Analysis of Aerial Platform Response to Wind-Induced Vibration

Transcription

1 Analysis of Aerial latform esponse to Wind-Induced Vibration Hongqi Jiang 1,, Xianbiao Mao 1, JingyuYan 1 State Key Laboratory for Geo-Mechanics and Deep Underground Engineering China University of Mining and Technology Xuzhou 1008, China School of Mechanical & Electrical Engineering Jiangsu Normal University Xuzhou 1116, China Abstract Due to the complicated characteristics of aerial platforms under effects of random dynamic wind, the traditional method face difficulties to reflect its dynamic response in real time. In this stud we investigate the random wind induced vibration response analysis method based on the finite element method and pseudo-excitation method. It treats the vibration of the fluctuating wind load as coherent random vibration under stationary random excitation, and it uses Davenport wind velocity spectrum, which does not change with height, to consider the correlation of wind excitation. The Aerial latform is employed as a numerical example to obtain the response spectra and root mean square (MS) of the Aerial latform in wind-induced vibrations. The results indicate that the vibration of the aerial platform has a large response in low frequenc and the one-third Octave acceleration MS is lower. Lastl the influences of the wind-induced vibration on comfort are analyzed. Keywords - virtual excitation method; aerial platform; wind-induced response I. INTODUCTION As a ind of engineering machinery and equipment, the Aerial latform is widely used in construction. The stability and security are one of the ey technologies of Aerial latform research. With the increase of high buildings, the operation difficulty of Aerial latform height is higher and higher; the tower arm slenderness ratio is more and more big, the wind load effect is more apparent. As the wind loading may produce larger deformation and vibration [1-3],it will serious impact on the safety of the Aerial latform and operation personnel. Natural wind in the process of flow due to the influence of various obstacles on the ground, its speed presents the random fluctuating characteristics. It is generally believed that natural wind is composed of the average wind and fluctuating wind [4],the speed of wind has an average component and a pulsating component. Therefore, under the effect of natural wind, the load structure of wind is composed of two parts: one is the average calm load under the action of the wind; the second is fluctuating load under the action of random pulse. The load structure caused by the static deformation can be obtained through static analysis of the structure; and fluctuating wind component will cause the induced vibration of the structure, the continuous vibration will cause structure fatigue damage, and also can cause the discomfort of worers. In conventional design, it often tae the wind load as the static force and then tae the certain wind vibration coefficient into consideration, and the calculation results can not fully reflect the dynamic response of wind load excitation. So it is necessary to carry out the dynamic response analysis of aerial wor machinery under the fluctuating wind load, in order to grasp the dynamic performance of the structure and improve the reliability of system design. II. BEFOE STYLING SIMULATION OF A FLUCTUATION WIND LOAD ON AEIAL LATFOM A. Fluctuating Wind Speed in A model The wind load of Aerial latform is multi-dimensional turbulent wind speed, and main effect of wind on the urface of the boom or nodes, multi-dimensional Simulation of time history of the Aerial latform structure was conducted by using the linear filtering method of auto-regression (A) model. the column vector of fluctuating wind speed timehistory u x, for M spatial correlated points is given by Eq.(1)[5]: ux, ut Nt, 1,,, (1) Where, is the order of A model; t is the time step of simulating wind speed time-history; N(t) is the vector of independent random process; is regress coefficient, can be obtained as Eq. (): u u t, 1,,, Where, u is Autocorrelation function, can be obtained as Eq. (3): Su n n dn 0 n u cos (3) Where, S u is turbulent wind speed Spectra. N can be obtained as Eq. (4): N () DOI /IJSSST.a ISSN: x online, print

2 0 t (4) N u There, turbulent wind is stationary random process with mean value of 0, correlation function matrix is: 11 1 n1 ndn There, i 0 Si Cholesy factorization. 1 1 n u 1 n n nn,thus, can be obtained by LL T There, Lis Lower triangular matrix, all elements can be obtained as Eq. (6): i 1 CiC i 1 Ci, 1 C ii ii Ci C 1 (6) The fluctuating wind speed time-history can be expressed as Eq. (7): v t C u t (7) B. Turbulent Wind Load At any time,the wind speed of in Aerial latform can be expressed as as Eq. (8): V x, z V z ux, (8) Where, V z is Average wind speed; u x, is fluctuating wind speed with mean value of 0. According to the Bernoulli equation, wind load can be expressed as Eq. (9): 1 Fx, s AV i z s AV i z u x, (9) x, px, Where, is Air density; s is wind pressure coefficient of the corresponding nodes ; A i is the area of corresponding nodes ; x, p x, is the average wind pressure and fluctuating wind pressure of corresponding nodes. III. FEQUENCY DOMAIN CHAACTEISTICS OF WIND- INDUCED VIBATION ESONSE ON AEIAL LATFOM A. Theory of seudo-excitation Method According to vibration theor under the zero initial condition, the constant coefficient linear frequency response function of the system is the ratio of input vector and output harmonic content, namely that: X t H (10) Y t (5) H is frequency response function; Where, X t is Fourier transform of x t ; Y t is Fourier transform of y t. When the linear systems is affected by the stationary random excitation function F t of the spectral density S, and the response of power spectrum is as (11) [5-7]. S XX H S (11) Where H is the frequency response function, which i t means when the random excitation of incentive is e,the corresponding harmonic response is it X t He.If the i t incentive e is multiplied by the constant S,namely that construct a virtual incentives function ~ i t,then the corresponding virtual response is: ~ i X t S H e (1) t The actual response can be obtained from power spectral density and cross power spectrum density and the calculation formula are as follows: ~ X ~ ~ X X H S S XX (13) ~ ~ it it F X S e S He S H SFX (14) ~ ~ it it X F S H e S He H S S XF (15) Where S XX represents the actual response of the power spectral densit S FX represents the actual incentive and the actual response of the power spectral densit S XF represents the actual response and actual incentive cross-power spectral density. If the system has more than one response, through the type (13) ~ (15) type, the available power spectrum matrix can be obtain. T S X ~ ~ T X, SFX F ~ ~ T X, S XF X ~ F ~ Where * represents complex conugate and T represents transpose. B. Wind Vibration esponse Analysis Based on Virtual Excitation Method Fluctuating wind loads on the structure caused by vibration, can be looed as more coherent random vibration problem under stationary random excitation, the dynamic differential equation is as (16). M Z t C Z t K Z t F t (16) Where, M C K represents the mass, damping and stiffness matrix of structure,respectively; Z t represents the node displacement vector; F t represents the wind load vector of fluctuating. According to the vibration mode decomposition method, the equation (16) can be rewritten according to the vibration mode [8,9]. DOI /IJSSST.a ISSN: x online, print

3 q z t u t u t 1 (17) Where, q is the selected number of vibration mode, u represents the displacement, represents vibration vector. According to the specification, the general tae Davenport fluctuating wind velocity spectrum is taen as the excitation spectrum; it does not change with height, since the power spectrum of its expression is: 4KV10 x0 100n S ff n, x0 (18) 3 n1 x 4 V10 0 Among them: n represents the pulsating wind frequency; V10 represents average wind speed when the height is 10 m; K is the coefficient which is related to surface roughness. As the fluctuating wind randomness, if tae the correlation between different random excitation, coh,the level of cross spectrum of fluctuating wind velocity can be expressed as [10] : S i S ii S coh i (19) 1 Where n C x x C y y Cz z coh exp, V10 Cx 16, C y Cz 10 represent the space attenuation coefficient x, z are the coordinate difference of the two points. Through (16) and (17),the load power spectrum matrix S can be obtained, obviously that S is the Hermite matrix, so it can be decomposed through LDL* method. Thus the (0) is obtained. * T S L DL (0) Where, L is the triangular matrix, D is a diagonal matrix. If tae the first column if the vector L,D no diagonal elements d,can construct virtual excitation vector n as follows: ~ it x t L d e, 1,,, n (1) The virtual response of the structure can be obtained. ~ T it z t H L d e () Where H represents the frequency response function H 1 i (3) Where represent the natural frequency and damping ratio, Through(1),the ower spectrum matrix z is as (4) n S ~ z ~ z T zz (4) IV. EAE YOU AE WIND VIBATION ESONSE ANALYSIS FO AEIAL LATFOM In the stud the Aerial platform is composed of rectangular cross section of the upper arm, lower arm. The upper arm head wor platform are used for transporting people and goods, the arm up and down are through the oil cylinder lifting, and adopts the light vehicle chassis. When the wor arm is in the elevated position, the steel processing can be adopted in oil cylinder, upper arm and lower arm can use the element simulation of Euler Bernoulli beam, oil cylinder can be simulated through using a one-dimensional bar element. the constraint processing are adopted in the lower arm oil cylinder and the lower arm, the simplified operation arm is as shown in Fig.1,It is the finite element model which is composed of seven nodes and seven units. The woring height is about 18m, L 13=7.96m, L 36=7.4m, L 3 =0.5m, L 56 =1.5m, L 67 =0.5m, E=0700Ma,Upper arm A 1= m,i 1= m 4, Lower arm A = m,i = m 4.Oil cylinder A= m,i= m 4.Landscape coefficient K is 0.039, the basic wind pressure is 0.9KN/m, the Davenport fluctuating wind speed spectrum is looed as the standard wind speed. TABLE I THE FIST 8 ODES VIBATION MODES Order time Natural equency (Hz) According to the A model, through the Matlab simulation program, the fluctuating wind load time-history was obtained there, Average wind speed is 15m/s and Davenport pulse wind speed spectrum was selected as the standard wind speed spectrum. the oughness coefficient on the ground is 0.16;the sampling frequency is 50Hz;The simulation time is 300s; t is 0.1s;the order of A is 4. The fluctuating wind load time-history in Aerial latform is as shown in Fig.. Simulation spectrum of wind load timehistory power spectrum compared with the target power spectrum have good consistency in Fig.3. Figure 1. Finite element model of aerial platform DOI /IJSSST.a ISSN: x online, print

4 Figure. Fluctuating wind load time-history Figure 5. Vertical displacement time history curve. Figure 3.Simulated spectrum compared with the target spectrum. Figure 6. Horizontal displacement spectrum of node 1. The fluctuating wind loads on the finite element model of the Aerial platform, The displacement time history curve of platform was obtained as shown in figure 4 and figure 5. From the Fig.4 to Fig.5 it can be seen that, Horizontal displacement is greater than vertical displacement, The maximum horizontal displacement of 6.mm. Figure 7. Horizontal acceleration spectrum of node 1. Figure 4. Horizontal displacement time history curve. In the frequency range of 0. Hz to 30 H through the Matlab simulation program, we obtain the assignments arm at the front of node 1 horizontal and vertical displacement DOI /IJSSST.a ISSN: x online, print

5 and the acceleration power spectrum are shown in Figure 6 to Figure 9. Figure 8. Vertical displacement spectrum of node 1. ecent studies have shown that[11,1],frequency sensitive frequency of human body in the up and down fluctuation is between 4 and 8 H and the sensitive frequency of vibration bac and forth is between 1- H and some area of the body can produce resonance, with the increase of frequenc sensitivit and the vibration will influence the comfort. The severe vibration response is less than 30 H and the influence of vertical vibration on comfort is about 70%,horizontal vibration is about 1%. In order to study the effect of vibration on personnel comfort degree, the response spectrum is calculated through pseudoexcitation method, in frequency range of 1 to 0 H a series of discrete frequency points are selected, through the type (5),the mean square root of acceleration can be calculated. 1.1 f 0.89 f r 1 S zzd (5) 3 Table II and table III lists the horizontal and vertical 1/3 frequency multiplication acceleration root mean square in the Location of operation room node 1.According to the international standard ISO 631 body fatigue/efficiency lower limit, the acceleration root mean square of the type of Aerial latform are standard 8 hours woring efficiency under the lower limit,which can ensure that worers in eight small basic is not influenced by wind vibration in the woring time. r TABLE II MEAN SQUAE OOT OF ACCELEATION OF ONE THID FEQUENCY DOUBLING (HOIZONTAL) Center frequency /Hz m s Center frequency /Hz m s TABLE III MEAN SQUAE OOT OF ACCELEATION OF ONE THID FEQUENCY DOUBLING (VETICAL) Center frequency /Hz m s Center frequency/hz m s IV. CONCLUSION As the complex characteristics of woring truc under random dynamic wind load, the traditional design can not reflect its dynamic response accuratel in the stud the finite element method and pseudo-excitation method are adopted in the wind induced vibration response analysis of woring truc, it can both accurately reflects the operation arm vibration response caused by a fluctuating wind load, and also can improve the efficiency of computing, and it can provide a feasible way for wind induced vibration analysis of woring truc. Through the analysis of the level of operation platform, vertical displacement and acceleration power spectrum, the first and second order frequency vibration response are significantl and the vertical vibration response is greater than the horizontal vibration response. With the increase of wind speed, The displacement and acceleration response is significant increase. One third acceleration mean square root of the woring arm operation platform at each frequency point is below the international body fatigue/efficiency standards of ISO631, and it has no significantly effects on the worers. EFEENCES [1] D. K. Sun, J. H. Lin, Y. H. Zhang, The wind induced randomvibration analysis of complex structures, Journal of mechanical engineering, vol.5, no. 3, pp , 001. [] Y. L. Xu, W. S. Zhang, J. M. Ko, The seudo - excitation method for vibration analysis of wind Excitedstructures, Journal of Wind Engineering and Industrial Aero Dynamics, vol. 83, pp , [3] W. T. Xu, J. H. Lin, Y. H. Zhang, D moving element method for random vibration analysis of of vehicles on Kirchhoff plate with Kelvin foundation, Journal of Latin America Solid and Structures, vol. 6, pp , 009. [4] F. L. Wang, W. gao, J. J. Chen, rescribed by ritual law incentive antenna structure under random vibration analysis, Journal of engineering mechanics, vol. 3, no., pp , 006. [5] J. H. Lin, Y. H. Zhang, andom vibration of the pseudo -excitation method, science press, 004. [6] Z. Y. Sun, H. Wang, Structural random vibration analysis of equivalent excitation method, Journal of engineering mechanics, vol. 7, no. 1, pp. 0-3, 010. DOI /IJSSST.a ISSN: x online, print

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