myari deformadi sxeulis meqanikis ganviTarebis etapebi XX ...

III. firfitis kide dayrdnobilia _ kidis Tavisufaldayrdnobas pasuxobs Semdegi pirobebi:ω ≡ 0,2⎡∂ωvΔω+ (1 − v)⎢ cos2⎣ ∂x22∂ ωθ + sin2∂y2⎫2⎪∂ ω ⎤ ⎬θ + sin 2θ⎥ = 0.∂x∂y⎪⎦ ⎭garda sasazRvro pirobebis am ZiriTadi saxeebisa,araiSviaTad gvxvdeba gamoyenebisaTvis gansakuTrebiT saintereso,Sereuli pirobebi, roca, magaliTad sazRvris erTi nawiliCamagrebulia, sxva dayrdnobili, da danarCeni Tavisufali.vinaidan w funqciisa da misi normaluri warmoebulissasazRvro mniSvnelobiT yovelTvis SeiZleba moiZebnos x da y-iTam funqciis kerZo warmoebulebis sasazRvro mniSvnelobebi,amocana erTi firfitis Runvis Sesaxeb brtyeli drekadobisTeoriis pirveli amocanis tolfasia. pirveli amocanissasazRvro pirobebi zustad emTxveva (64) pirobas.Tavisufal sazRvarze (70) pirobas, rogorc es iyoaRniSnuli s.lexnickis (1938) da i. vekuas (1942) naSromebSi, maTisaTanado gardaqmnebiT daiyvaneba kompleqsuri cvladis funqciisTeoriis sasazRvro amocanamde, romelic (65)-is analogiuria.gansxvaveba mdgomareobs mxolod imaSi, rom mudmiva x (65)-is+marcxena nawilSi icvleba sxva mudmivaTi: x = ( 3+v)(1− v), xolomarjvena nawili moicema ict + c1saxis mamravlis sizustiT, sadacc _ nivTieri, c 1-kompleqsuri mudmivaa. Tumca, caladbmuli aresgansaxilvel SemTxvevaSi es mudmivebi SeiZleba miviCnioTYnulad.da bolos kideebis Tavisufali dayrdnobis (71) pirobebiSeiZleba ϕ da ψ funqciebiT Caiweros saxiT (a. kalandia, 1953)(71)⎪⎧⎛Re⎨λ′0ϕ( t)− ⎜⎪⎩ ⎝⎧ dtRe⎨⎩dsdtds⎞⎟⎠2[ tϕ′′( t)+ ψ ′(t)]⎪⎫⎫⎬ = g1(t),⎪⎪⎭ ⎪⎬⎫[ ϕ(t)+ tϕ′( t)+ ψ ( t)] ⎬ = g ( ), ⎪ ⎪ 2t⎭⎭L-ze (72)sadac g 1,g2− L -ze mocemuli funqciebia, λ0= 2(1 + v) /(1 − v).83