3. The components of a second-order symmetric tensor tare T12=2 Tm-1 T21=2 T 1 The components of a vector V are V=5 V3=3 Vy-2 Please calculate the following (a) t•V (b) V•t

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3. The components of a second-order symmetric tensor t are
T=3
T21=2
T-1
T12=2
T-1
T2=2
T 1
The components of a vector V are
Vi=5
V=3
Vy=-2
Please calculate the following
(a) t•V
(b) V•t
(c) t:T
(d) V [r•V]
(e) VV
4. Please calculate V•V, VV, V•V for the following velocity field.
Vz=0
Vy=0
Vy=0
(a) Vi=by
(b) V1=bx
(c) V;=by
(d) V1=-by
V2=bx
V-bx
Vy0
Vy=0
Transcribed Image Text:3. The components of a second-order symmetric tensor t are T=3 T21=2 T-1 T12=2 T-1 T2=2 T 1 The components of a vector V are Vi=5 V=3 Vy=-2 Please calculate the following (a) t•V (b) V•t (c) t:T (d) V [r•V] (e) VV 4. Please calculate V•V, VV, V•V for the following velocity field. Vz=0 Vy=0 Vy=0 (a) Vi=by (b) V1=bx (c) V;=by (d) V1=-by V2=bx V-bx Vy0 Vy=0
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