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( ) ( ) ( ) 3 3 3 1 2 3 3 3 3 3 4 5 6 A � senh� A � cosh� A � sen � dM S � 1 L EI L d� A � cos � A � sen� A � cos� ξ ξ ξ ξ ξ ξ � � + + + 

 = − = 
 − + − 

 � � (9) ( ) ( ) ( ) 1 2 3 4 5 6 B � senh� � B � cosh� � B � sen� � d� T � GJ L GJ L B � cos� � B � sen� � B � cos� � d� + − + � � = = 
 + − + � � (10) Applying the appropriate end conditions for displacements and forces of the beam element in Eqs 5,6 give F = KU (11) or 1,1 1,2 1,3 1,4 1,5 1,6 1 1 2,2 2,3 2,4 2,5 2,6 1 1 3,3 3,4 3,5 3,6 1 1 4,4 4,5 4,6 2 2 5,5 5,6 2 2 6,6 2 2 K K K K K K S H K K K K K M � K K K K T � K K K S H Symmetric K K M � K T � � � � � � � � � � � � � � � � � � � � � � � � � = � �
0.8 0.9 1 Dimensionless beam length ΨH, xa Ψxa H -3 -4 -1 -2 0 2 1 3 4 Third modal shape 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 xaΨ H Dimensionless beam length ΨH, xa -3 -4 -1 -2 0 2 1 3 4 Fourth modal shape Dimensionless beam length H, Ψxa H xaΨ 0 0.40.30.20.1 0.80.70.60.5 10.9 -3 -4 -1 -2 0 2 1 3 4 First modal shape Fig.4.
Table 1.
References [1] H.
Friberg: International Journal of Numerical Methods in Engineering Vol. 19 (1983), p. 479

' (1) whereby b, た, k."
T •lng 1 "Fu u-u0 (MPa) 1/10 free-GB 1/4 1/10 sealed-GB 1/4 Fig. 1 Stress-strain curves for AA1100 at 27°C and g% = 6.0 x 10 -5 s -1.
T 1 Fu •lng .
References [1] B.
Forum Vol. 475-479 (2005) p. 421

Chemical compositions are listed in Table 1.
Fig. 3 The deformation structures of pure iron at a strain rate of (a) 2000 s-1, (b) 6000 s-1, and (c) 8500 s-1 Fig. 4 Deformation twins of pure iron at the strain rate of (a) 2000 s-1 and (b) 6000 s-1 under ambient temperature Fig.5 and Fig.6 shows the typical deformation microstructure of Fe-30Mn-3Si-4Al TWIP steel.
Fig. 5 The deformation structures of the Fe-30Mn-3Si-4Al TWIP steel at the strain rate of (a) 700 s-1, (b) 2500 s-1, and (c) 5100 s-1 Fig. 6 Deformation twins of TWIP steel after deformation of the Fe-30Mn-3Si-4Al TWIP steel at a strain rate of (a) 700 s-1, (b) 2500 s-1, and (c) 5100 s-1 under ambient temperature Discussions Comparison of Dynamic Mechanical Properties Pure iron has a BCC structure while Fe-30Mn-3Si-4Al TWIP steel has a FCC structure.
The following observations were made: (1) For pure iron, yield stress and the max strain increase with increasing strain rate from 650 to 8500 s-1, showing strain rate hardening effect
References [1] R.

In terms of behavior non-Newtonian fluids (Fig. 1) are divided into dilatant (>1) and pseudoplastic (<1) ones [1, 2, 6, 16].
Fig. 1.
Table 1.
References [1] A.S.
Aharony, Multifractal in Physics: Successes, Dangers and Challenges, Physica A. 168 (1990) 479-489

Refer to Table 1
F : {0, 1}k ×{0, 1}∗ → {0, 1}k, a pseudo random function h : {0, 1}∗ → {0, 1}k, one way hash function L(·), OP (·), and PA : polynomial functions K ∈ {0, 1}k : each entity’s secret keys set α, δ; randomly generated numbers LK, OK : masked keys for LOD level verification and option value verification E(·), D(·) : an encryption and decryption function Ui : a user Mi : a mobile device Definitions Def 1.
Decrypt; F−1(Fri (D))) = h(OP11(O112)), Fh(OP11 (O112)) (O112) Decrypt; F−1(Fh(OP11 (O112)) (O112) ) = (O112) == Detailed Process of NPLP 1 and 2; A user Ui authenticate oneself to one’s mobile device Mi.
References [1] M.
Pal, Privacy-Preserving 1-n-p Negotiation Protocol, HICSS ’08 Proceedings of the Proceedings of the 41st Annual Hawaii International Conference on System Sciences, Page 479, 2008

Table 1.
Machining time and surface roughness obtained in WEDM of AISI D2 tool steel Run Ton Toff SV WS Machining time (s) S/N ratio for machining time (dB) Surface roughness (µm) S/N ratio for surface roughness (dB) 1 1 1 1 1 5441.67 -74.714 2.475 -7.872 2 1 2 2 2 4186.33 -72.437 2.316 -7.296 3 1 3 3 3 3213.67 -70.140 2.419 -7.673 4 2 1 2 3 3497.00 -70.874 2.334 -7.363 5 2 2 3 1 2498.00 -67.952 2.355 -7.441 6 2 3 1 2 2843.67 -69.078 2.576 -8.220 7 3 1 3 2 2283.67 -67.173 2.362 -7.467 8 3 2 1 3 3465.00 -70.794 2.323 -7.319 9 3 3 2 1 2607.33 -68.324 2.551 -8.135 Fig 2.
Eng. 400, 1-18
Prod. 198, 472-479
Measurement 118, 1-13

Eng. 1 (2013) 1-8
Eng. 1 (2017) 1-9
Eng. 479 (2019) 1-7
Eng. 1 (2016) 1-9
Eng. 1 (2016) 1-9

RL values indicate that the type of isotherms will be unfavorable (RL>1), linear (RL=1), favorable (01) or irreversible (RL<0) [17].
Mater., 137(1), 464-479 (16 pages)
Mater., 153(1-2), 588-599 (12 pages)
Mater., 153(1), 263-275 (13 pages)
Bioresource Technol., 98(1), 14-21 (8 pages)

Its geometrical parameters are shown in Fig.1.
(No.5070061) References [1] M.A.
Vol. 1, pp.1-9
Technol., Vol. 5 (2001) No.1, pp.1-21 [6] X.P.
Liu: Machining Science and Technology, Vol. 9 (2005) No.4, pp.463-479.

Table 1.
Fig. 1.
In Fig. 4(a) bands at 894-933 cm-1 belong to the O-Si-O in the network of silicate which deviates to the right in Fig. 6 (b and c) at 887 cm-1 and 879 cm-1 respectively.
References [1] M.
Sadami, Study of diopside ceramics for biomaterials, Journal of Materials Science: Materials in Medicine, (1999), volume 10, 475–479