Influence of foundation mass and surface roughness on dynamic response of beam on dynamic foundation subjected to the moving load

Transcription

1 IOP Confrnc Sris: Earth and Environmntal Scinc PAPER OPEN ACCESS Influnc of foundation mass and surfac roughnss on dynamic rspons of bam on dynamic foundation subjctd to th moving load To cit this articl: Tinh Tran Quoc t al 018 IOP Conf. Sr.: Earth Environ. Sci Rlatd contnt - Dynamic rspons for structural halth monitoring of th Pnang (I) cabl-stayd bridg M I Mohammd, E Sulaman and F Mustapha - Modling and xprimntal validation of a linar ultrasonic motor considring rough surfac contact Qibao Lv, Zhiyuan Yao and Xiang Li - Vibration Analysis of Fram Structurs Using Wavlt Finit Elmnts M Musuva and C Mars Viw th articl onlin for updats and nhancmnts. This contnt was downloadd from IP addrss on 31/08/018 at :09

2 Influnc of foundation mass and surfac roughnss on dynamic rspons of bam on dynamic foundation subjctd to th moving load Tinh Tran Quoc 1, Toan Khong Trong 1,* and Hai Luong Van 1 Faculty of Civil Enginring, HUTECH Univrsity, Ho Chi Minh City, Vitnam Faculty of Civil Enginring, Ho Chi Minh City Univrsity of Tchnology (HCMUT), Vitnam National Univrsity HCMC, Vit nam *Corrsponding author: kt.toan@hutch.du.vn Abstract. In this papr, Improvd Moving Elmnt Mthod (IMEM) is usd to analyz th dynamic rspons of Eulr-Brnoulli bam structurs on th dynamic foundation modl subjctd to th moving load. Th ffcts of charactristic foundation modl paramtrs such as Winklr stiffnss, shar layr basd on th Pastrnak modl, viscolastic dashpot and charactristic paramtr of mass on foundation. Bams ar modld by moving lmnts whil th load is fixd. Basd on th principl of th publicly virtual balancing and th thory of moving lmnt mthod, th motion diffrntial quation of th systm is stablishd and solvd by mans of th numrical intgration basd on th Nwmark algorithm. Th influnc of mass on foundation and th roughnss of th bam surfac on th dynamic rspons of bam ar xamind in dtails. Kywords: Improvd Moving Elmnt Mthod, dynamic foundation modl, mass on foundation, roughnss amplitud, roughnss wavlngth, moving load. 1. Introduction Th bam typ structurs on foundation is on of th most widly usd in many filds of nginring lik civil, industry, traffic infrastructurs, Espcially, th structural lmnts which support th moving load of transportation mans such as th foundation undr moving load of vhicls of transport, railway tc. Most publishd rsarch paprs, as considration of analytical solutions for bam rsting on foundation, th rsarchrs hav mainly mployd th Winklr-Typ Foundation [1]. This is th most classic modl known as th on-paramtr modl assuming th soil blow foundation is rplacd by non-mass springs, linar lastic springs and springs ar considrd indpndnt of ach othr. On of th short comings of th Winklr hypothsis is that assums th foundation to closly spacd indpndnt linar springs which ar not affctd byond loadd rgion, thus th dformation of foundation is just limitd load without taking into account for th affct of adjacnt rgions. Contnt from this work may b usd undr th trms of th Crativ Commons Attribution 3.0 licnc. Any furthr distribution of this work must maintain attribution to th author(s) and th titl of th work, journal citation and DOI. Publishd undr licnc by Ltd 1

3 Consquntly, it crats th intrruption btwn loading and unloading foundation, but in rality th surfac of soil foundation is not indicatd any intrruptions. From that point, ths foundations hav yt rflctd th ral charactristic rspons of soil foundation subjctd to moving load Figur 1. q(x,t) q(x,t) (a) Winklr foundation (b) Practical soil foundation Figur 1. Displacmnt of lastic foundation undr uniform prssur. On of th ways to ovrcom th drawbacks in th Winklr modl is to find a way dscribing th continuous intraction among th springs by adding to th abov surfac of non-mass spring layr such as bnding bams, tnsil strsss, shar layr or in considration of th possibl sliding of soil foundation, ths layrs hav unchangd paramtrs and th charactristics of th continuous intraction of th springs in th Winklr modl, th paramtr is so calld th scond paramtr. Igniting up this ida proposd by Filonnko-Borodich [] dscribd th continuous intraction of springs by introducing a thin lastic tnsil mmbran undr a constant tnsil forc T. Following this proposal, Pastrnak [3] hypothsizd that th top surfac of th springs ar fully connctd to a bam whos bam is only subjctd to sloping dformation with shar modulus G. Th common charactristics of thos foundation modls which ar rgardlss to th affcts of soil foundation mass rst on rspons of th uppr structur. In rcnt yars, Q Do Kin and T Khong Trong [4] usd th xprimntal rsults show that th foundation mass involvd in oscillation has a significant ffct on th dynamic bhavior of th plat. Thn T Pham Dinh t al. [5] also mployd th xprimntal rsults to dtrmin th ffct paramtrs of th foundationamtrs of foundation massd Mr. Hoang Phuong Hoa (016)[5] has also mployd th xprimntal rsults to dfin th aff mass on th kintic bhavior of a fr-stp systm.th rsults also show that th influnc of th charactristic paramtrs on th ffct of th foundation mass F on oscillation has a significant ffct. P Nguyn Trong t al. [6] systmatizd th foundation modls and proposd a nw foundation modl usd in th bhavioral analysis of intraction structur on foundation. Th author proposd a nw foundation modl incorporating th complt paramtrs such as lastic stiffnss and stiffnss of shar layr basd on th Pastrnak-Typ Foundation, th cofficint of viscolastic foundation and in particular, considring th ffct of foundation mass on th bhavior of th bam structur calld a "dynamic foundation modl. Following up th afor-mntiond studis, P NguynTrong t al. [7] analyzd th affct of foundation mass paramtr in th dynamic foundation modl placd on th bam s sparat oscillation. Th rsults show that th foundation mass paramtrs hav a significant ffct on th dynamic rspons of th bam, which incrass th ovrall vibration mass of th bams, thrby rducing th oscillation frquncy of th systm. Rcntly, many modls of structurs rsting on viscolastic and Pastrnak foundation hav bn dvlopd. H Luong Van t al. [8] and P Phung Van t al. [9] analyzd dynamics rspons of composit plats rsting on viscolastic foundation. P PhungVan t al. [10] analyzd dynamics rspons of Mindlin plats on viscolastic foundation subjctd to a moving sprung vhicl. T Nguyn Thoi t al. [11] anylazd th dynamics rspons of composit plats on th Pastrnak foundation subjctd to moving mass. P Lou and F T K Au [1] hav studid th rspons of Eulr-Brnoulli bam undr moving mass vhicls by mploying an Finit Elmnt Mthod (FEM). FEM has bn usd widly to solv many complicatd problms, but ncountrd issus whn th mass movs to th margin of th lmnts and also from on lmnt to anothr whil vctor of moving mass must b updatd at vry tim stp. So as to mak good thos shortcomings. C G Koh t al. [13] has proposd to put a moving coordinat to solv th proposd a moving mass of railway track. This mthod is calld Moving Elmnt Mthod (MEM). In this mthod, th railway is considrd as an infinit Eulr-Brnoulli rsting on bam on Winklr foundation and th train is simplifid by a mass-spring-dashpot systm. T Tran Minh t al. [14] has mployd MEM to study

4 th dynamic rspons of xprss railway undr inconstant spd of moving mass. K K Ang t al. [15] has studid a calculation to mploy MEM to xamin th dynamic rspons of th rail on viscolastic foundation with moving mass. K K Ang and J Dai [16] analyzd th raction of th high-spd railway on foundation which has inconstant stiffnss, th author mployd th Moving Elmnt Mthod to hav analytical solutions for th rspons of th train. K K Ang t al. [17] has usd MEM to rsarch th dynamic rspons of th railway systm. Th railway modl is as a mass spring systm which includs train body, cross sction and whls. Rcntly, T Tran Minh t al. [18] also utilizd th Moving Elmnt Mthod to analyz th dynamics of th xprss railway. In which th railway track is modlld basd on Eulr-Brnoulli bam on th lastic two-paramtr, th impacts of rducing vlocity procss and th roughnss lvls of railway track ar also invstigatd. MEM has a lot of advantags such as th load would nvr approach th margin bcaus th limitd lmnts systm always movs, and th moving load would not hav to mov from this lmnt to anothr, so it avoids updating th mass vctor. This mthods nabl th limitd lmnts with diffrnt lngths and ach intraction distanc can b dividd mor ffctiv. Howvr, th wak point of MEM is that must b r-updatd th th stiffnss matrix and dashpot matrix at vry tim stp. It rsultd in incrasing th volum of calculation, prolonging th tim of analysis and wasting th rsourcs. T Nguyn Van [19] has rcntly analyzd th dynamics of structural bam on Pastrnak foundation utilizd th Improvd Moving Elmnt Mthod (IMEM). Th author rprsntd a nw mthod basd on th MEM, an aim to provid th mthod of solving th main diffrntial quations in a fastr mannr and saving rsourcs. Within th contxt of this papr, th author will us th IMEM has bn proposd to invstigat th two-paramtr viscolasticity undr moving load in considration of th simultanous ffct of charactristic paramtr for mass foundation and th influnc of th roughnss of bam surfac. Th mass matrics, stiffnss matrics and damping matrics for moving lmnts ar illustratd in dtails aftrward. Th obtaind rsults ar hlpful documnts for studying and dsigning th structural bam undr practical moving load.. Thortical basis Th two paramtr viscolastic foundation includs th ffct of mass foundation rfrrd to th dynamics foundation. Th dynamics foundation modl has invstigatd th complt mntiondabov paramtrs such as lastic stiffnss k w, cross sction, dashpots c, foundation mass m. Th dynamic rspons of a finit lngth Eulr-Brnoulli bam with Young s lastic modulus E, momnt of inrtia I and mass pr unit lngth of th rail bam m as shown in Figur. Th continuity in th dynamics foundation modl is spcifid by th paramtr of shar layr k s basd on th cut layr of Pastrnak foundation modl. According to P Nguyn Trong t al. [6], Th quation of motion xprssing th rlation btwn forc and displacmnt at ach position foundation undr th ffct of th load q (x, t) which can b xprssd as follows: q( x,t ) k ww( x,t ) ks c m m d w( x,t ) dw( x,t ) d w( x,t ) (1) dx dt dt Mass on foundation m Elastic stiffnss kw Bam m,e,i q(x,t) stiffnss of shar layr ks Dashpot c stiffnss layr Figur. Bam modl on dynamic foundation. 3

5 Th bam modl on dynamic rspons undr moving load pursuant to P. Nguyn Trong t al. [6] combind with th ovrhanging mass systm proposd by C G Koh t al. [13] papr modl is shown in th following: r Car body Bogi m 1 u 1 k 1 c 1 m Sub ovrhanging systm u V k c Main ovrhanging systm Whl-axl m 3 u 3 k 3 c 3 Mass on foundation m Elastic stiffnss kw y Bam m,e,i Fc Fc Contact forc stiffnss of shar layr ks x Dashpot c stiffnss layr Figur 3. Th Bam rsting on th dynamic foundation modl subjctd to a moving load. Th concntratd mass m, dynamic rspons of mass on oscillating foundation modl can b writtn as follows: In which F F H F H F F F m H () F F F xprimntal paramtrs charactriz th ffct of th mass foundation paramtr; dnsity mass foundation; dpth of foundation; charactristic paramtr affctd by dpth of foundation H F and xprimntal paramtrs F dscrib th continuous intraction of lastic springs Winklr modl. Th Eq. () can b r-writtn as follows: m H (3) Whn applid to a systm of forc F such that th displacmnt of a sction l=1 unit, can b xprssd as follow: F F F l.k k (4) Th moving vhicls hav thr mass: m1 m m3 and dnot on dirction so it has thr numral dgrs of frdom. 4

6 k 11 u 1 =1 k 1 k 13 m 1 m 1 m 1 k 1 k 1 c 1 -k 1 -c 1 k 1 =0 k u =1 k 3 c 1 =0 m m m k 31 k =0 c =0 k c -k k 3 k 33 -c u 3 =1 m 3 m 3 k d1 k 3 =0 m 3 k3=0 kd3 c 3 =0 k d c 3 =0 k 3 c 3 Bam (a) Diagram 1 Bam (b) Diagram Figur 4. Th diagrams dfin th mass matrics, stiffnss, dashpot of vhicl motion. Tabl 1. Dtrmining th stiffnss and dashpot of vhicl. Diagram 1 Diagram Diagram 3 Stiffns Dashpot Stiffns Dashpot Stiffns Dashpot k 11=k 1 c 11=c 1 k 1=-k 1 c 1=-c 1 k 13=0 c 13=0 k 1=-k 1 c 1=-c 1 k = k 1+k c = c 1+c k 3= -k c 3=-c k 31=0 c 31=0 k 3= -k c 3= -c k 33= k + k 3 c 33= c + c 3 k d1=0 c d1=0 k d= 0 c d= 0 k d3= -k 3 c d3= -c 3 Mass matrics can b xprssd in th following: m1 0 0 M vhicl 0 m 0 (5) 0 0 m 3 c1 c1 0 C vhicl c1 c1 c c (6) 0 c c c 3 k1 k1 0 K vhicl k1 k1 k k (7) 0 k k k 3 According to th coordinats in th Figur 3, th gnral quation of th car modl Q Do Kin and H Luong Van [1] can b xprssd mathmatically as follows m u& c ( u& u & ) k ( u u ) m g (8) Bam (c) Diagram 3 m u& c ( u& u &) c ( u& u & ) k ( u u ) k ( u u ) m g (9) m u& k ( u u ) c ( u& u &) m g F (10) c 5

7 in which m 1, m, m 3; c 1, c, c 3; k 1, k, k 3 in turn ar mass, dashpots of th vhicl, vrtical springs and whls; u 1, u & 1, u & 1; u, u &, u & ; u 3, u & 3, u& 3 in turnvrtical displacmnts, vlocity, car body acclration, and whl-axl; g gravitational acclration; F c th contact forc btwn whls and bam, causd by th non-flat of th bam or th roughnss of th bam. Th contact forc Fc (with th roughnss at th contact point btwn th moving load and th bam) is dfind according to C G Koh t al. [13]as follows: F c u& u& k u u F (11) c 3 d 3 3 d 3 t whr: Ft c3y& t k3yt th track forc, producd by th roughnss of th bam; u d dnots th vrtical displacmnt at th contact point of th bam; u 3 dnots th vrtical displacmnt of th whl-axl; y t dnots th magnitud of th track irrgularity at th contact point, according to C G Koh t al. [13], th track irrgularity profil can b writtn in trms of a sinusoidal function as follows: S yt at sin whr a t, t dnots th amplitud and th roughnss wavlngth on bam, rspctivly; S dnots th road sction that th objct is moving In th moving lmnt mthod, C G Koh t al. [13] which uss x-y coordinats. Whr x axis is th bam cours. Th moving r-y coordinats whos origin is attachd to th contact forc as in Figur 5. Thrfor, this coordinats movs along with th vlocity V as a moving load. y x=r+s r t (1) MEM Fix load Fc Moving Bam lmnt x Foundation Figur 5. Th coordinats of Moving Elmnt Mthod (MEM). x r s Th rlationship two axs of coordinats ar dmonstratd as follows: (13) y=y whr: x = fixd axis; r = movabl axis; s = displacmnt ; V(a,t) = vlocity function; t = moving tim; a = acclration. Th connction btwn th drivativ oprators of th coordinats whn th load movs with various vlocitis as follows: 4 4 w( x,t ) w ( r,t ) 4 4 x r w( x,t ) w ( r,t ) x r * * (14) (15) 6

8 * * * * w( x,t ) w ( r,t ) t w ( r,t ) r w ( r,t ) w ( r,t ) V t t t r t t r (16) * * * * a V V w( x,t ) w ( r,t ) w ( r,t ) r w ( r,t ) w ( r,t ) t t r t r r. t whr w(x,t) = transvrs dflction of th bam in th x-y axial coordinats; w * (r,t) = dflction of th bam in r-y coordinats. By applying principl of virtual work and using displacmnt functions N, w can writ M, C, K as gnralizd mass, dashpots and stiffnss matrics of th bam as follows: l 0 (17) T M m m N N dr (18) l C T c N N dr (19) l l l 0 T T T K EI ( N ) N dr k w N Ndr k N N dr (0),rr,rr s,rr l T F m m V N N dr (1) l l T T,r,rr d 0 0 0,r F m m a cv N N r m m V N N dr () l T P F N d r (3) with (.) r and (.) rr in turn ar first drivativ and scond drivativ of r. To lmnts of th bam, th Hrmition intrpolation N is writtn as follows: N 1 r 3r l ( l ) 3 ( l ) c (4) N r l r (l ) r(l ) 3 (l ) 1 N r r l 3 ( l ) (5) (6) 1 ( l ) 3 N 4 r l r ( l ) 3 Basd on finit lmnt mthod and using numral dgr of frdom tchniqu rspctivly to matrics of th gnral coordinats lmnts, th moving quation of th whol bam modl on th foundation is writtn as follows: & 1 (7) Mz & + C- F z + K - F z = P (8) 7

9 whr: M, C, K, P rspctivly ar global mass, damping and stiffnss matrics and th global load vctor; F 1, F dnot thos lmnts which dpnds on tim, F 1 and F ar not forcs but hav th forc unit so thy can b considrd to b Psudo-forc. Th Eq. (8) is th main diffrntial quation of th traditional MEM, in th Eq. (8), w can s th lft sid is comprisd of lmnts which chang ovr tim, thos lmnts ar th Psudo-forc F 1 and F matrics. Thrfor, whn solving th problm w nd to updat th global mass, damping and stiffnss matrics and this prolongs th procssing tim. To fix this limitation of th traditional MEM, w lik to mov th Psudo-forcs from th lft sid of th Eq. (8) to th right sid. This ida is calld Improvd Moving Elmnt Mthod. Aftr th moving, th Eq. (8) is writtn as follows: Mz & + Cz & + Kz = P + F z& F z (9) 1 Solving th diffrntial motion Eq. (9) is put to act upon th hlp of computr which is basd on Nwmark algorithm. This algorithm is a calculation program writtn by Matlab languag and th rliability as wll as th calculation mthod of th program ar compard to th rsults of othr authors which ar availabl in th rfrnc. 3. Survy sampl 3.1. Vrifying th calculation program In this part, th articl xamins som numrical xampls to vrify th corrctnss and th rliability of th Matlab program. Th rsults ar compard to thos of othr authors. Hr is th vrification of th high spd train moving on bam with hanging mass which is usd by C G Koh t al. [13] Figur 3. Th paramtrs of th train, th bam and th foundation ar dmonstratd in Tabl and Tabl 3. Tabl. Vhicl paramtrs. Car Body Bogi Whl-axl m kg m 50 kg m kg k N/m k N/m k N/m c Ns/m c Ns/m c Ns/m Bam Tabl 3. Bam and Foundation paramtrs. Foundation m 60 kg/m k w 1x10 7 N/m E x10 11 N/m c 4900 Ns/m I 3.06x10-5 m 4 L 50m In th first xampl, th bam is displacd whil th train is moving on th bam with constant vlocity, without considration of th scond foundation paramtr affction. (vlocity V=0m/s, roughnss amplitud margin a t=0.5mm and roughnss wavlngth t=0.5m). 8

10 Figur 6. Bam displacmnt at th intraction point: (a) C G Koh t al. [13]and (b) Articl In th nxt vrification, th bam is displacd whn th train movs on th bam with changabl vlocity, without considration of th scond foundation paramtr affction (first vlocity V= 0m/s, thn moving with constant acclration a max=10m/s, aftr sconds it rachs th vlocity V max =0m/s, thn it movs with constant dclration a min= -10m/s, and it stops aftr sconds. Th total analyzing tim is t = 6s, without considration of th bam roughnss). Figur 7. Bam displacmnt at th intraction point: (a) C G Koh t al. [13] and (b) Articl. From ths survyd rsults, compard to thos of othr authors and th rsults of th papr indicats that is wll-matchd with othrs as statd in th rfrncs. It provs th calculation program is rliability. Thnc, w hav th groundwork to continu to analyz th affction of foundation paramtrs, mass modl, th roughnss of th bam surfac mting th dynamic rspons of bam. 3.. Numrical survy rsult In th papr, th ovrhanging mass paramtrs and bam paramtrs ar shown in Tabl and Tabl 3. Thy will b usd to invstigat th papr s problms. Cas 1: Survy influnc of mass foundation on dynamic rspons of bam whn th vhicl is moving with constant vlocity, rgardlss to th affct of th bam roughnss. In th first survy, th papr rsarchs th moving vhicls with vlocity V=0m/s. Th charactristic paramtrs of dynamics modl proposd by T Pham Dinh t al. [] writtn as: k w = N/m, k s= N, c= Ns/m and F=1800kg/m 3. Th charactristic paramtrs β F show th simultanous influnc of vrtical dpth foundation H F and xprimntal paramtrs F, thy ar in turn to invstigat such as β F =0; β F =0.5; β F =1; β F =1.5; β F =; β F =.5 and β F =3. 9

11 Figur 8. Th displacmnt of bam at intraction point. From th rsults as shown Figur 8 which displays th charactristic paramtrs for mass foundation β F has significant influnc on oscillation of bam, with th incras in β F mass which will incras in mass foundation m participating th oscillation that is qual to th jump of participating th ovrall oscillation of bam, which will wakn th bam or in othr way, it will softn th bam. Thus th displacmnt of th bam will also jump up and rach out th absolut valu. Cas : Conducting survy of simultanous ffct of mass foundation and load vlocity of dynamic bhaviour of bam. In th scond survy, th papr rsarchs th moving vhicls on bam with constant vlocity, in turn: V=10m/s; 0m/s; 30m/s; 40m/s; 50m/s; 60m/s; 70m/s; 80m/s, 90m/s; 100m/s; 110m/s; 10m/s; 130m/s; 140m/s; 150m/s; 160m/s; 170m/s; 180m/s; 190m/s; 00m/s. All charactristic paramtrs of dynamic foundation modl is drivd th sam as Cas 1, th charactristic paramtrs alon β F for th affct of mass foundation will tak turn to b conductd survy as β F =0; β F =0.5; β F =1; β F =1.5 and β F =. Figur 9. Th max displacmnt of bam at intraction point. In this problm, th ffct of charactristic paramtrs of foundation modl and dynamic rspons of bam subjctd to moving load as givn th diffrnt valus of vlocity paramtrs to b 10

12 considrd. Th rsults of analysis as shown Figur 9. Th moving vlocity is rcognizd V=10m/s up to V=70m/s. Th largr mass on oscillating foundation is, Th highr displacmnt of bam is, on th contrary, whn vlocity abov V=80m/s up, if mass on oscillating foundation on bam systm is high thn th displacmnt of bam is rducd and proximity to a crtain valu. Th rsults as shown Figur 9 indicat th mass paramtrs on foundation has considrabl influnc on th dynamic charactristics of th systm and from th point, it incrass dynamic rspons of bam which is quivalnt to th incras in charactristics paramtrs affctd by mass on foundation. Simultanously, th rsults obtaind also to indicat that th charactristic paramtrs of moving vhicl as th vlocity of movmnt which has a significant ffct on th dynamic rspons of th bam structur. Cas 3: Conducting survy of simultanous ffct of th mass on foundation and th roughnss amplitud on bam of dynamic bhaviour of bam. In th following survy, th papr survys th moving vhicl on bam with th vlocity V=60m/s, th paramtrs on dynamic foundation modl is drivd from th Cas 1, th spcific paramtrs βf offr th ffct of mass on foundation which will tak turn to b survyd as βf =0; βf =0.5; βf =1; βf =1.5 and βf=. In addition, th roughnss on th bam is rprsntd as a function of tim rgulation on th surfac of bams yt=atsin(s/t) with at,t in trms of amplitud and wavlngth of th roughnss of th bam surfac. In this problm kps th whol roughnss wavlngth on bam t=0.5m, th chang in th roughnss amplitud in turn at=0.5mm; 1.5mm;.0mm;.5mm; 3.0mm; 3.5mm and 4.0mm. Figur 10. Maximum displacmnt of bam kps th whol roughnss wavlngth on bam t =0.5m changing th spcific paramtr on foundation mass β F and th roughnss amplitud. Th ffct of th roughnss amplitud on bam: Basd on th rsults obtaind in Figur 10 whn kping th whol roughnss wavlngth on bam t=0,5m and th charactristic paramtrs of th foundation mass β F only changs in th amplitud of th roughnss. Th rsults show that as incrasing th valu of roughnss amplitud on bam th valu of displacmnt of bam incras. Th biggr valu a t is, th biggr valu of bam displacmnt is. This provs that th displacmnt of bam dpnds vry larg on th amplitud of roughnss on bam, whn th roughnss amplitud inchs up, thn th valu of displacmnt on bam also inchs up at th almost linar rat. Th ffct of th mass charactristic paramtr of foundation β F considring th roughnss on th surfac of bam: Th analyzd rsults as shown Figur 10 indicats that if considring th ffct of roughnss amplitud on bam thn dynamic rspons of bam is spcifid as follows: th roughnss amplitud within th approximatly from a t=0,5 1,5mm whn incrasing th valu of charactristic 11

13 paramtrs β F of foundation mass, th displacmnt valu also ascnts. On th contrary, whn th roughnss amplitud from 1,5mm up abov. As th incras in valu of charactristic paramtrs β F of mass foundation, thn th displacmnt valu also dcrass, th highr valu of β F is, th lowr valu of displacmnt of bam is. But whn th mass has rachd th crtain valu thn th displacmnt incrass insignificantly. Thus, th mass paramtrs of foundation is fairly important, it will incras th dynamic rspons of systm as th bam surfac is flat or th roughnss of amplitud is small. On th contrary, dcrasing th dynamic rspons of systm whn th bam surfac has gratr roughnss of amplitud. Cas 4: Conducting survy of simultanous ffct of th mass on foundation and th roughnss amplitud on bam of dynamic bhaviour of bam. In th survy, th paramtrs of th problm is drivd from th Cas 3, th roughnss alon of th problm still kps th whol roughnss amplitud on bam at=0.5mm, th altrnation of th roughnss wavlngth t=0.5m; 1.0m; 1.5m;.0m;.5m; 3.0m; 3.5m; 4.0m and 4.5m. Figur 11. Th maximum displacmnt of bam as th roughnss amplitud on bam is kpt as a whol by a t=0.5mm, th chang in th charactristic paramtrs of mass on foundation β F and th roughnss wavlngth. Basd on th rsults of Figur 11 with th valu of roughnss wavlngth on bam is big thn th displacmnt of bam is rducing, on th othr hand, whn th wavlngth rachs a crtain valu, th displacmnt diagram tnds to mov sidways to a crtain valu, spcially as βf=0,5 thn th displacmnt valu will b ud= mm; mm; mm; mm; mm; mm; mm and mm corrsponding to th wavlngth valu which in turn t=0.5m; 1.0m; 1.5m;.0m;.5m; 3.0m; 3.5m and 4.0m Howvr, th valu of roughnss wavlngth on bam rachs at a crtain fixd valu, if th valu of charactristic paramtrs of mass on foundation thn th displacmnt valu of bam will incras, th biggr valu βf is, th incrasing of displacmnt valu of bam is, it is spcifid as th roughnss of wavlngth t=1.5m, th valu of displacmnt: ud= mm; mm; mm; mm and mm rspctivly to th charactristic paramtrs of mass on foundation in turn as writtn βf =0; βf =0.5; βf =1.0; βf =1.5 and βf =.0. 1

14 4. Conclusions Th papr has prsntd th gnralizd rsults of dynamic bam motion analysis on moving load considring th concurrnt influnc of th charactristic paramtrs for th ffct of foundation mass and th roughnss of bam surfacs as wll as th vlocity of th moving load. Th motion quation of th structural systm is usd basd on Improvd Moving Elmnt Mthod. Th rsults ar obtaind to display that th mass on oscillating foundation has th influnc on th oscillation of bam. With th incras in th charactristic paramtrs of foundation mass βf will incras th mass on oscillation foundation m, it is quivalnt to th incras in th gnral mass on oscillation foundation of systm, from that point, th systm will b waknd, consquntly th displacmnt amplitud of bam will b also raisd up. On th othr hand, if considring th ffct of th roughnss amplitud on bam thn th dynamic rspons of bam will b gratly ffctd. Spcially th roughnss amplitud incrass from th zro (flat) to at=1.5mm. Th highr paramtr valu βf of th mass on foundation is, th biggr displacmnt valu of bam is. In rvrs, whn th roughnss amplitud is 1.5mm biggr as incrasing th charactristic paramtr valu βf of th mass on foundation th displacmnt valu of bam is dcrasd but whn th mass rachs to a crtain valu, th displacmnt is incrasd insignificantly. Thrfor, th paramtr mass on foundation is xtrmly important, it crats th incras in dynamic rspons of systm whn th surfac of bam is almost smooth (flat) or th roughnss amplitud is small. In rsrv, dynamic rspons of systm is dcrasd whn th bam surfac has a biggr amplitud of roughnss. In addition, th vlocity of moving load also has influnc considratly on dynamic bhaviour of bam, th study rsults obtaind to show that th highr vlocity of motion is, th lowr displacmnt of bam is. Th valu of roughnss wavlngth on bam is rising thn th displacmnt of bam is going down and whn th wavlngth rachs up to a crtain valu, th displacmnt diagram tnds to mov horizontally asymptotically to a crtain valu. Th analytical solution rsults of th papr prsnts th study of dtrmining accuratly th paramtr valus of mass on oscillating foundation which is maningful and propr with th practical application, particularly its application in analytical problm mting th rquirmnts on th dynamic rspons of th structural systm intracting with th foundation modls undr moving loads. Bsids, th unvnnss of th structur surfac and th lmnt motion of vlocity of load which is absolutly ncssary to b considrd and corrct to its bst fatur of th structural bam. 5. Rfrncs [1] Winklr E Di lhr von dr lastizitat und fstigktit (Pragu: Dominicus) [] Flamnco-Borodich 1940 Som Approximat thoris of lastic foundation (Moscow: Uchnyi Zapiski Moskovskogo Gosudarstvnnogo Univrsitta Mkhanica in Russian) pp 3 18 [3] Pastrnak P L 1954 On a nw mthod of analysis of an lastic foundation by mans of two constants (Moscow: Gosudarstvnno lzdatlstvo litraturi po Stroitlstvui Arkhitktur in Russian) [4] Q Do Kin and T Khong Trong 005 Exprimntal studis dtrmin th ffct of mass on foundation with sparat oscillating frquncy of plat on th lastic foundation Construction journal pp 3-35 [5] T Pham Dinh, H Hoang Phuong and P Nguyn Trong 016 Exprimntal studis dfin th paramtrs influncing on dynamic rspons of mass on foundation of fr on-paramtr systm Construction journal pp [6] Nguyn T P, H Hoang Phuong and T Pham Dinh 015 Systmatiz th foundation modls and propos nw foundation modls usd in th analytical problm of rspons of bam intraction with th foundation Construction journal pp

15 [7] P Nguyn Trong, H Hoang Phuong, T Pham Dinh and Q Do Kin 015 Th ffcts of mass paramtrs on dynamic foundation modl of sparat oscillating of bam Construction journal pp [8] H Luong Van, T Nguyn Thoi, G R Liu and P Phung Van 014 A cll-basd smoothd finit lmnt mthod using thr-nod shar-locking fr Mindlin plat lmnt (CS-FEM-MIN3) for dynamic rspons of laminatd composit plats on viscolastic foundation Enginring Analysic with Boundary Elmnt 4 pp 8-19 [9] P Phung Van, T Nguyn Thoi, H Luong Van, C Thai Hoang and H Nguyn Xuan 014 A cllbasd smoothd discrt shar gap mthod (CS-FEM-DSG3) using layrwis dformation thory for dynamic rspons of composit plats rsting on viscolastic foundation Computr Mthods in Applid Mchanics and Enginring 7 pp [10] P Phung Van, H Luong Van, T Nguyn Thoi and H Nguyn Xuan 014 A cll basd smoothd discrt shar gap mthod (CS FEM DSG3) basd on th C0 typ highr ordr shar dformation thory for dynamic rsponss of Mindlin plats on viscolastic foundations subjctd to a moving sprung vhicl. Intrnational Journal for Numrical Mthods in Enginring 98 pp [11] T Nguyn Thoi, H Luong Van, P Phung Van, T Rabczuk and D Tran Trung 013 Dynamic rsponss of composit plats on th Pastrnak foundation subjctd to a moving mass by a cll-basd smoothd discrt shar gap (CS-FEM-DSG3) mthod Intrnational Journal of Composit Matrials 3 pp 19-7 [1] P Lou and F T K Au 013 Finit lmnt formula for intrnal forcs of Brnoulli Eulr bams undr moving vhicls Journal of Sound and Vibration 33 pp [13] C G Koh, J S Y Ong, D K H Chua and J Fng 003 Moving lmnt for train-track dynamics Intrnational Journal for Numrical Mthods in Enginring 56 pp [14] T Tran Minh, K K Ang and H Luong Van 014 Vrtical dynamic rspons of non-uniform motion of high-spd rails Journal of Sound and Vibration ( [15] K K Ang, T Tran Minh and H Luong Van 013 Track vibrations during acclrating and dclrating phass of high-spd rails (Sapporo Japan: Thirtnth East Asia-Pacific Confrnc on Structural Enginring and Construction EASEC 13) [16] K K Ang and J Dai 013 Rspons analysis of high-spd rail systm accounting for abrupt chang of foundation stiffnss Journal of Sound and Vibration 33 pp [17] K K Ang, J Dai, T Tran Minh and H Luong Van 014 Analysis of high-spd rail accounting for jumping whl phnomnon Intrnational Journal of Computational Mthods 11 ( [18] T Tran Minh, K K Ang and H Luong Van 016 Vrtical dynamic rspons of high-spd rails during suddn dclration Intrnational Journal of Computational Mthods [19] T Nguyn Van 016 Analytical solutions for dynamics of inhomognous bam on Pastrnak foundation undr moving load mploying th Improvd Moving Elmnt Mthod (Vit Nam: Mastr thsis Ho Chi Minh City Univrsity) [0] Z Fng and R Cook 1983 Bam lmnts on two-paramtr lastic foundations Journal of Enginring Mchanics 109 pp [1] Q Do Kin and H Luong van 010 Structural dynamics (Vit Nam: Ho Chi Minh City National Univrsity Publishing Company) [] T Pham Dinh, D Nguyn Thanh and P Nguyn Trong 014 Th ffcts of mass on foundation on dynamic rspons of bam undr moving load Construction journal pp