Механика очага землятресения. Спецкурс. Воронина Е.В. - 65 стр.

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63
l
S
—
c
S
— -
t
S
— -
V
V
l
S
t
S
,
iijj
Tn
=τ
,
ij
τ
—
j
n
—
l
S
l
ii
S
WTudS
=
∫
, (14.1)
i
u
—
2
1
2
i
V
d
KudV
dt
=
ρ
∫
. (14.2)
,,
1
2
ijij
V
d
UedV
dt
=τ
∫
. (14.3)
g
t
S :
0
lim
t
S
gW KU
→

=− −

. (14.4)
V
V
t
S .
()
12
,
xxvtx
′
=−
t
S
22
δ× ε
,
()
()()
11 11
0
,0 , 0 , 0
lim
gTxuxuxdx
+δ
δ→
−δ
′
′′′
=+−−
∫

. (14.5) 
                                                                                           63

        Imklv Sl — \g_rgyy ih\_joghklv
S c — ih\_joghklv knhjfbjh\Zgghc lj_-
sbgu St — ih\_joghklv dhgpZ lj_sb-
gu ^\b`msZyky \f_kl_ k gbf \ h[t_f_ V
f_`^m ih\_joghklyfb < h[t_f_ V kj_^Z
mijm]Zy b ih^qbgy_lky aZdhgm =mdZ
        KqblZ_f qlh \g_rgb_ h[t_fgu_
kbeu hlkmlkl\mxl GZijy`_gby gZ ih
\_joghklyo Sl b St aZ^Zxlky \ \b^_
Ti = τi , j n j  ]^_ τi, j — dhfihg_glu l_g
ahjZ gZijy`_gbc n j — ghjfZev d ih
\_joghklb jZaju\Z JZ[hlZ gZijy`_
gbc gZ \g_rg_c ih\_joghklb Sl jZ\gZ                          Jbk D hij_^_e_gbx ^bgZfbq_   

                                                              kdbo iZjZf_ljh\ jZaju\Z
              W = ∫ Ti ui dS ,                  (14.1)
                    Sl

]^_ ui — kdhjhklv kf_s_gby gZ jZaju\_ Baf_g_gb_ dbg_lbq_kdhc wg_j
]bb hij_^_eblky dZd
                                          d 1 2
                                   K =      ∫ ρui dV .                                 (14.2)
                                          dt V 2
     Baf_g_gb_ ihl_gpbZevghc wg_j]bb hij_^_ey_fhc dZd wg_j]by ^_
nhjfbjh\Zgby jZ\gh
                                          d 1
                               U =          ∫ τi, j ei, j dV .                         (14.3)
                                          dt V 2
      Ihlhd wg_j]bb g ijhoh^ysbc q_j_a dhgqbd lj_sbgu hij_^_ey_lky
dZd ij_^_e ihlhdZ wg_j]bb ijhoh^ys_]h q_j_a ih\_joghklv St :
                             g = W − lim St →0  K − U  .                          (14.4)

       LZd dZd ih\_joghklv dhgqbdZ lj_sbgu ^\b`_lky \f_kl_ k lj_sbghc
lh \_ebqbgZ h[t_fZ V y\ey_lky nmgdpb_c \j_f_gb Ke_^h\Zl_evgh baf_
g_gb_ dbg_lbq_kdhc wg_j]bb b wg_j]bb ^_nhjfbjh\Zgby \dexqZ_l \ k_[y
baf_g_gb_ wg_j]bb \gmljb h[t_fZ V b ihlhd wg_j]bb q_j_a ih\_joghklv St .
       JZkkfhljbf ^\b`msmxky kbkl_fm dhhj^bgZl ( x1′ = x − vt , x2 )  Imklv
ih\_joghklv St ij_^klZ\ey_l kh[hc ijyfhm]hevgbd kh klhjhgZfb 2δ × 2ε ,
lh]^Z
                                    ( )
                             +δ
                  g = lim ∫ T x1′ ,0 u ( x1′ , +0 ) − u ( x1′ , −0 ) dx1′ .       (14.5)
                         δ→ 0 −δ

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