{[ promptMessage ]}

Bookmark it

{[ promptMessage ]}

E0-190-2008_(9)1D_Shear_Propagation(BASIC)

# While ft zv due to a forward propagating wave

This preview shows page 1. Sign up to view the full content.

This is the end of the preview. Sign up to access the rest of the document.

Unformatted text preview: F(t-z/V) due to a forward propagating wave propagating in the positive z direction. Wave propagation from t=0 to t=t1 Putting : , (8) (9) then, The shear stress τ is also expressed by: (10) The coefficient G/V denotes impedance: : Impedance Eq.(10) is expressed by: ∂E(ς ) ∂F(η) τ( z, t ) = ρV { − } ∂ς ∂η (11) (12) [problem-1] Proof that Eq.(7) is the solution of Eq.(6). (proof) (a) (b) (c) (d) Substituting Eq.(b) and Eq.(d) into Eq.(6): (e) (3) Transmission and Reflection Consider the wave propagation in two semi-infinite media as shown in the figure. E11((t+z/V1) E t +z/V1 : Transmission Wave G1 ρ1 G2 ρ2 Medium 1 Medium 2 z E2(tt+z/V22) E ( +z/V ) : Incident Wave F (t - z/V 2 F22(t-z/V2)) : Reflection wave When the wave E2(t+z/V2) propagates upward and reaches at the interface (z=0) between two media, this wave is divided into the transmission wave E1(t+z/V1) and the reflection wave F2(t-z/V2) . The displacement and shear stress in medium 1: (13) ρ1,V1 Medium 1 (14) E1(t+z/V1) u1(z,t) τ1(z,t) where, (15) z Medium 2 ρ2,V2 Similarly, for medium 2: (16) (17) ρ1,V1 where, (18) Medium 1 (19) τ2(z,t) u2(z,t) z E2(t+z/V2) F2(t-z/V2) Medium 2 ρ2,V2 The boundary conditions at the interface(z=0): (20) (21) Medium 1 ρ1,V1 E1(t+z/V1) τ1(z=0,t) u1(z,t) τ2(z=0,t) u2(z,t) z E2(t+z/V2) Medium 2 F2(t-z/V2) ρ2,V2 Substitutin...
View Full Document

{[ snackBarMessage ]}

Ask a homework question - tutors are online