Mmaji nke ahịrị: elasticity nke components na usoro bụ n'okpuru iwu hooke, na damping ike eme n'oge ngagharị bụ hà nhata nke mbụ equation nke generalized ọsọ (oge ewepụtara nke generalized coordinates).
echiche
Usoro ntanetị na-abụkarị ihe atụ nke na-adịghị ahụkebe nke vibration nke ezigbo usoro. Usoro ntụgharị nke eriri na-emetụta ụkpụrụ nke superposition, ya bụ, ọ bụrụ na nzaghachi nke usoro ahụ bụ y1 n'okpuru ọrụ nke ntinye x1, na y2 n'okpuru ọrụ nke ntinye x2. Mgbe ahụ nzaghachi nke usoro n'okpuru ọrụ ntinye x1 na x2 bụ y1 + y2.
Na ndabere nke superposition ụkpụrụ, ihe aka ike ntinye nwere ike decomed n'ime nchikota nke usoro nke enweghi ngwụcha nke mkpali, na mgbe ahụ, ngụkọta nzaghachi nke usoro nwere ike nweta. usoro nke harmonic components site Fourier transform, na mmetụta nke ọ bụla harmonic akụrụngwa na usoro nwere ike nyochaa iche iche.Ya mere, a pụrụ ịkọwa àgwà nzaghachi nke usoro linear na mgbe niile parameters site na nzaghachi mkpali ma ọ bụ nzaghachi ugboro ugboro.
Nzaghachi nke mkpali na-ezo aka na nzaghachi nke usoro ahụ na mkpali nke otu, nke na-egosipụta njirimara nzaghachi nke usoro ahụ na ngalaba oge. site na Fourier mgbanwe.
nhazi ọkwa
Enwere ike kewaa vibration linear ka ọ bụrụ ụda ahịrị ahịrị nke sistemụ nnwere onwe nke otu-ogo yana usoro ịma jijiji nke ọtụtụ ogo-nke nnwere onwe.
(1) akara ụda nke usoro nke otu ogo-nke nnwere onwe bụ akara ụda nke nwere ike ikpebi ọnọdụ ya site na nhazi mkpokọta. harmonic vibration, free ịma jijiji, attenuation ịma jijiji na mmanye ịma jijiji.
Mfe nkwekọ nkwekọ: mmegharị mmegharị nke ihe dị n'akụkụ ọnọdụ nhata ya dịka iwu sinusoidal siri dị n'okpuru ọrụ nke iweghachi ike dabara na mbupụ ya.
Mgbaji agbaji agbaji: ịma jijiji nke njupụta ya na-abawanye site na ọnụnọ nke esemokwu na nguzogide dielectric ma ọ bụ oriri ume ọzọ.
Mmanye mmanye: ịma jijiji nke sistemụ na-enwe mkpali mgbe niile.
(2) ụda ahịrị nke usoro multi-degree-of-freedom bụ vibration nke usoro ntanetị na n≥2 degrees nke nnwere onwe. nke usoro nwere ike na-anọchi anya dị ka a linear Nchikota nke isi modes.Ya mere, isi mode superposition usoro ọtụtụ-eji na ike nzaghachi analysis nke multi-dof usoro.N'ụzọ dị otú a, nha na analysis nke. njirimara ịma jijiji nke okike nke usoro ahụ na-aghọ nzọụkwụ na-emekarị n'ime usoro dị ike nke usoro ahụ. A pụkwara ịkọwa àgwà dị ike nke usoro multi-dof site na njirimara ugboro ugboro. Ebe ọ bụ na e nwere njirimara njirimara ugboro ugboro n'etiti ntinye na mmepụta ọ bụla, ugboro ole A na-arụ matrix e ji mara ya. E nwere njikọ doro anya n'etiti njirimara ugboro ugboro na ọnọdụ isi. Ntugharị njirimara nke njupụta nke ọtụtụ nnwere onwe dị iche na nke usoro nnwere onwe.
Linear vibration nke otu ogo nke nnwere onwe usoro
A linear vibration nke nwere ike kpebisie ike na ọnọdụ nke a usoro site a generalized coordinate.Ọ bụ ihe kasị mfe na kasị isi vibration site na nke ọtụtụ isi echiche na àgwà nke ịma jijiji nwere ike nweta.Ọ na-agụnye mfe harmonic vibration, damped vibration na mmanye vibration. .
Harmonic ịma jijiji
N'okpuru omume nke iweghachi ike nke kwekọrọ na nchụpụ ahụ, ihe ahụ na-emeghachi omume n'ụzọ na-ezighị ezi n'akụkụ ọnọdụ nha ya (FIG. 1) .X na-anọchi anya mgbanwe na t na-anọchi anya oge. Okwu mgbakọ na mwepụ nke ịma jijiji a bụ:
(1)Ebe A bụ oke uru nke nchụpụ x, nke a na-akpọ njupụta, ma na-anọchi anya ike nke ịma jijiji;Omega n bụ njupụta n'akụkụ njupụta nke vibration kwa nkeji, nke a na-akpọ ugboro ugboro, ma ọ bụ okirikiri okirikiri; a na-akpọ oge mbụ. N'ihe gbasara f= n/2, a na-akpọ ọnụọgụ oscillation kwa sekọnd; ọ na-ewe iji oscillate otu okirikiri, na nke a na-akpọ period.Amplitude A, ugboro f (ma ọ bụ angular ugboro n), nke mbụ na-adọ, mara dị ka mfe harmonic vibration atọ ọcha.
FIG. 1 mfe harmonic ịma jijiji usoro
Dị ka e gosiri na FIG. 2, a na-emepụta oscillator dị mfe nke harmonic site na m na-ejikọta ya site na mmiri linear. Mgbe a na-agbakọ ngbanwe nke vibration site na ọnọdụ nhata, nha ụda bụ:
Ebee ka isi ike nke mmiri dị. Ngwọta n'ozuzu maka nhata dị n'elu bụ (1) .A nwere ike ikpebi site na ọnọdụ mbụ x0 na mbido mbụ na t = 0:
Ma omega n na-ekpebi naanị site na njirimara nke usoro n'onwe ya m na k, na-adabere na ọnọdụ mmalite ndị ọzọ, ya mere a na-akpọ omega n dị ka ugboro ugboro.
FIG. 2 otu ogo nke nnwere onwe usoro
Maka oscillator dị mfe harmonic, nchikota nke ike ya na ike ike ya na-adịgide adịgide, ya bụ, a na-echekwa ike ọkụ zuru ezu nke usoro ahụ. N'ime usoro nke vibration, ike ike na ike ike na-agbanwe mgbe niile n'ime ibe ha.
Ihe ịma jijiji na-akụda mmụọ
A vibration nke njupụta nke na-anọgide na-attenuated site esemokwu na dielectric iguzogide ma ọ bụ ndị ọzọ ume oriri.N'ihi na micro vibration, na ọsọ bụ n'ozuzu bụghị nnọọ nnukwu, na-ajụ iguzogide bụ proportally na ike nke mbụ ike, nke nwere ike dee dị ka c bụ. N'ihi ya, e nwere ike dee nha ụda nke otu ogo nnwere onwe na linear damping dị ka:
(2)Ebe, m = c/2m ka a na-akpọ paramita damping, na. Enwere ike dee ihe ngwọta izugbe nke usoro (2):
(3)Enwere ike kewaa mmekọrịta ọnụọgụgụ dị n'etiti omega n na PI n'ime ikpe atọ ndị a:
N> (n'ihe banyere obere damping) urughuru emepụtara attenuation vibration, nha nhata bụ:
Ngosipụta ya na-ebelata ka oge na-aga dịka iwu nkọwapụta nke egosiri na nha nha, dị ka egosiri na ahịrị nwere ntụpọ na FIG. 3.Strictly ikwu, nke a vibration bụ aperiodic, ma ugboro nke elu ya nwere ike kọwaa dị ka:
A na-akpọ ọnụego mbelata njupụta, ebe oge nke vibration dị. A na-akpọ logarithm eke nke nbibi nbibi nke ọnụ ọgụgụ logarithm mwepu (amplitude). nnwale nnwale delta na, iji usoro dị n'elu nwere ike gbakọọ c.
N'oge a, enwere ike dee azịza nke nha anya (2):
Tinyere ntụzịaka nke ngwa ngwa mbụ, enwere ike kewaa ya na ikpe atọ na-adịghị eme mkpọtụ dị ka egosiri na FIG. 4.
N <(n'ihe banyere nnukwu damping), a na-egosipụta ihe ngwọta maka nha anya (2) na nhazi (3) . N'oge a, usoro ahụ anaghịzi eme mkpọtụ.
Mmanye amanye
Vibration nke usoro n'okpuru excitation mgbe nile. Vibration analysis tumadi enyocha nzaghachi nke usoro na excitation.periodic excitation bụ a ahụkarị mgbe excitation.Since oge excitation nwere ike mgbe niile decomposed n'ime nchikota nke ọtụtụ harmonic excitation, dị ka superposition ụkpụrụ, naanị. A na-achọ nzaghachi nke usoro ahụ maka mkpali ọ bụla kwekọrọ. Enwere ike dee ogo nke sistemu mgbochi nnwere onwe:
Nzaghachi bụ nchikota akụkụ abụọ. Otu akụkụ bụ nzaghachi nke vibration damped, nke na-ere ngwa ngwa na oge. Azịza nke akụkụ ọzọ nke ịma jijiji mmanye nwere ike dee:
FIG. Usoro ịma jijiji 3 damped
FIG. Usoro 4 nke ọnọdụ mbụ nwere oke egwu
Pịnye na
H / F0 = h (), bụ oke nke nkwụsi ike nzaghachi amplitude ka excitation njupụta, na-akọwa njupụta-ugboro e ji mara, ma ọ bụ uru ọrụ; ibe n'ibe maka otu ọnọdụ nzaghachi na mkpali nke frasi, characterization nke frasi ugboro e ji mara. Mmekọrịta dị n'etiti ha na Egosiri ugboro mkpali na FIG. 5 na FIG. 6.
Dị ka a na-ahụ site na njupụta nke ugboro ugboro (FIG. 5), n'ihe gbasara obere damping, njupụta-frequency curve nwere otu ọnụ ọgụgụ kasị elu. nke a na-akpọ ugboro ole resonant nke usoro ahụ. N'ihe gbasara obere damping, ụda ụda adịghị iche na ugboro ugboro nke okike.Mgbe oge na-akpali akpali dị nso. eke ugboro, njupụta na-abawanye sharply. A na-akpọ ihe a na-eme ka a na-akpọ resonance. Na resonance, uru nke usoro ahụ na-eme ka ọ dịkwuo elu, ya bụ, vibration na-amanye bụ ihe kachasị njọ. Ya mere, n'ozuzu, na-agbalịsi ike mgbe niile izere resonance, ọ gwụla ma ụfọdụ ngwá ọrụ na ngwá ọrụ na-eji resonance iji nweta nnukwu ihe. ịma jijiji.
FIG. 5 njupụta ugboro okirikiri
Enwere ike ịhụ site na usoro ugboro ugboro (ọnụọgụ 6), n'agbanyeghị nha nke damping, na omega zero phase iche ibe n'ibe = PI / 2, enwere ike iji njirimara a rụọ ọrụ nke ọma n'ịtụle resonance.
Na mgbakwunye na mkpali na-adịgide adịgide, usoro mgbe ụfọdụ na-ezute mkpali na-adịghị agbanwe agbanwe. Ọ nwere ike kewaa ya n'ụzọ abụọ: otu bụ mmetụta mberede. Nke abụọ bụ mmetụta na-adịgide adịgide nke aka ike.
Ngwá ọrụ dị ike maka nyochaa ịma jijiji na-adịghị agbanwe agbanwe bụ usoro nzaghachi mkpali. Ọ na-akọwa njirimara dị ike nke usoro ahụ na nzaghachi na-adịru nwa oge nke ntinye mkpali nke unit nke usoro. A na-akọwakarị ọrụ dị ka:
Ebe 0- na-anọchi anya isi ihe dị na t-axis na-abịaru nso efu site n'aka ekpe; 0 gbakwunyere bụ isi ihe na-aga 0 site n'aka nri.
FIG. Usoro ugboro ugboro 6
FIG. 7 enwere ike were ntinye ọ bụla dị ka nchikota nke usoro ihe mkpali
Usoro ahụ kwekọrọ na nzaghachi h (t) nke a na-emepụta site na mkpali unit na t = 0, nke a na-akpọ ọrụ nzaghachi mkpali. ọrụ nzaghachi mkpali nke usoro ahụ, anyị nwere ike ịchọta nzaghachi nke usoro ahụ na ntinye ọ bụla x (t) .N'oge a, ị nwere ike iche x (t) dị ka nchikota nke usoro ihe mkpali (FIG. 7) Nzaghachi nke usoro bụ:
Dabere na ụkpụrụ superposition, ngụkọta nzaghachi nke sistemụ dabara na x(t) bụ:
Nke a integral ka a na-akpọ convolution integral ma ọ bụ a superposition integral.
Linear ịma jijiji nke ọtụtụ ogo-nke nnwere onwe usoro
Vibration nke usoro ahịrị nwere n≥2 ogo nnwere onwe.
Ọgụgụ 8 na-egosi subsystems abụọ dị mfe resonant jikọtara site na mmiri na-ejikọta ya. N'ihi na ọ bụ usoro nnwere onwe nke abụọ, a chọrọ nhazi abụọ nke onwe ha iji chọpụta ọnọdụ ya. E nwere ugboro abụọ eke na usoro a:
Ugboro ọ bụla kwekọrọ na ọnọdụ nke vibration. The harmonic oscillators na-eme oscillations harmonic nke otu ugboro, synchronously na-agafe n'ọnọdụ nhata na synchronously iru oke ọnọdụ. Na isi vibration kwekọrọ omega otu, x1 bụ hà x2; isi vibration kwekọrọ na omega omega abụọ, omega omega otu. Na isi vibration, mgbanwe nke ọ bụla ruru. uka na-edebe ụfọdụ mmekọrịta na-etolite a ụfọdụ mode, nke a na-akpọ isi mode ma ọ bụ eke mode.The orthogonality nke uka na isi ike dị n'etiti ndị isi ụdịdị, nke na-egosipụta nnwere onwe nke ọ bụla vibration. The eke ugboro na isi mode na-anọchi anya ndị isi ụdịdị. njirimara ịma jijiji dị iche iche nke ọtụtụ ogo nke usoro nnwere onwe.
FIG. 8 usoro nwere otutu ogo nnwere onwe
A usoro nke n degrees nke nnwere onwe nwere n eke frequencies na n isi modes.Ọ bụla vibration nhazi nke usoro nwere ike na-anọchi anya dị ka a linear Nchikota nke isi modes.Ya mere, isi mode superposition usoro ọtụtụ-eji na ike nzaghachi analysis nke multi -dof usoro. N'ụzọ dị otú a, nha na nyocha nke eke vibration e ji mara nke usoro na-aghọ a na-emekarị nzọụkwụ na ike imewe nke usoro.
A pụkwara ịkọwa àgwà dị ike nke usoro multi-dof site na njirimara ugboro ugboro. Ebe ọ bụ na e nwere ọrụ njirimara ugboro ugboro n'etiti ntinye na mmepụta ọ bụla, a na-arụ matrix njirimara ugboro ugboro. site na nke usoro nnwere onwe otu.
Elastomer na-ama jijiji
The n'elu multi-ogo nke nnwere onwe usoro bụ ihe dị ka n'ibu nlereanya nke elastomer.An elastomer nwere enweghi ngwụcha ọnụọgụ nke degrees nke nnwere onwe.There a quantitative iche ma ọ dịghị mkpa dị iche n'etiti abụọ. Ọ bụla elastomer nwere enweghi ngwụcha ọnụ ọgụgụ nke eke frequencies na. ọnụ ọgụgụ na-enweghị ngwụcha nke ụdị dabara adaba, na e nwere orthogonality n'etiti ụdị nke uka na isi ike. Nhazi ọ bụla vibrational nke elastomer. nwekwara ike na-anọchi anya dị ka a linear superposition nke isi modes. Ya mere, maka ike nzaghachi analysis nke elastomer, superposition usoro nke main mode ka na ọdabara (lee linear vibration nke elastomer).
Were vibration nke a eriri. Ka anyị kwuo na a mkpa eriri nke uka m kwa unit ogologo, ogologo l, na- tensioned na ma nsọtụ, na esemokwu bụ T. N'oge a, eke ugboro nke eriri na-ekpebi ihe ndị na-esonụ. nhata:
F = na/2l (n= 1,2,3…).
Ebe, bụ mgbasa ngwa ngwa nke transverse ife n'akụkụ ntụziaka nke eriri. The eke frequencies nke eriri na-eme ka multiples nke isi ugboro n'elu 2l. Nke a integer multiplicity na-eduga na a obi ụtọ harmonic Ọdịdị. N'ozuzu, ọ dịghị. dị otú ahụ integer otutu njikọ n'etiti eke frequency nke elastomer.
Ụdị ụzọ atọ mbụ nke eriri esemokwu ahụ ka egosiri na FIG. 9. E nwere ụfọdụ ọnụ na isi mode curve.Na isi vibration, ọnụ adịghị ama jijiji.FIG. 10 na-egosi ọtụtụ ụdịdị efere okirikiri a na-akwado okirikiri nwere ahịrị nodal nwere okirikiri na dayameta.
Enwere ike ikwubi usoro nhazi nke nsogbu vibration nke elastomer dị ka nsogbu uru oke nke nha anya dị iche iche. Otú ọ dị, a pụrụ ịchọta ngwọta ziri ezi naanị na ụfọdụ n'ime ihe ndị kachasị mfe, n'ihi ya, anyị ga-amalite na ngwọta dị ka ihe ngwọta maka mgbagwoju anya elastomer. nsogbu vibration. Ihe kachasi mkpa dị iche iche dị ka ngwọta bụ ịgbanwe enweghi ngwụcha na njedebe, ya bụ, discretize ndị aka na-enweghị multi-ogo nke nnwere onwe. usoro (usoro na-aga n'ihu) n'ime usoro nnwere onwe nke nwere njedebe multi-ogo (sistemụ pụrụ iche) .E nwere ụdị ụzọ abụọ nke discretization nke a na-ejikarị eme ihe na nyocha injinia: usoro mmewere njedebe na usoro njikọ modal.
FIG. 9 ụdị eriri
FIG. 10 ụdị efere okirikiri
Usoro mmecha agwụcha bụ usoro ihe mejupụtara nke na-ewepụta usoro dị mgbagwoju anya n'ime ọnụ ọgụgụ dị oke ọnụ ma jikọta ha na ọnụ ọgụgụ dị oke ọnụ. nkesa nkesa nke ọ bụla mmewere na-lekwasị na onye ọ bụla ọnụ na a ụfọdụ usoro, na-mechanical nlereanya nke pụrụ iche usoro na-enwetara.
Modal njikọ bụ nbibi nke a mgbagwoju Ọdịdị n'ime ọtụtụ mfe substructures. Na ndabere nke ịghọta vibration e ji mara nke ọ bụla substructure, substructure na-synthesized n'ime a n'ozuzu Ọdịdị dị ka nhazi ọnọdụ na interface, na vibration morphology nke izugbe. A na-enweta ihe owuwu site na iji morphology vibration nke akụkụ nke ọ bụla.
Ụzọ abụọ ahụ dị iche iche na ndị metụtara ya, a pụkwara iji ya mee ihe dị ka ntụnye aka. Usoro nhazi nke modal nwekwara ike ijikọta nke ọma na nyocha nyocha iji mepụta usoro nyocha na nyocha nke nyocha maka ịma jijiji nke nnukwu usoro.
Oge nzipu: Eprel-03-2020
