Waves in fluids and solids Part 5 docx

... automatically and shows obtained results in corresponding windows of the program interface (a program is made in a Borland C++ Builder medium and provides automatic transfer of main results into Excel ...    3 D   (curve 1 in Fig. 5a) and the Einstein density of states  * , where   is the frequency of the first van Hove singularity (dashed line 3 in Fig. 5...

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... 18 (1 951 ) 316. Mindlin R.D. Vibrations of an infinite elastic plate and its cut-off frequencies, Proc Third US Nat. Congr. Appl. Mech., (1 958 ) 2 25. Mindlin R.D. Waves and vibrations in isotropic, ... surface of the second layer and with open other surfaces strings number 15 and 16 in expressions ( 35) must be replaced with: Waves in Fluids and Solids 86...

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... Chapter 5 Multiple Scattering of Elastic Waves in Granular Media: Theory and Experiments 127 Leonardo Trujillo, Franklin Peniche and Xiaoping Jia Chapter 6 Interface Waves 153 Hefeng Dong and ... Chapter 10 Acoustic Waves in Bubbly Soft Media 257 Bin Liang, Ying Yuan, Xin-ye Zou and Jian-chun Cheng Chapter 11 Inverse Scattering in the Low-Frequency Region by Usin...

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... (Stovas&Ursin, 2007). Acoustic Waves in Layered Media - From Theory to Seismic Applications 25  1 2 2 2 2 2 Im cos sin sin sin sin cos Im sin Im 1 1sin 1 sin sin sin sin cos Im sin sin 1 i D i D ... 0,02 0,04 0,06 0,08 0,10 -3 ,5 0,0 3 ,5 M4 M2 M1 r=0.48 Time [s] -3 ,5 0,0 3 ,5 -3 ,5 0,0 3 ,5 -3 ,5 0,0 3 ,5 M64 M32 M16 M8 -3 ,5 0,0 3 ,5 -3 ,5 0,0 3 ,5 -3...

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... exploited by Mindlin (1 951 a, b, 1 958 , 1960), Mindlin and Medick (1 959 ), Mindlin and Onoe (1 957 ), Onoe (1 955 ), and Tolstoy and Usdin (1 953 ). The latter authors reported highly intricate behavior ... appearing in the right-hand side of (5. 5) are known as the transfer matrices. Taking into account (5. 5), the boundary conditions (5. 2) can be expressed in the followi...

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... (18) 138 Waves in Fluids and Solids Waves in Fluids and Solids 118 (Tarasov, 1 950 ) of the flexure stiffness of single layers (Lifshitz, 1 952 b). However, the crossing of the low-lying optical ... This opens the possibility to engineer a novel and useful method for investigating the complex response 128 Waves in Fluids and Solids Waves in Fluids a...

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... (1990). As the starting point, we take the Laplace transform of 139 Multiple Scattering of Elastic Waves in Granular Media: Theory and Experiments Waves in Fluids and Solids 162 infinite water depth. ... 55 –86 152 Waves in Fluids and Solids Waves in Fluids and Solids 160 22 000 0 .   (32) in the water, and 22 111 0 , p    ...

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... collected in underwater and seismic experiments. Waves in Fluids and Solids 172 separate different modes and obtain higher resolution. By combining both v z and v x dispersion data the final ... and (b). As is seen in this Figure, implantation of water instead of air in PTC results in decreasing the optical contrast and, accordingly, in reducing the band-...

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... Waves in Fluids and Solids 200 vibrating molecules. The standing waves are induced in each globule of the crystal. The pulsating modes arising in the PNC globules are ... kinds of non-elastic scattering in medium, e.g., the Raman scattering, the Brillouin scattering, the Bragg scattering etc. In the case of Raman scattering the oscillatory quanta corresponding ......

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... 3.382E-02 5. 948E-02 — — 4.000E-02 2.073E-02 3.317E-02 2.1 95 2.617 2 .50 0E-02 3.903E-03 6.190E-03 3 .55 2 3 .57 2 2.000E-02 1.422E-03 2. 150 E-03 4 .52 4 4.738 1.000E-02 4.298E- 05 6.367E- 05 5.049 5. 078 ... 1 x E , 1 x E  in the x-direction and 2 y  , 1 y E , 1 y E  in the y-direction are defined similarly. Waves in Fluids and Solids 218 3.2.1 Theore...

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