Строительная теплофизика / 3

L_ieh\hc [ZeZgk ihf_s_gbc b l_iehaZljZlu gZ hlhie_gb_ a^Zgby

H[sbc l_iehh[f_g gZ ih\_joghklb \ ihf_s_gbb

Dhebq_kl\h l_ieZ dhlhjh_ \hkijbgbfZ_l beb hl^Z_l ijhba\hevgZy ih\_joghklv ι \ j_amevlZl_ emqbklh dhg\_dlb\gh]h l_iehh[f_gZ \ ihf_s_gbb jZ\gZ dhebq_kl\m l_ieZ dhlhjh_ i_j_^Z_lky d ih\_joghklb beb hl\h^blky hl g__ l_iehijh\h^ghklvx

EL + .L + 7W = FRQVW

=^_ EL emqbklZy DL dhg\_dlb\gZy b LL dhg^mdlb\gZy l_iehijh\h^ghklvx khklZ\eyxsb_ l_iehh[f_gZ gZ ih\_joghklyo \ ihf_s_gbb

L_iehijh\h^ghklvx i_j_^Z_lky dhebq_kl\h l_ieZ 7L dhlhjh_ ijb kj_^gbo ih \k_c iehsZ^b )L agZq_gbyo l_fi_jZlmjgh]h ]jZ^b_glZJUDGhdheh ih\_joghklb ∂ WL ∂ Q b

agZq_gbyo dhwnnbpb_glZ l_iehijh\h^ghklb λ L khklZ\ey_l

7L = −λ ∂ WL )L

∂ Q

< klZpbhgZjguo mkeh\byo dh]^Z JUDG ∂ WL \ lhes_ HD hklZ_lkyFRQVW\h \j_f_gb

∂ Q

mjZ\g_gb_ m^h[gh aZibkZlv \ \b^_

7L = .LC τ L − WkjL )L

]^_ .CL dhwnnbpb_gl l_iehhl^Zqb hl \gmlj_gg_c ih\_joghklb HDFτ , ^h \g_rg_c

kj_^u l_fi_jZlmjZ dhlhjhc WkjL H[s__ mjZ\g_gb_ l_ieh\h]h [ZeZgkZ ih ih\_joghklbL\ ihf_s_gbb bf__l \b^

]^_ ?±bgl_gkb\ghklv emqbklh]h ihlhdZ%l f ?wn±wnn_dlb\guc emqbkluc ihlhd h[sbc ihdb^Zxsbc ih\_joghklv ?iZ^±iZ^Zxsbc emqbkluc ihlhd qZklv ?wn gZ ih\_joghklv HD

Mq_l fgh]hdjZlgh]h hljZ`_gby hl ih\_joghklb \ ihf_s_gbb agZqbl_evgh mkeh`gy_l jZkq_l l_ieh\h]h [ZeZgkZ ih\_joghklb b \ lh`_ \j_fy g_ hdZau\Z_l [hevrh]h \ebygby gZ dhg_qgu_ j_amevlZlu < kljhbl_evghc ijZdlbd_ h[uqgh h]jZgbqb\Zxlky mq_lhf lhevdh i_j\h]h hljZ`_gby < wlhf kemqZ_ l_ieh\hc [ZeZgk ih\_joghklb k mq_lhf \ujZ`_gby

;h]hkeh\kdbc KLN Klj

E = ∑ & (L− M \L− M τ −τ M ϕ − M )

]^_ ϕ ih\_joghkl_c M

Hibku\Z_lky h^gbf mjZ\g_gb_f

M

]^_ ϕ L M dhwnnbpb_gl h[emq_gghklb ih\_joghklb gZ ih\_joghklvM Kh ±dhwnnbpb_gl baemq_gby Z[khexlgh q_jgh]h l_eZ& <l f k( kl_i_gv q_jghlu beb hlghkbl_evguc dhwnnbpb_gl baemq_gby ih\_joghklb[_ajZaf_jgZy \_ebqbgZ ( & &

]^_ K±dhwnnbpb_gl baemq_gby ih\_joghklb k_jh]h l_eZ(<

\L M dhwnnbpb_gl mqblu\Zxsbc i_j_oh^ hl q_l\_jlhc kl_i_gb Z[khexlghc L d jZaghklb

W \ K ]^_

α NL dhwnnbpb_gl dhg\_dlb\gh]h l_iehh[f_gZ kj_^gbc ih ih\_joghklb

4L ijhqb_ bklhqgbdb b bklhdb l_ieZ gZ ih\_joghklb

< khhl\_lkl\bb k hkh[_gghklyfb l_iehh[f_gZ \k_ ih\_joghklb \ ihf_s_gbb fh`gh jZa^_eblv gZ ljb oZjZdl_jgu_ ]jmiiu hoeZ`^Zxsb_ gZ]j_\Zxsb_ b g_cljZevgu_

HoeZ`^Zxsbfb ih\_joghklyfb ihf_s_gbc \ abfgbc i_jbh^ ]h^Z [m^ml \gmlj_ggb_ ih\_joghklb gZjm`guo HD < wlhf kemqZ_ \ mjZ\g_gbb τ L aZf_gyxl gZ τ %

l_fi_jZlmjm \gmlj_gg_c ih\_joghklb gZjm`ghc HD DCL gZ ijb\_^_gguc dhwnnbpb_gl l_iehi_j_^Zqb DC+ dhwnnbpb_gl l_iehi_j_^Zqb hl \gmlj_gg_c ih\_joghklb HD d gZjm`ghfm \ha^mom hlg_k_gguc d iehsZ^b )L)L hij_^_ey_lky ih jZaf_jZf \gmlj_gg_c ih\_joghklb HD h[jZs_gghc \ ihf_s_gb_

L_fi_jZlmjZ \g_rg_c kj_^u WkjL ijbf_gy_lky jZ\ghc W+ gZjm`gh]h \ha^moZ

>ey gZ]j_luo ih\_joghkl_c abfhc wlh gZ]j_\Zl_evgu_ ijb[hju beb hlhibl_evgu_ iZg_eb agZq_gb_ hl^_evguo \_ebqbg \ mjZ\g_gbb [m^ml ke_^mxsb_

τ L L_fi_jZlmjZ hlhibl_evgh]h ijb[hjZ τ i.CL dhwnnbpb_gl l_iehhl^Zqb hl hlhibl_evgh]h ijb[hjZ HI d l_iehghkbl_ex.CG I hl l_iehghkbl_ey d ih\_joghklb HIWkjL kj_^gyyWl_iehghkbl_ey \ HI±WLG

>ey g_cljZevguo ih\_joghkl_c±\gmlj_ggbo kl_g b i_j_djulbc \mjZ\g_gbb khklZ\eyxsZy i_j_^Zqb l_ieZ l_iehijh\h^ghklv 7L

Wlb ih\_joghklb \ klZpbhgZjguo mkeh\byo g_ gZ]j_\Zxlky b g_ hoeZ`^Zxlky kh klhjhgu HD

Ih\_joghklb \gmlj_ggbo kl_g fh]ml bf_lv iheh`bl_evguc ljZ^bpbhgguc [ZeZgk ihemqZy \ j_amevlZl_ emqbklh]h l_iehh[f_gZ hij_^_e_ggh_ dhebq_kl\h l_ieZ LZdh_ `_ dhebq_kl\h l_ieZ hgb [m^ml hl^Z\Zlv dh\_dpb_c \ha^mom ihf_s_gby < l_iehh[f_g_ fh`_l mqZkl\h\Zlv l_ieh kheg_qghc jZ^bZpbb ijhgbdZxs_c q_j_a emq_ijhajZqgu_ HD Ijyfu_ kheg_qgu_ emqb gZ]j_\Zxl hl^_evgu_ qZklb \gmlj_ggbo h]jZ`^_gbc >bnnmagZy jZkk_yggZy jZ^bZpby 4ΙΙ j jZkij_^_ey_lky jZ\ghf_jgh < jZkq_l_ l_iehh[f_gZ ^himkdZ_lky ijbgbfZlv qlh \ky ijyfZy 4Ιj b jZkk_yggZy 4ΙΙ j jZ^bZpby g_ihkj_^kl\_ggh g_ihkj_^kl\_ggh ijhgbdZxsb_ \ ihf_s_gb_ jZ\ghf_jgh jZkij_^_eyxlky ih iehsZ^b \k_o \gmlj_ggbo ih\_joghkl_c

< mjZ\g_gbb l_ieh\h]h [ZeZgkZ \k_o ih\_joghkl_c ^hihegbl_evgh_ keZ]Z_fhc 4L jZ\gZ ^he_ ijhgbdZxs_c jZ^bZpbb <_ebqbgm fh`gh hij_^_eblv \ \b^_

4L = 4ΙΙ S )L ∑ )L

]^_ )L kmffZ \k_o ih\_joghkl_c ihf_s_gby

< ihf_s_gbb fh]ml [ulv f [ ih\_joghklb dhlhju_ hfu\Zxlky kljm_c hoeZ`^_ggh]h beb gZ]j_lh]h \ha^moZ ih^Z\Z_fh]h \ ihf_s_gb_

Ih gZijZ\e_gbx ^\b`_gby kljmb baf_gy_lky W< b kdhjhklv 9< \ha^moZ \ kljm_ Z ke_^h\Zl_evgh b mkeh\by l_iehh[f_gZ < h[s_c ihklZgh\db mjZ\g_gby l_ieh\h]h [ZeZgkZ lZdhc ih\_joghklb ^he`gh [ulv ^ [

aZibkZgh \ bgl_]jZevghc nhjf_ mqblu\Zxs_c baf_g_gb_ mkeh\bc l_iehh[f_gZ \ gZijZ\e_gbb ^\b`_gby kljmb LZdZy aZibkv hkeh`gbl j_r_gb_ b ^ey p_e_c bg`_g_jgh]h jZkq_lZ __ `_eZl_evgh mijhklblv >ey wlh]h ih\_joghklv jZa[b\Zxl gZ we_f_glZjgu_ iehsZ^db \ ij_^_eZo dhlhjuo \k_ iZjZf_lju ijbgbfZxl hkj_^g_ggufb >ey dZ`^hc we_f_glZjghc iehsZ^db ih\_joghklb khklZ\eyxl k\h_ mjZ\g_gb_ l_ieh\h]h [ZeZgkZ ih nhjfme_

L_ieh\hc [ZeZgk \ha^moZ \ ihf_s_gbb

<ha^mo ihf_s_gby khijbdZkZykv k gZ]j_lufb ih\_joghklyfb gZ]j_\Z_lky beb hoeZ`^Z_lky Djhf_ lh]h hg ihemqZ_l beb hl^Z_l l_ieh \ ijhp_kk_ \ha^mohh[f_gZ < g_[hevrbo ihf_s_gbyo ih^ \ebygb_f dhg\_dlb\guo lhdh\ b \_glbeypbhgguo kljmc \ha^mo ^hklZlhqgh ohjhrh i_j_f_rb\Z_lky \ ke_^kl\bb q_]h _]h W\ ijb jZkq_l_ l_iehh[f_gZ fh`gh kqblZlv ihklhygghc \h \k_f h[t_f_ ihf_s_gby Hkj_^g_ggZy l_fi_jZlmjZ ih\_joghklb lZd`_ ijbgbfZ_lky ihklhygghc MjZ\g_gb_ l_ieh\h]h [ZeZgkZ \ha^moZ \ ihf_s_gbb bf__l \b^

∑ α DL (τ − τ \ ) )L ± 4< =

]^_ α .L kj_^g__ agZq_gb_ dhwnnbpb_glZ dhg\_dlb\gh]h l_iehh[f_gZ gZ ih\_joghklb 4\ dhebq_kl\h dhg\_dlb\gh]h l_ieZ dhlhjh_ g_ihkj_^kl\_ggh i_j_^Z_lky \ha^mom ihf_s_gby beb aZ[bjZ_lky hl g_]h

< \_ebqbgm 4\ \oh^bl l_ieh \ghkbfh_ ijblhqghc \_glbeypb_c b \ j_amevlZl_ g_hj]Zgbah\Zggh]h ijh\_ljb\Zgby ihf_s_gby Z lZd`_ dhg\_dlb\gh]h l_iehh[f_gZ \u^_ey_lky beb hl[bjZ_lky l_ieh \ dhg\_dlb\guo dZgZeZo gZ]j_\Zl_evguo ijb[hjh\ b ^jm]h]h l_ieh\h]h h[hjm^h\Zgby

>ey kljmb ijblhqgh]h \ha^moZ g_h[oh^bfh kZfhklhyl_evgu_ mjZ\g_gby l_ieh\h]h [ZeZgkZ < gZijZ\e_gbb ^\b`_gby kljmx jZa[b\Zxl gZ we_f_glZjgu_ h[f_gu \ khhl\_lkl\bb k jZa[b\dhc gZ we_f_glZjgu_ iehsZ^db hfu\Z_fhc ih\_joghklb MjZ\g_gb_ l_ieh\h]h [ZeZgkZ ^ey dZ`^h]h we_f_glZjgh]h h[t_fZ jbk bo ]jZgbpu gZ jbkmgd_ h[hagZq_gu imgdlbjhf fh`gh aZibkZlv \ \b^_

/Q− F ρ WQ− + ∆ /Q F ρ W\ − /Q F ρ Wg + α .Q τ Q − Wg ∆ )Q =

]^_ /Q− /Q h[t_fgu_ jZkoh^u \ha^moZ \ kljm_ f_`^m we_f_glZjgufb h[t_fZfb (Q − )− Q b Q − (Q + )

Jbk L_iehh[f_g gZklbeZxs_cky kljmb Z l_ieh\hc [ZeZgk we_f_glZjgh]h h[t_fZ \ha^moZ \ kljm_ [ l_ieh\hc [ZeZgk \ha^moZ ihf_s_gby

< nhjfme_ kρ h[t_fgZy l_ieh_fdhklv \ha^moZ

WQ− b WQ kj_^g__ agZq_gb_ l_fi_jZlmju \ha^moZ \ ij_^_eZo we_f_glZjguo h[t_fh\ kljmb gZ mqZkldZo Q b Q

∆ /Q h[t_fguc jZkoh^ \ha^moZ dhlhjuc ih^f_rb\Z_lky d kljm_ ba ihf_s_gby k W\ \ ij_^_eZo we_f_glZjgh]h h[t_fZ Q

τ Q kj_^gyy l_fi_jZlmjZ ih\_joghklb \ ij_^_eZo we_f_glZjgh]h h[t_fZ Q

α .Q kj_^gbc dhwnnbpb_gl dhg\_dlb\gh]h l_iehh[f_gZ gZ ih\_joghklb \ ij_^_eZo we_f_glZjgh]h h[t_fZ Q

JZkoh^ \ we_f_glZjghf h[t_f_ D kljmb jZ\_g

/. = ∑ ∆ /Q + /

< h[s_f kemqZ_ dh]^Z l_fi_jZlmjZ moh^ys_]h ba ihf_s_gby \ha^moZ W mo ≠ W\

/. F ρ . W5 − ∑ ∆ /Q F ρ \ W\ = (/. − / ) F ρ (W. − W\ )+ / F ρ (W. − W mo )

]^_ /. b W. jZkoh^ \ha^moZ b l_fi_jZlmjZ \ dhgp_ ihke_^g_]h we_f_glZjgh]h h[t_fZ D gZ ]jZgbp_ k \ha^mohf ihf_s_gby ]^_ mkeh\gh aZdZgqb\Z_lky kljmy

/ dhebq_kl\h ijblhqgh]h \ha^moZ ih^Z\Z_fh]h \_glbeypb_c

MjZ\g_gb_ l_ieh\h]h [ZeZgkZ \ha^moZ ihf_s_gby \ wlhf kemqZ_ bf__l \b^

∑ α DL (τ L − τ \ ) )L + /. F ρ (W. − W\ )+ / F ρ (W. − W mo )± 4< =

=

< kmffm i_j\h]h keZ]Z_fh]h \oh^yl \k_ khklZ\eyxsb_ dhg\_dlb\gh]h l_iehh[f_gZ djhf_ ih\_joghklb hfu\Z_fhc kljm_c <lhjh_ b lj_lv_ keZ]Z_fu_ mqblu\Zxl l_ieh ijblhqghc gZklbeZxs_c kljmb >ey k\h[h^ghc kljmb \ ihf_s_gbb ihemq_gu h[h[s_ggu_ aZ\bkbfhklb k ihfhsvx dhlhjuo fh`gh hij_^_eblv \k_ __ iZjZf_lju g_h[oh^bfu_ ^ey jZkq_lZ h[s_]h l_iehh[f_gZ \ ihf_s_gbb

Ihwlhfm ijb k\h[h^guo kljmyo h[uqgh g_ gm`gh ijb[_]Zlv d jZa[b\d_ gZ we_f_glZjgu_ h[t_fu

IhegZy kbkl_fZ mjZ\g_gbc h[s_]h l_iehh[f_gZ \ ihf_s_gbb

< h[s_f l_iehh[f_g_ \ ihf_s_gbb mqZkl\mxl \k_ _]h ih\_joghklb \ha^mrgu_ kljmb b \ha^mo ihf_s_gby

JZkkfZljb\Zy ihegmx nbabdh fZl_fZlbq_kdmx ihklZgh\dm aZ^Zqb h l_iehh[f_g_ \ ihf_s_gbb ijbgbfZxl \ dZq_kl\_ hkgh\ghc kbkl_fm mjZ\g_gbc khklhysmx ba mjZ\g_gbc l_ieh\h]h [ZeZgkZ ih\_joghklb we_f_glZjguo ih\_joghkl_c b h[t_fh\ gZklbeZxsboky kljmc h[t_fh\ k\h[h^guo kljmc b mjZ\g_gb_ l_ieh\h]h [ZeZgkZ \ha^moZ Ijbf_qZgb_ y __ g_ ijb\h`m ihkdhevdm hgZ hq_gv ]jhfha^dZy b keh`gZ d \hkijbylbx

Kbkl_fZ mjZ\g_gbc ;h]hkeh\kdbc KLN khklhbl ba [hevrh]h qbkeZ mjZ\g_gbc qlh aZljm^gy_l __ j_r_gb_ M^h[gh j_rZlv ihegmx kbkl_fm mjZ\g_gbc l_iehh[f_gZ \ ihf_s_gbb gZ we_dljbq_kdhc ZgZeh]h\hc fh^_eb ;h]hkeh\kdbc KLN ξ Djhf_ lh]h wlh j_r_gb_ fh`_l [ulv mki_rgh ijh\_^_gh k ihfhsvx dhfivxl_jZ

Kbkl_fZ ba ^\mo mjZ\g_gbc h[s_]h l_iehh[f_gZ \ ihf_s_gbb

>ey oZjZdl_jbklbdb h[s_c l_fi_jZlmjghc h[klZgh\db \ ihf_s_gbb h[uqgh ^hklZlhqgh bf_lv kj_^g__ agZq_gb_ l_fi_jZlmju lj_o oZjZdl_jguo ]jmii ih\_joghkl_cgZ]j_\Zxsbo hoeZ`^Zxsbo b g_cljZevguo b \ha^moZ jbk

< wlhf kemqZ_ ^ey \k_o ih\_joghkl_c hlghkysboky d h^ghc dZl_]hjbb fh`gh khklZ\blv h^gh mjZ\g_gb_ l_ieh\h]h [ZeZgkZ

< kbkl_fm mjZ\g_gbc l_iehh[f_gZ \ ihf_s_gbb \hc^ml mjZ\g_gb_ l_ieh\h]h [ZeZgkZ ^ey \k_o h[h]j_\Zxsbo ih\_joghkl_c mjZ\g_gb_ ^ey \k_o hoeZ`^Zxsbo ih\_joghkl_c gZjm`guo HD mjZ\g_gb_ ^ey \k_o ih\_joghkl_c \gmlj_ggbo HD b mjZ\g_gb_ ^ey \ha^moZ

Jbk Ko_fZ l_iehh[f_gZ \ ihf_s_gbb Z ljb oZjZdl_jgu_ dZl_]hjbb ih\_joghkl_c [ h^gh mjZ\g_gb_ k mq_lhf dhwnnbpb_glZ iheghc h[emq_gghklb \ h^gh mjZ\g_gb_ k mq_lhf kj_^g_cWmkeh\ghc ih\_joghklb

H[uqgh ijb jZkq_l_ l_iehh[f_gZ \ ihf_s_gbb aZ^ZguW\gmlj_ggbo ih\_joghkl_c gZjm`guo HD 2\ b \ha^moZ W\ < wlhf kemqZ_ g_h[oh^bfh j_rblv kbkl_fm ba ^\mo mjZ\g_gbc ^ey ihemq_gbyWh[h]j_\Zxsbo ih\_joghkl_c 2i ijb ba\_klghc __ iehsZ^b )i b jZkiheh`_gby \ ihf_s_gbb b kj_^g_c 2\i ih\_joghklb \gmlj_gg_c HD Fh`_l [ulv aZ^ZgZ 2i gZ]j_\Zxs_c ih\_joghklb lh]^Z h^gbf ba g_ba\_klguo [m^_l __ iehsZ^v )i

NhjfZ aZibkb mjZ\g_gbc l_ieh\h]h [ZeZgkZ h[h]j_\Zxsbo b \gmlj_ggbo ih\_joghkl_c \ kbkl_f_ ba ^\mo mjZ\g_gbc khklhbl \ hij_^_e_gbb hkj_^g_gghc ih \k_f ih\_joghklyf h^ghc dZl_]hjbb qbke_gguo agZq_gbc dhwnnbpb_glh\ b ^jm]bo iZjZf_ljh\ ijhp_kkZ l_iehh[f_gZ

G_h[oh^bfh hij_^_eblv dhwnnbpb_glu h[emq_gghklb kh \k_o ih\_joghkl_c h^ghc dZl_]hjbb gZ \k_ ih\_joghklb ^jm]hc dZl_]hjbb gZoh^blv hkj_^g_ggu_ agZq_gby dhwnnbpb_glh\ ijb\_^_ggh]h baemq_gby dhg\_dlb\gh]h l_iehh[f_gZ l_iehi_j_^Zqb b l ^

>ey hij_^_e_gby dhwnnbpb_glh\ h[emq_gghklb m^h[gh \hkihevah\Zlvky k\hckl\Zfb aZfdgmlhklb b \aZbfghklb emqbkluo ihlhdh\

Hkj_^g_gb_ dhwnnbpb_glZ dhg\_dlb\gh]h l_iehh[f_gZ f [ aZljm^g_gh l_f qlh ih\_joghklb h^ghc dZl_]hjbb jZaebqgh hjb_glbjh\Zgu \ ijhkljZgkl\_ b bf_xl jZaebqgu_ ûW gZijbf_j ih wlbf ijbqbgZf ^ey iheZ b ihlhedZ dhwnnbpb_glu dhg\_dlb\gh]h l_iehh[f_gZ .d fh]ml hlebqZlvky \ jZaZ b [he__ LZdb_ ljm^ghklb h[uqgh f [ ij_h^he_gu f_lh^hf ihke_^h\Zl_evgh]h ijb[eb`_gby

J_r_gb_ kbkl_fu ba ^\mo mjZ\g_gbc lZd `_ dZd b iheghc kbkl_fu g_m^h[gh \ bg`_g_jghc ijZdlbd_ ihwlhfm `_eZl_evgh ^Zevg_cr__ mijhs_gb_ jZkq_lghc ko_fu

H^gh mjZ\g_gb_ h[s_]h l_iehh[f_gZ \ ihf_s_gbb

Ijb jZkq_l_ l_iehh[f_gZ \ ihf_s_gbb h[uqgh aZ^Zxlky agZq_gbyfb 2\ gZ \gmlj_ggbo ih\_joghklyo gZjm`guo HD bW\ \ ihf_s_gbb AgZq_gby wlboW^Zgu \ KGbI

L_fi_jZlmjm \gmlj_ggbo HD ijb[ebabl_evgh fh`gh kqblZlv jZ\ghcW\ \ ihf_s_gbb Ihwlhfm \ lZdhc ihklZgh\d_ bkdhfhc \_ebqbghc \ jZkq_l_ y\ey_lky lhevdhWbeb iehsZ^v h[h]j_\Zxs_c ih\_joghklb hlhibl_evguo ijb[hjh\ HI

G_h[oh^bfhklv hij_^_e_gby lhevdh h^ghc g_ba\_klghc ^Z_l \hafh`ghklv aZf_gblv kbkl_fm mjZ\g_gbc h^gbf mjZ\g_gb_f l_iehh[f_gZ \ ihf_s_gbb

Emqbkluc l_iehh[f_g \ ihf_s_gbb fh`gh ij_^klZ\blv dZd l_iehh[f_g baemq_gb_f f_`^m iZg_evx b gZjm`ghc ih\_joghklvx jbk [ ijb gZebqbb \gmlj_ggbo h]jZ`^Zxsbo ih\_joghkl_c 2\i

IZg_ev \ ihf_s_gbb jbk [ i_j_^Z_l hij_^_e_ggh_ dhebq_kl\h l_ieZ ih\_joghklyf gZjm`guo HD Wlh l_ieh i_j_^Z_lky ijyfuf û4i gh b dhk\_gguf û4 i ghhljZ`_gb_f hl \gmlj_gg_c ih\_joghklb baemq_gb_f

Dhebq_kl\h l_ieZ û4i gh f [ ih^kqblZgh ih nhjfme_

= & ε ij − E − (τ −τ ) ϕ − )

]^_ iehsZ^dZ±iehsZ^dZ

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K ihfhsvx dhwnnbpb_glZ ijyfhc h[emq_gghklb k iZg_eb I gZ gZjm`gh_ h]jZ`^_gb_ GH 3i gh k mq_lhf ijbgyluo ijb jZkkfhlj_gbb aZ^Zqb l_iehh[f_gZ \ ihf_s_gbb ^hims_gbc b h[hagZq_gbc mjZ\g_gb_ ^ey hij_^_e_gby ihegh]h dhebq_kl\Z l_iehlu 4ie i_j_^Z\Z_fh_ iZg_evx baemq_gb_f g_ihkj_^kl\_ggh b dhk\_ggh ih\_joghklb gZjm`guo h]jZ`^_gbc fh`gh aZibkZlv \ \b^_

4ie = ∆ 4i−gh + ∆ 4i′−gh

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N±dhwnnbpb_gl iheghc h[emq_gghklb k iZg_eb gZ ih\_joghklv gZjm`ghc HD jZ\guc kmff_ dhwnnbpb_glh\ ijyfhc b dhk\_gghc h[emq_gghklb

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Ijb wlhf 3 3 ihwlhfm \ nhjfme_ bg^_dku hims_gu

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b dhg\_dlb\ghc khklZ\eyxsbo

4i = [k N E (τ i −τ gh )+ α e (τ i −τ \ ) )i ]= [α ′e (τ i − τ gh )+ α d (τ i − W\ )] )i

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Jbk Dhwnnbpb_gl iheghc h[emq_gghklb ^ey ^\mo Z b [ \ZjbZglh\ jZkiheh`_gby \ ihlhd_

BBBBB^Zggu_ jZkq_lZ gZ we_dljhfh^_eb

jZkq_l ih nhjfme_