap wind vibration response and equivalent static wind load calculating, on general middle-grade microcomputer, can realize the quick calculating of this class formation, can satisfy the needs of structural design analysis.

Description of drawings:

Fig. 1 algorithm flow chart of the present invention;

This algorithm of Fig. 2 goes out certain high-rise building top dynamic displacement with the CQC algorithm computation and compares with the result of calculation that different wind directions change;

Fig. 3 wide span house cap wind vibration response calculates the contrast of required time;

The contrast of the required internal memory of array during Fig. 4 wide span house cap wind vibration response calculates.

Embodiment:

The wind pressure signal of using the synchronous pressure instrumentataion measurement structure of multiple spot surface obtains acting on the excitation time-histories of buildings, directly by the Fourier transform compute mode coordinate of excitation truncated function and the Fourier transform of displacement of joint response, the power spectral density function of compute mode response and main nodes displacement response then, and obtain being used for the covariance that the response of equivalent static wind load compute mode coordinate and displacement of joint respond thus.Algorithm flow of the present invention is seen Fig. 1.

Result of practical application:

The comparison of Fig. 2 for adopting this method and CQC to calculate the maximum dynamic displacement of certain high-rise building under the different wind directions, the result of calculation of visible this method and CQC method is consistent.

Fig. 3 and Fig. 4 are respectively the comparisons of CPU time and array EMS memory occupation situation in calculating, its calculating object is a large-scale sports center structure that comprises roof system, from Fig. 3, Fig. 4 can find out, the present invention takies CPU computing time less than 1/10th of CQC method, EMS memory occupation has only about 1/5th of CQC method, therefrom can see superior part of the present invention, should be noted that, for this example, because the common middle-grade microcomputer of memory problem can not satisfy its calculation requirement, the calculating of this example is finished on DELL 670 workstations, and the time contrast only has relative meaning; In order to contrast two kinds of algorithms, the scale of solving a problem has been done suitable restriction simultaneously,, might also be difficult to adopt the CQC method to be calculated at good workstation, thereby can't compare if do not limit.

For complex engineering structure comparatively, be that it has solved the problem that the CQC method all can not be calculated on good workstation even save the meaning of memory headroom, the present invention makes the practicability and the engineering application of the calculating of the charming appearance and behaviour response of complicated wide span house cap structure and equivalent static wind load become possibility.In the in-depth process of structural design, the parameter of structure can be among the adjustment always, in case structural parameters are adjusted, wind vibration analysis and equivalent load calculate and just must carry out again, and the present invention can make the response of prestissimo to structural modifications.

Claims (1)

1, a kind of detection computations method that is used for wide span house cap and super-high building structure wind vibration response is that the blast on the wind tunnel test test structure surface by above-mentioned BUILDINGS MODELS distributes, and calculates realization in view of the above, it is characterized in that:

1) utilize the high-speed synchronous pressure instrumentataion that the blast on BUILDINGS MODELS surface is carried out mould/number conversion at a high speed in the wind-tunnel, i.e. A/D conversion obtains N _pThe discrete blast time-histories data sample vector { p of the digitizing of * 1 dimension _T(t) }, t=i Δ t wherein, Δ t is a sampling interval, i=1,2 ... N, j=1,2 ... Np; N is a sample points, and T=N Δ t is the sampling time, and Np is synchronous pressure measurement measuring point number, and the result of sampling is stored in the computing machine; { p in essence _T(t) } be equivalent to the truncated sample sequence of actual blast time-histories { p (t) }, that is:

2) calculate the Fourier transform of this truncated sequence vector:

$\left\{P(f,T)\right\}={\∫}_{-\∞}^{+\∞}\left\{p_T\left(t\right)\right\}{e}^{-i2\mathrm{\πft}}\mathrm{dt}$

3) obtain the modal coordinate of structure under the effect of above truncated function vector and the Fourier transform of displacement of joint response with modal analysis method:

{Q(f，T)}＝[h _p(f)] ^*[Φ] ^T[R]{P(f，T)}

{Y(f，T)}＝[Φ]]{Q(f，T)}

Wherein: [h _p(ω)] be the frequency response function matrix under the modal coordinate, [Ф) be vibration shape matrix, [R] is the load allocation matrix, Q, Y represent the Fourier transform of the truncated function of modal coordinate q (t) and displacement of joint y (t) respectively; Distinguish the estimation of the power spectral density function of compute mode response and displacement of joint response by above result:

$\left[S_{q_T{q}_T}\left(f\right)\right]=\frac{1}{T}{\left\{Q(f,T)\right\}}^{*}{\left\{Q(f,T)\right\}}^T$

$\left[S_{y_T{y}_T}\left(f\right)\right]=\frac{1}{T}{\left\{Y(f,T)\right\}}^{*}{\left\{T(f,T)\right\}}^T$

4) employing overlapping sampling mode obtains the truncated sample function of different time sections, repetitive process 2) 3) to what calculated

With

Carry out arithmetic mean to improve the precision that spectrum is estimated, finally obtain the power spectral density function of modal response and displacement of joint response:

$\left[S_{\mathrm{qq}}\left(f\right)\right]=\stackrel{\‾}{\⟨\left[S_{q_T{q}_T}\left(f\right)\right]\⟩}$

$\left[S_{\mathrm{yy}}\left(f\right)\right]=\stackrel{\‾}{\⟨\left[S_{y_T{y}_T}\left(f\right)\right]\⟩}$

The covariance matrix of corresponding modal response is:

$\left[C_{\mathrm{qq}}\right]={\∫}_0^{\∞}\left[S_{\mathrm{qq}}\left(f\right)\right]\mathrm{df}$

And the covariance matrix of displacement of joint response is:

[C _yy]＝[Ф][C _qq][Ф] ^T

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