Mkpọtụ kwụ ọtọ: ike nke ihe ndị dị na sistemụ ahụ dabere na iwu hooke, ike mmiri mmiri nke a na-emepụta n'oge mmegharị ahụ kwekọrọ na nha anya mbụ nke ọsọ nkịtị (ihe sitere na oge nke nhazi izugbe).
echiche
Sistemụ kwụ ọtọ na-abụkarị ihe nlereanya nkịtị nke mkpọtụ nke sistemụ n'ezie. Sistemụ mkpọtụ kwụ ọtọ na-etinye ụkpụrụ superposition, ya bụ, ọ bụrụ na nzaghachi nke sistemụ ahụ bụ y1 n'okpuru ọrụ nke ntinye x1, na y2 n'okpuru ọrụ nke ntinye x2, mgbe ahụ nzaghachi nke sistemụ n'okpuru ọrụ nke ntinye x1 na x2 bụ y1+y2.
Dabere na ụkpụrụ superposition, enwere ike ịgbasa ntinye aka n'ụzọ na-enweghị usoro n'ime mkpokọta nke usoro mkpali enweghị ngwụcha, wee nweta nzaghachi zuru oke nke sistemụ ahụ. Enwere ike ịgbasa mkpokọta nke akụkụ harmonic nke mkpali oge ụfọdụ n'ime usoro ihe harmonic site na Fourier transform, enwere ike inyocha mmetụta nke akụkụ harmonic ọ bụla na sistemụ ahụ iche. Ya mere, enwere ike ịkọwa njirimara nzaghachi nke sistemụ linear nwere paramita na-adịgide adịgide site na nzaghachi mkpali ma ọ bụ nzaghachi ugboro ugboro.
Nzaghachi mkpali na-ezo aka na nzaghachi nke sistemụ ahụ na mkpali nkeji, nke na-akọwa njirimara nzaghachi nke sistemụ ahụ na mpaghara oge. Nzaghachi ugboro ugboro na-ezo aka na njirimara nzaghachi nke sistemụ ahụ na ntinye harmonic nke nkeji. Mgbanwe Fourier na-ekpebi mmekorita dị n'etiti ha abụọ.
nhazi ọkwa
Enwere ike kewaa mkpọtụ ahịrị n'ime mkpọtụ ahịrị nke sistemụ nnwere onwe otu-ogo na mkpọtụ ahịrị nke sistemụ nnwere onwe dị iche iche.
(1) ịma jijiji nke otu ogo nke nnwere onwe bụ ịma jijiji nke nwere ike ikpebi ọnọdụ ya site na nhazi zuru oke. Ọ bụ ịma jijiji kachasị mfe nke enwere ike isi nweta ọtụtụ echiche na njirimara nke ịma jijiji. Ọ gụnyere vibration harmonic dị mfe, vibration efu, mmụgharị attenuation na ịmanye vibration.
Mkpọtụ dị mfe: mmegharị nke ihe dị nso n'ọnọdụ nguzozi ya dịka iwu sinusoidal si dị n'okpuru ọrụ nke ike mgbake nke kwekọrọ na mbugharị ya.
Mkpọtụ dara ada: mkpọtụ nke oke ya na-ebelata mgbe niile site na ọnụnọ nke esemokwu na nguzogide dielectric ma ọ bụ oriri ike ndị ọzọ.
Mmanye ịma jijiji: ịma jijiji nke sistemụ n'okpuru mkpali mgbe niile.
(2) ịma jijiji ahịrị nke sistemụ nnwere onwe dị iche iche bụ ịma jijiji nke sistemụ ahịrị nwere ogo n≥2 nke nnwere onwe. Sistemụ nke ogo n nwere ugboro n eke na ụdị n bụ isi. Nhazi ịma jijiji ọ bụla nke sistemụ ahụ nwere ike ịnọchite anya dị ka njikọta ahịrị nke ụdị isi. Ya mere, a na-eji usoro superposition bụ isi eme ihe nke ukwuu na nyocha nzaghachi ike nke sistemụ ọtụtụ dof. N'ụzọ dị otu a, nha na nyocha nke njirimara ịma jijiji eke nke sistemụ ahụ na-aghọ nzọụkwụ nkịtị na nhazi ike nke sistemụ ahụ. Enwere ike ịkọwa njirimara ike nke sistemụ ọtụtụ dof site na njirimara ugboro ugboro. Ebe ọ bụ na enwere ọrụ njirimara ugboro ugboro n'etiti ntinye na mmepụta ọ bụla, a na-ewu matrix njirimara ugboro ugboro. Enwere mmekọrịta doro anya n'etiti njirimara ugboro ugboro na ụdị isi. Usoro njirimara oke-ugboro nke sistemụ nnwere onwe dị iche na nke sistemụ nnwere onwe otu.
Mkpọtụ kwụ ọtọ nke otu ogo nke sistemụ nnwere onwe
Mkpọtụ kwụ ọtọ nke enwere ike iji nhazi zuru oke chọpụta ọnọdụ nke sistemụ. Ọ bụ mkpọtụ kachasị mfe na nke kachasị mkpa nke enwere ike isi nweta ọtụtụ echiche na njirimara nke ịma jijiji. Ọ gụnyere mkpọtụ harmonic dị mfe, mkpọtụ damped na ịmanye.
Mkpọtụ Harmonic
N'okpuru ọrụ nke iweghachi ike dịka mgbanwe ahụ si dị, ihe ahụ na-agbanwe n'ụzọ sinusoidal dị nso na ọnọdụ nhazi ya (FIG. 1). X na-anọchite anya mgbanwe ahụ na t na-anọchite anya oge ahụ. Ngosipụta mgbakọ na mwepụ nke ịma jijiji a bụ:
(1)Ebe A bụ uru kachasị nke mbugharị x, nke a na-akpọ oke, ma na-anọchite anya ike nke mkpọtụ ahụ; Omega n bụ oke mmụba nke mkpọtụ ahụ kwa sekọnd, nke a na-akpọ ugboro angular, ma ọ bụ ugboro gburugburu; Nke a bụ nke mbụ. N'ihe gbasara f= n/2, a na-akpọ ọnụọgụ nke oscillations kwa sekọnd ugboro; Mgbanwe nke a, T=1/f, bụ oge ọ na-ewe iji mee ka otu okirikiri gbagharịa, nke a na-akpọkwa nke ahụ period. Oke A, ugboro f (ma ọ bụ ugboro angular n), nke mbụ, nke a maara dị ka ihe atọ dị mfe nke harmonic vibration.
FIG. 1 usoro mkpọtụ ụda olu dị mfe
Dịka egosiri na FIG. 2, a na-emepụta oscillator harmonic dị mfe site na oke m nke mmiri kwụ ọtọ jikọtara. Mgbe a na-agbakọ mgbanwe mkpọtụ site na ọnọdụ nhazi, nha anya mkpọtụ bụ:
Ebee ka isi ike nke isi mmiri dị. Ngwọta izugbe maka nha anya dị n'elu bụ (1).A enwere ike ịchọpụta ya site na ọnọdụ mbụ x0 na ọsọ mbụ na t=0:
Mana a na-ekpebi omega n naanị site na njirimara nke sistemụ ahụ n'onwe ya m na k, n'adabereghị na ọnọdụ mbụ ndị ọzọ, yabụ a makwaara omega n dị ka ugboro eke.
FIG. 2 otu ọkwa nke sistemụ nnwere onwe
Maka oscillator harmonic dị mfe, mkpokọta ike kinetic ya na ike nwere ike ịdịgide, ya bụ, a na-echekwa ike mekaniki zuru oke nke sistemụ ahụ. N'ime usoro ịma jijiji, ike kinetic na ike nwere ike na-agbanwe mgbe niile ka ọ bụrụ ibe ha.
Mkpọtụ ahụ na-eme ka mmiri damping
Mkpọtụ nke esemokwu na nguzogide dielectric ma ọ bụ oriri ike ndị ọzọ na-ebelata oke ya mgbe niile. Maka obere mkpọtụ, ọsọ ahụ anaghị adịkarị oke ibu, nguzogide etiti ahụ na-adaba na ọsọ ahụ na ike mbụ, nke enwere ike ide dị ka c bụ ihe na-ebelata ụda. Ya mere, enwere ike ide nha anya nke otu ogo nnwere onwe yana damping linear dị ka:
(2)Ebe a na-akpọ m =c/2m paramita damping, na. Ngwọta izugbe nke usoro (2) enwere ike ide:
(3)Enwere ike kewaa mmekọrịta ọnụọgụgụ dị n'etiti omega n na PI n'ime ikpe atọ ndị a:
N > (n'ihe gbasara obere mmiri ozuzo) ihe ndị na-eme ka attenuation pụta, nha anya mmiri ahụ bụ:
Oke ya na-ebelata ka oge na-aga dịka iwu exponential egosiri na nha anya si dị, dịka egosiri na ahịrị ntụpọ dị na FIG. 3. N'ikwu ya n'ụzọ doro anya, mkpọtụ a na-adịkarị, mana enwere ike ịkọwa ugboro ole elu ya dị ka:
A na-akpọ ya ọnụego mbelata olu, ebee ka oge ịma jijiji dị. A na-akpọ logarithm eke nke ọnụego mbelata olu logarithm mbelata (ọnụọgụ olu). N'ụzọ doro anya, =, n'ọnọdụ a, hà nhata 2/1. Ozugbo site na delta nnwale nnwale, enwere ike ịgbakọ ya site na iji usoro dị n'elu c.
N'oge a, enwere ike ide ihe ngwọta nke nha anya (2):
Tinyere ntụziaka nke ọsọ mbụ, enwere ike kewaa ya n'ime ikpe atọ na-anaghị eme mkpọtụ dịka egosiri na FIG. 4.
N < (n'ihe gbasara nnukwu mmiri ozuzo), a na-egosi ihe ngwọta maka nha nhata (2) na nha nhata (3). N'oge a, sistemụ ahụ anaghịzi ama jijiji.
Mmanye ịma jijiji
Ịma jijiji nke sistemụ n'okpuru mkpali na-adịgide adịgide. Nyocha ịma jijiji na-enyochakarị mmeghachi omume nke sistemụ ahụ na mkpali. Mkpali oge bụ ihe mkpali nkịtị. Ebe ọ bụ na enwere ike ịgbasa mkpali oge niile n'ime mkpokọta nke mkpali harmonic dị iche iche, dịka ụkpụrụ superposition si dị, naanị nzaghachi nke sistemụ ahụ na mkpali harmonic ọ bụla dị mkpa. N'okpuru ọrụ nke mkpali harmonic, enwere ike ide nha nhata nke mmegharị nke otu ogo nke sistemụ nnwere onwe damped:
Azịza ya bụ mkpokọta akụkụ abụọ. Otu akụkụ bụ mmeghachi omume nke mkpọtụ mmiri mmiri, nke na-ere ngwa ngwa ka oge na-aga. Enwere ike ide mmeghachi omume nke akụkụ ọzọ nke mkpọtụ a manyere amanye:
FIG. 3 usoro mkpọtụ mmiri mmiri
FIG. 4 gbagọrọ agbagọ nke ọnọdụ mbụ atọ nwere oke mbelata dị mkpa
Pịnye na
H /F0= h(), bụ oke nke oke nzaghachi kwụsiri ike na oke mkpali, nke na-akọwa njirimara ugboro ole a na-akpọ amplitude, ma ọ bụ ọrụ uru; Bits maka nzaghachi ọnọdụ kwụsiri ike na mkpali nke usoro, njirimara nke njirimara ugboro ole a na-akpọ amplitude. E gosipụtara mmekọrịta dị n'etiti ha na ugboro ole a na-akpọ mkpisi na FIG. 5 na FIG. 6.
Dịka a pụrụ ịhụ site na usoro ịgbasa ugboro ugboro (Foto 5), n'ihe gbasara obere ịgbasa, usoro ịgbasa ugboro ugboro nwere otu elu. Ka obere ịgbasa ahụ dị obere, otú ahụ ka elu ahụ dị elu; A na-akpọ ugboro ole kwekọrọ na elu ahụ ugboro ugboro resonant nke sistemụ ahụ. N'ihe gbasara obere ịgbasa, ugboro ugboro resonance adịghị iche na ugboro nkịtị. Mgbe ugboro mkpali dị nso na ugboro okike, oke ahụ na-abawanye nke ukwuu. A na-akpọ ihe a resonance. Na resonance, a na-eme ka uru nke sistemụ ahụ dịkwuo elu, ya bụ, ịma jijiji a manyere bụ nke kachasị ike. Ya mere, n'ozuzu, na-agba mbọ mgbe niile izere resonance, ọ gwụla ma ụfọdụ ngwa na akụrụngwa iji resonance nweta nnukwu mkpọtụ.
FIG. 5 usoro ugboro olu
Enwere ike ịhụ ya site na usoro ugboro ugboro nke usoro (foto 6), n'agbanyeghị nha nke damping, na bits nke ọdịiche nke usoro omega efu = PI / 2, enwere ike iji njirimara a mee ihe nke ọma n'ịtụle resonance.
Na mgbakwunye na mkpali na-adịgide adịgide, sistemụ na-ezute mkpali na-adịghị akwụsi ike mgbe ụfọdụ. Enwere ike kewaa ya n'ụdị abụọ: otu bụ mmetụta mberede. Nke abụọ bụ mmetụta na-adịgide adịgide nke enweghị ike ime ihe. N'okpuru mkpali na-adịghị akwụsi ike, nzaghachi nke sistemụ ahụ adịghịkwa akwụsi ike.
Ngwaọrụ dị ike maka inyocha mkpọtụ na-adịghị akwụsi ike bụ usoro nzaghachi mkpali. Ọ na-akọwa njirimara ike nke sistemụ ahụ yana nzaghachi nwa oge nke ntinye mkpali nkeji nke sistemụ ahụ. Enwere ike igosipụta mkpali nkeji dị ka ọrụ delta. Na injinia, a na-akọwakarị ọrụ delta dị ka:
Ebe 0- na-anọchite anya isi ihe dị na axis t nke na-erute efu site n'aka ekpe; 0 gbakwunyere bụ isi ihe na-aga 0 site n'aka nri.
FIG. Usoro ugboro ugboro nke 6
FIG. 7 Enwere ike ịtụle ntinye ọ bụla dị ka mkpokọta nke usoro ihe mkpali
Sistemụ ahụ kwekọrọ na nzaghachi h(t) nke mkpali nkeji na t=0 mepụtara, nke a na-akpọ ọrụ nzaghachi mkpali. Anyị na-eche na sistemụ ahụ na-anọpụ iche tupu mkpali ahụ, h(t)=0 maka t<0. Anyị maara ọrụ nzaghachi mkpali nke sistemụ ahụ, anyị nwere ike ịchọta nzaghachi nke sistemụ ahụ na ntinye ọ bụla x(t). N'oge a, ị nwere ike iche na x(t) dị ka mkpokọta nke usoro ihe mkpali (FIG. 7). Azịza nke sistemụ ahụ bụ:
Dabere na ụkpụrụ superposition, nzaghachi zuru oke nke sistemụ kwekọrọ na x(t) bụ:
A na-akpọ integral a integral convolution ma ọ bụ integral superposition.
Mkpọtụ kwụ ọtọ nke sistemụ nnwere onwe dị iche iche
Ịma jijiji nke sistemụ kwụ ọtọ nwere n≥2 ogo nnwere onwe.
Foto nke 8 na-egosi sistemụ resonant abụọ dị mfe nke ejiri spring jikọọ. Ebe ọ bụ na ọ bụ sistemụ nnwere onwe nke ogo abụọ, achọrọ nhazi abụọ nọọrọ onwe ha iji chọpụta ọnọdụ ya. E nwere ugboro abụọ eke na sistemụ a:
Ugboro ọ bụla kwekọrọ na ụdị mkpọtụ. Oscillators harmonic na-eme oscillations harmonic nke otu ugboro, na-agafe n'ọnọdụ nhazi ma na-eru n'ọnọdụ dị oke njọ. Na isi mkpọtụ nke kwekọrọ na omega otu, x1 hà nhata x2; Na isi mkpọtụ nke kwekọrọ na omega omega abụọ, omega omega otu. Na isi mkpọtụ, oke mwepụ nke oke ọ bụla na-ejide njikọ ụfọdụ ma na-emepụta ụdị ụfọdụ, nke a na-akpọ isi mode ma ọ bụ ụdị okike. Orthogonality nke oke na isi ike dị n'etiti ụdị ndị bụ isi, nke na-egosipụta nnwere onwe nke mkpọtụ ọ bụla. Ugboro okike na ụdị isi na-anọchite anya njirimara vibration dị n'ime nke usoro nnwere onwe dị iche iche.
Usoro FIG. 8 nwere ọtụtụ ọkwa nnwere onwe
Usoro nke n ogo nnwere onwe nwere ugboro n eke na ụdị n isi. Nhazi mkpọtụ ọ bụla nke sistemụ ahụ nwere ike ịnọchite anya dị ka njikọta ahịrị nke ụdị isi. Ya mere, a na-eji usoro superposition isi eme ihe nke ukwuu na nyocha nzaghachi ike nke sistemụ multi-dof. N'ụzọ dị otu a, nha na nyocha nke njirimara ịma jijiji eke nke sistemụ ahụ na-aghọ nzọụkwụ nkịtị na nhazi ike nke sistemụ ahụ.
Enwere ike ịkọwa njirimara ike nke sistemụ multi-dof site na njirimara ugboro ugboro. Ebe ọ bụ na enwere ọrụ njirimara ugboro ugboro n'etiti ntinye na mmepụta ọ bụla, a na-ewu matriks njirimara ugboro ugboro. Usoro njirimara nke oke-ugboro nke sistemụ nnwere onwe ọtụtụ dị iche na nke sistemụ nnwere onwe otu.
Elastomer ahụ na-ama jijiji
Usoro nnwere onwe dị elu dị n'elu bụ ihe nlereanya mekaniki nke elastomer. Elastomer nwere ọnụọgụgụ nnwere onwe na-enweghị njedebe. Enwere ọdịiche ọnụọgụgụ mana enweghị ọdịiche dị mkpa n'etiti ha abụọ. Elastomer ọ bụla nwere ọnụọgụgụ na-enweghị njedebe nke ugboro eke na ọnụọgụgụ na-enweghị njedebe nke ụdịdị kwekọrọ, enwerekwa orthogonality n'etiti ụdịdị nke oke na isi ike. Nhazi vibration ọ bụla nke elastomer nwekwara ike ịnọchite anya dị ka superposition linear nke ụdịdị isi. Ya mere, maka nyocha nzaghachi ike nke elastomer, usoro superposition nke ụdịdị isi ka dị irè (lee vibration linear nke elastomer).
Were mkpọtụ nke eriri. Ka anyị kwuo na eriri dị gịrịgịrị nke oke m kwa ogologo nkeji, ogologo l, na-agbatị na nsọtụ abụọ ahụ, nrụgide ahụ bụkwa T. N'oge a, a na-ekpebi ugboro eke nke eriri ahụ site na nha anya a:
F = na/2l (n= 1,2,3…).
Ebee ka ọsọ mgbasa nke ebili mmiri transverse dị n'akụkụ eriri ahụ dị. Ugboro eke nke eriri ndị ahụ bụ ọtụtụ ugboro nke isi ihe karịrị 2l. Ọnụọgụ integer a na-eduga na nhazi harmonic dị mma. N'ozuzu, enweghị njikọ integer dị otú ahụ n'etiti ugboro eke nke elastomer.
E gosiri ụdị atọ mbụ nke eriri a na-agbatị agbatị na FIG. 9. E nwere ụfọdụ n'ime eriri ndị dị na isi ihe dị n'ụdị. Na isi ihe dị n'ime, n'ime eriri ndị ahụ anaghị ama jijiji. FIG. 10 na-egosi ọtụtụ ụdị ihe eji eme ihe nke efere okirikiri a na-akwado gburugburu ya nwere ụfọdụ ahịrị nodal nke nwere okirikiri na dayameta.
Enwere ike ikwubi usoro kpọmkwem nke nsogbu mkpọtụ elastomer dị ka nsogbu uru ókè nke nha nhata dị iche iche. Agbanyeghị, azịza kpọmkwem nwere ike ịchọta naanị n'ọnọdụ ụfọdụ kachasị mfe, yabụ anyị ga-eji azịza kpọmkwem maka nsogbu mkpọtụ elastomer dị mgbagwoju anya. Isi ihe dị iche iche nke ngwọta dị iche iche bụ ịgbanwe enweghị ngwụcha gaa na njedebe, ya bụ, kewaa sistemụ nnwere onwe dị iche iche na-enweghị aka (usoro na-aga n'ihu) ka ọ bụrụ usoro nnwere onwe dị oke ọnụ (usoro dị iche iche). E nwere ụdị ụzọ abụọ nke nhazi nke ejiri mee ihe n'ọtụtụ ebe na nyocha injinia: usoro ihe dị oke ọnụ na usoro njikọta modal.
FIG. 9 ụdị eriri
FIG. 10 ụdị efere okirikiri
Usoro ihe dị na njedebe bụ usoro ihe mejupụtara nke na-ewepụ ihe owuwu dị mgbagwoju anya ka ọ bụrụ ọnụọgụgụ ihe dị na njedebe ma jikọta ha na ọnụọgụgụ ihe dị na njedebe. Nkeji ọ bụla bụ elastomer; A na-egosipụta mgbanwe nke ihe site na ọrụ njikọ nke mgbanwe n'etiti ihe. Mgbe ahụ, a na-etinye paramita nkesa nke ihe ọ bụla na node ọ bụla n'ụdị ụfọdụ, a na-enwetakwa ụdị igwe nke sistemụ dị iche.
Nhazi Modal bụ mmebi nke usoro mgbagwoju anya n'ime ọtụtụ usoro dị mfe. Dabere na nghọta nke njirimara ịma jijiji nke usoro ọ bụla, a na-emepụta usoro ahụ n'ime usoro izugbe dịka ọnọdụ nhazi dị na interface si dị, a na-enwetakwa usoro ịma jijiji nke usoro izugbe site na iji usoro ịma jijiji nke usoro ọ bụla.
Ụzọ abụọ a dị iche ma nwee njikọ, a pụkwara iji ha mee ihe dị ka ntụaka. Enwere ike ijikọta usoro njikọta modal na nha nnwale nke ọma iji mepụta usoro nyocha echiche na nnwale maka ịma jijiji nke nnukwu sistemụ.
Oge ozi: Eprel-03-2020
