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"xO=U RwmU} w Qo =Q}t l} |Oa@xU |=tv "2 pmW

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Q = � � (d2 � (2r)2) � _u4 (6)

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x@ xDU@=w |]NQ}e Qo =Q}t � Qvi � sQH sDU}U l} sm =L |xrO=at |rm pmW|wQ}v p=ta= uwO@ �5 |xrO=at Fx QDt=Q=B QO CaQU Q}F-=D p}rOx@� CaQU w u=mt

%CU= u}vJ �O=R; C=W=aDQ=� ?w=vDt |HQ=N�u+ c

m� _u+ !2

nu+ sgn( _u) � Fxm

= 0 (12)

%R= Ow@ Oy=wN CQ=@a �|Q=@H= C=W=aDQ=� ?w=vDt |HQ=N |wQ}v p=ta= =@ w�u+ c

m_u+ !2

nu+ sgn( _u) � Fxm

= F � cos(t)m

(13)

|wQ}v F '|HQ=N |wQ}v ?w=vD 'sDU}U |a}@] Tv=mQi !n =q

km u; QO xm

7 pmW QO xOW xO=O u=Wv CQ=Jwri "CU= Ctqa u}}aD `@=D sgn w l} QLD'C}=yv QO "CU= sDU}U Q@ sm =L |]NQ}e |xrO=at uOt; CUO x@ |xwLv Qou=}@xO=iDU= =@ Q=yJ x@DQt =Dwm � nv=Q |OOa VwQ R= xO=iDU= =@ 'u(t) 'sDU}U MU=B

"OwW|t x@U=Lt xOW xO=O |x}rw= \}=QW =@ ode45 QwDUO w ?rDt Q=Ri=sQv R=%OwW|t x@U=Lt Q} R\@=wQ T=U=Q@ x}=B x@ xDi=} p=kDv= |wQ}v pm w |}=Q}t |wQ}vFDamping = c � du(t)

dt+ sgn( _u) � Fx (14)

FTransmitted = c _u+ k u+ Fx (15)

w u=mt x@ xDU@=w |]NQ}e Qo =Q}t � Qvi � sQH sDU}U O}OWD C=W=aDQ= Cr=L QO%OwW|t xDiQo Q_v QO u}vJ l} QLD Tv=mQi 'CaQU

= !n =rkm

(16)

|R=Ux}@W "3MU=B Q@ �� """w |wQv=Qo 'xvRwQ Q]k 'Qvi |DNU 'sQH Q}_v �� sDU}U C=YNWtCQ=@a xOW xDiQo Q_v QO Q}O=kt 'Q_v OQwt |UQQ@ QO "OQ=Po|t Q}F-=D sDU}U |xvt=O

%R= CU=l = 1 cm; k = 1000 N:m(�1); m = 20 Kg;

d = 4 cm; D = 20 cm; � = 0 0493 Pa:s;

u0 = 0 m; _u0 = 0 9 m:s(�1); � = 900 kg:m�3;

"p=}U |HwQN =} |OwQw K]U u} QDmJwm "6 pmW

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(hr=11)

SA2 = �((rp +A2:HA2 � sin(�A2)� rp(HA2 �A2: cos(�A2)))(?11)

%u; QO xmHA1 = (2:A1: sin(�A1)

d+ 1):A1: cos(�A1) nQR@ \wQNt `=iDQ=

�A1 = tan�1(d2 � rpA1u� upA1

) ji= =@ A1 |x} w=RHA2 = (2:A2: sin(�A2)

d+ 1):A2: cos(�A2) nQR@ \wQNt `=iDQ=

�A2 = tan�1(d2 � rpA2u� upA2

) ji= =@ A2 x} w=Ru=} QH w uwDU}B CmQL CyH x@ xHwD =@ 11 |x]@=Q QO SA2 w SA1 u}vJty\}=QW w Ow}k 'xt=O= QO "OvDUy |HwQN =} |OwQw K]U 'xvRwQ R= |Qw@a p=}U

"OwW|t |UQQ@ CaQU w u=mt x@ xDU@=w |]NQ}e Qo =Q}t |RQt

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&Ow@ Oy=wN'|}=Hx@=H |xR=Ov= Q=OktV}=Ri= =@ 3 |xrO=at j@] x=ov; 'OW=@ s > 1 Qo = �?

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= 5 %R= Ow@ Oy=wN CQ=@a ?}DQDx@ !n w |=yQDt=Q=B 'Q}O=kt u}= R= xO=iDU= =@"!n =

p50 = 7 071 rad � s�1 wC=W=aDQ= |=Q@ w = 35 rad � s�1 w F = 100 N |Q=@H= C=W=aDQ= |=Q@Q=Okt " = !n = 50 rad � s�1 w ~ = 0 0123 'F = 50 N O}OWDxDiQo Q_v QO 0 5 w 1 =@ Q@=Q@ [4w3]u}W}B C=ar=]t QO s w n |rmW |=yQDt=Q=BQ@=Q@ sDU}U |v=Uwv |xvt=O xv}W}@ '3 VN@ QO xOW u=}@ O}k j@] xm CU= xOW

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=yCWwv=B1. nonlinear displacement-velocity-dependent damper2. nonlinear displacement-dependent damper3. perturbatien theory4. passive5. semi-active6. active7. magnetorheological8. electrorheological9. barrier Lyapunov function10. quadratic Lyapunov function11. linear matrix inequality12. H2/linear quadratic Gaussian13. active mass damper14. model reference adaptive control15. clipped voltage law16. nonlinear displacement-dependent

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