Algorithm of resonance orders for the objects

Transcription

1 IOP Conferene Seres: Materals Sene and Engneerng PAPER OPEN ACCESS Algorthm of resonane orders for the objets To te ths artle: Yongang Zhang and JanXue Zhang 8 IOP Conf. Ser.: Mater. S. Eng. 6 Vew the artle onlne for updates and enhanements. Ths ontent was downloaded from IP address on 8//8 at :

2 IOP Publshng IOP Conf. Seres: Materals Sene and Engneerng 4689 (8) 6 do:.88/899x///6 Algorthm of resonane orders for the objets Zhang Yongang,,a and Zhang JanXue,b Dalan Unversty of Tehnology. Chna Dalan Tandao Marne Tehnology CO.,TD. Chna a td8@6.om, b zhangjanxue@yeah.om Abstrat. In mehanal engneerng, the objet resonane phenomena often our when the external ndent wave frequeny s lose to objet of the natural frequeny. Objet resonane phenomena get the maxmum value when the external ndent frequeny s equal to objet the natural frequeny. Experments found that resonane ntenson of the objet s hanged, dfferent objets resonane phenomena present dfferent haratersts of ladders. Based on objet orders resonane haratersts, the alulaton method of objet orders resonane s put forward n the paper, and the applaton for the lght and sound waves on the seven order resonane haratersts by people feel, the result error s less than %.Vsble n ths paper, the method has hgh auray and usablty. The alulaton method reveals that some objet resonane our present order haraterst only four types, namely the frstorders resonane haratersts, thrdorders haratersts, fve orders haraterst, and seven orders haraterst.. Introduton People have long found that any objet has ts nherent frequeny. It has been more works that the researh resonane phenomenon of nature objets has many years when nature objets affeted by outsde wave, and developed many theores and models, suh as vbraton modal learnng n engneerng mehans et. It s taken out a lot of works through atual measurement for resonane phenomenon of objets that the peoples have been used by all knds of preson nstruments and methods. But the people gnore the human organs brng us the resonane phenomenon of sound and lght feelng. The human organ s able to feel the nature many subtle hanges followng human organ evoluton, and even human desgn nstrument annot. The human organs feel seven olors of lght wave s also a knd of human's own organs preson nstrument measurng results. Human organs of the preson nstrument brng feelngs that the resonane phenomenon by external flutuaton has some propertes. Whle not all objets by external fore resonane have these propertes, but at least the human organs by external fore resonane have the propertes of seven resonane orders. Suh as human heard sound that (4) fa tone s strongest and the hghest tone. From () dou tone to (4) fa tone the sound s gradually strengthen, and from the (4)fa tone to () x tone wll be gradually dmnsh. Nature evoluton also showed the haratersts of the resonane orders, suh as green plants n nature, beause the sunlght green lght order s loaton n the enter and the energy strongest, but also nature plants evoluton s that maxmum ways absorb solar energy. It s also lookng for ways to present ther own form that plants evoluton hange green. Content from ths work may be used under the terms of the Creatve Commons Attrbuton. lene. Any further dstrbuton of ths work must mantan attrbuton to the author(s) and the ttle of the work, journal taton and DOI. Publshed under lene by IOP Publshng td

3 IOP Publshng IOP Conf. Seres: Materals Sene and Engneerng 4689 (8) 6 do:.88/899x///6 The artle researh the phenomenon of both the human eye to feel seven olors of the sun's rays and the human ears hear seven sales of the sound. Why are ts seven? Not eght or nne! It s found that the struture of seven resonane orders of the frequeny s the mddle order of frequenes as the enter where other some orders are n both sdes of the quassymmetral dstrbuton regularly. On the bass of resonane wave of a quarter wavelength effet, we desgned the method for alulatng the other sx resonant orders on both sdes when mddle resonant order wavelength knows. The alulaton results of the method have good agreement wth the realty measured values. In ths paper t s found the haraterst of three rng struture of resonane orders that both frst rng and seond rng out of sdes s the symmetry and nner thrd rng of resonane order s asymmetry or quas symmetr dstrbuton.. Wavelength of resonane order alulaton formula Resonane order wavelength of the objet alulaton formula s R Where the oeffents alulaton formula of resonane orders s () R ( ) ( ) R R () Where s any resonane order frequeny orrespondng to the wavelength; s the enter order of nherent frequeny orrespondng to the wavelength. When R=: where. Corresponds to two resonanes orders around the outer boundary, where s namely the frst lap of two resonane orders endpont wavelengths., where. Corresponds to the seond rng of the two resonant orders, where s the seond rle nward two resonane orders endpont wavelengths. The both frst rng and seond rng are symmetry on two sdes of left and rght when R=. When R=:, where 9. Corresponds to the thrd rng of the resonane order where s orresponds to the sde of short wavelength of the enter frequeny. If there are two endponts of the enter frequeny t s seleted the endpont of wavelengths longer for the enter frequeny. The tme havng two endponts wavelength need to alulate that both one endpont s shortwave endpont of the enter frequeny wth and other endpont s the thrd rng of the resonane order wavelength wth. When R=:, where. It orresponds to the endpont wavelength of the enter frequeny whh s on one sde of the long wave dreton, and s the thrd lap long wave sde. Why s t seleted the endpont of wavelengths longer for the enter frequeny? Beause the long

4 IOP Publshng IOP Conf. Seres: Materals Sene and Engneerng 4689 (8) 6 do:.88/899x///6 wavelength sde resonane wave moment of all three resonane orders s greater than other three resonane orders on one sde of short wavelengths. So t need has four endpont of resonane wave orders to balane on one sde of short wavelengths or the thrd rng s asymmetry to balane. The thrd rng s asymmetry on two sdes of left and rght when both R= and R=.. The verfaton of seven olors of sun lght wth the method olors Frequeny( Wavelength Calulaton method of The MHz) of ( nm ) of ths paper results realty realty Red Orang e Yello w reen 6 6 Chon gkwa ng blue Purple red green green The error..9% orange green green % yellow green green Resonan e oeffe nt 98..% green green green..44% 9 hongkw green green % blue green green 4..% purple green green 6..8% Table.. Seven olors wavelengths alulaton result lst Although the orange lght alulaton error s larger, but does not exlude the error generated by the delmtaton of both the red and orange lght, beause red lght band wdth s nm, orange lght band too narrow s nm. If the wavelength of delmtaton of both the red and orange lght s 66 nm, t may be more reasonable []. 4. Verfaton for seven resonane orders of sound wth the method Regster () () () (4) () (6) () of seven sales n mddlepart, (4) sale s as the enter frequeny. We apply equaton () to alulate other sx sales wavelength of the sound [] []. Sale Frequeny(H z) of realty () (6) () 69.. Wavelength( m) of realty Method n the paper Calulato n results The error.8 6.% %.4.9% 9 Resonane oeffent (4) 8..8 =. 8 4 Wavelength of Center frequeny () 4..6 () () %.69.%..% Table Seven sales wavelength alulaton result n aoust medant lst

5 SAMSE IOP Publshng IOP Conf. Seres: Materals Sene and Engneerng 4689 (8) 6 do:.88/899x///6 Sale Frequeny(H z) of realty ( ) Wavelength( m) of realty Method n the paper. Calulat on results Calulato n error.4% Resonan e oeffen t 6 ( ) % ( ) % 9 ( 4 =. ) Wavelength of Center, Where ( ).9.6 ( ) ( ) %.88.%.4.% Table Seven wavelength sales alulaton result n aoust bass lst Sale Frequeny(H z) of realty ( ) ( 6 ) Wavelength( m) of realty Method n the paper.9 ( ) 8... ( 4 ) =. 8 ( ) 8..6 Calulato n results Calulat on error 6.%.4%.% 9 Resonane oeffent 4 4 Wavelength of Center, Where..98% ( ) % ( ) % Table 4 Seven sales wavelength alulaton result n aoust treble lst The alulaton errors are bg to % from table (), table ( ) and table 4 ( ) sales by the omparson. From the alulaton results of the alulaton model by desgn n ths paper, n table () sale wavelength alulated value s.8m wth onde to table 4 ( ) of the measured wavelength value of.86m, and table ( ) sale wavelength alulated value s.m wth onde to table () sale of the measured wavelength value of.m. Calulaton results n ths method show a seamless lnk up for three parts of treble, medant and bass, and ts share a ommon outsde border order for Fg, where horzontal axs s wavelength oeffent of = R. 4

6 IOP Publshng IOP Conf. Seres: Materals Sene and Engneerng 4689 (8) 6 do:.88/899x///6 Fg.. Seven sales of sound dstrbuton shemat dagram n hgh, medant and bass part The fat n real mus t s halfdown the hromat to use for medant () and the bass sounds ( ) and treble department ( ).. Conluson It an be seen from the above alulaton that the resonane order of the objet an be presented a frst order, the thrd orders, also fve orders, only seven orders, but nne orders s unlkely, beause the oeffents of both and are near the onvergene, so t an't dvde agan. And resonane boundary of the objets s the value of a thrd wavelength of enter natural frequeny. It annot be hanged for the value of the resonane frequeny boundary. When the absolute value of the dfferene between foregn ndent wavelength and enter natural frequeny wavelength s less than a thrd, the resonane wll be ours by the ndent wave to response. Ths s a thrd wavelength effet for begnnng resonane of two boundary orders [4][][6][][8][9]. 6. Referenes [] Bran Smts, An RB to Spetrum Converson for Refletanes. Journal of raphs Tools., 4(4):. [] Morfey, C.. (ed.) () Dtonary of Aousts. Aadem Press, San Dego. [] Smth, K.B., Brown, M.. and Tappert, F.D. (99b) Aoust ray haos ndued by mesosale oean struture. J. Aoust. So. Amer., 9, 9 9. [4] Y.. Zhang,Y. C., "Numeral Smulaton of abnormal wave hgh hange ndued by exavated waterway wth Boussnesq equaton, " Chna Oean Engneerng,(),6,998. [] Y.. Zhang, Y.C., "A new form of Boussnesq equaton wth mproved lnear dsperson haratersts," Chna Oean Engneerng,(),,999. [6] Y.. Zhang, et al, "Sound lght rado wave dut effet and apply n oean",chna eletron ndustry publshng ompany, 4. [] Y.. Zhang, et al, " Algorthms of wave refletve rtal angle on nterfae", Internatonal Conferene on Optal and Photon Engneerng (OPEN 6) n Chengdu, Chna. [8] Y.. Zhang, PCT/CN/89, "The alulaton method of wave refletve ndex on nterfae". [9] Y.. Zhang, PCT/CN6/964, " The alulaton method of four patterns of resonane order of the objet"