Natural vibrations of nanodimensional piezoelectric bodies with contact-type boundary conditions

Eremeev, V. A.; Наседкин, А. В.

doi:10.3103/s0025654415050027

Cited by 10 publications

(3 citation statements)

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“…Ïðèìåíÿÿ ñòàíäàðòíóþ êîíå÷íî-ýëåìåíòíóþ òåõíèêó äëÿ àïïðîêñèìàöèè ñëàáîé ïîñòàíîâêè çàäà÷è (1) (17) ãäå U, Φ Φ Φ Φ Φ − âåêòîðû óçëîâûõ ïåðåìåùåíèé è ýëåêòðè÷åñêèõ ïîòåíöèàëîâ, ìàòðèöû îïèñàíû â [16,17], à âåêòîðû ïðàâûõ ÷àñòåé îïðåäåëÿþòñÿ âíåøíèìè âîçäåéñòâèÿìè. Â îòëè÷èå îò çàäà÷ äëÿ òåë îáû÷íûõ ðàçìåðîâ [19], çäåñü â ìàòðèöû K uu , K uϕ è K ϕϕ âõîäÿò ìàòðèöû K Γuu , K Γuϕ è K Γϕϕ , îáóñëîâëåííûå ãðàíè÷íûìè óñëîâèÿìè (10), (12)…”

Section: êîíå÷íî-ýëåìåíòíûå àïïðîêñèìàöèèunclassified

“…Íèaeíèé òîðåö áðóñà ñ÷èòàåòñÿ aeåñòêî çàùåìëåííûì (òî åñòü ÿâëÿåòñÿ ïîâåðõíîñòüþ Γ u ñ u Γ = 0 â (11)), à âåðõíèé òîðåö è áîêîâàÿ ïîâåðõíîñòü ÿâëÿþòñÿ ïîâåðõíîñòÿìè Γ σ ñ p Γ = 0 â (10). Áóäåì òàêaeå ñ÷èòàòü áîêîâóþ ïîâåðõíîñòü x = a, 0 ≤ z ≤ l ïîâåðõíîñòüþ Γ D , íà êîòîðîé âûïîëíÿþòñÿ óñëîâèÿ (12) ñ q Γ = 0, íà ãðàíè x = 0 ïðèìåì óñëîâèÿ ñèììåòðèè.…”

Section: ×èñëåííûå ýêñïåðèìåíòûunclassified

“…Àíàëîãè÷íûå ðåçóëüòàòû ïðè íåñâÿçàííûõ ìåõàíè÷åñêèõ è ýëåêòðè÷åñêèõ ïîâåðõíîñòíûõ ýôôåêòàõ, à òàêaeå ðåçóëüòàòû, èëëþñòðèðóþùèå âëèÿíèå ìåõàíè÷åñêèõ è ýëåêòðè÷åñêèõ ãðàíè÷íûõ óñëîâèé äëÿ çàäà÷è î êîëåáàíèÿõ íàíîðàçìåðíîãî ñòåðaeíÿ, ïðèâåäåíû â [12,13]. Ðèñ.…”

Section: ×èñëåííûå ýêñïåðèìåíòûunclassified

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About Models of Nanosized Piezoelectric Materialswith Coupled Surface Effects

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2017

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Ðàññìàòðèâàþòñÿ äèíàìè÷åñêèå çàäà÷è äëÿ ïüåçîýëåêòðè÷åñêèõ íàíîðàçìåðíûõ òåë ñ ó÷åòîì ïîâåðõíîñòíûõ ýôôåêòîâ è çàòóõàíèÿ. Äëÿ ýòèõ çàäà÷ ïðåäëîaeåíà íîâàÿ ìàòåìàòè÷åñêàÿ ìîäåëü, îáîáùàþùàÿ ìîäåëü óïðóãîé ñðåäû ñ äåìïôèðîâàíèåì ïî Ðýëåþ è ìîäåëü Ãóðòèíà − Ìóðäîõà ó÷åòà ïîâåðõíîñòíûõ ýôôåêòîâ. Íîâàÿ ïîñòàíîâêà çàäà÷è ó÷èòûâàåò ýëåêòðîìåõàíè÷åñêóþ ñâÿçàííîñòü ìåõàíèçìîâ çàòóõàíèÿ è ïîâåðõíîñòíûõ ýôôåêòîâ êàê â îáúåìå òåëà, òàê è íà ïîâåðõíîñòè. Îáñóaeäàþòñÿ îñîáåííîñòè èñïîëüçîâàíèÿ ìåòîäà êîíå÷íûõ ýëåìåíòîâ äëÿ ÷èñëåííîãî ðåøåíèÿ ðàññìàòðèâàåìûõ çàäà÷. Ïîêàçàíî, ÷òî äëÿ ñòàòè÷åñêèõ è íåñòàöèîíàðíûõ çàäà÷ óðàâíåíèÿ, ïîëó÷åííûå ìåòîäîì êîíå÷íûõ ýëåìåíòîâ, ìîaeíî ïðèâåñòè ê ôîðìàì, ñîäåðaeàùèì òîëüêî ñèììåòðè÷íûå êâàçèîïðåäåëåííûå ìàòðèöû. Îòìå÷àåòñÿ, ÷òî äëÿ íåñòàöèîíàðíûõ çàäà÷ è äëÿ çàäà÷ îá óñòàíîâèâøèõñÿ êîëåáàíèÿõ âîçìîaeíî ïðèìåíåíèå ìåòîäà ñóïåðïîçèöèè, ïðèâîäÿùåãî ê íåçàâèñèìûì óðàâíåíèÿì äëÿ àìïëèòóä êîëåáàíèé îòäåëüíûõ ìîä. ×èñëåííûå ïðèìåðû äåìîíñòðèðóþò âëèÿíèå ïîâåðõíîñòíûõ ìîäóëåé íà ëîêàëüíûå è íà èíòåãðàëüíûå õàðàêòåðèñòèêè êîëåáàòåëüíûõ ïðîöåññîâ íàíîðàçìåðíûõ ïüåçîýëåêòðè÷åñêèõ òåë. Êëþ÷åâûå ñëîâà: ïüåçîýëåêòðè÷åñòâî, íàíîìåõàíèêà, ïîâåðõíîñòíûå íàïðÿaeåíèÿ, ïüåçîýëåêòðè÷åñêèå ïîâåðõíîñòíûå ýôôåêòû, ìîäåëü Ãóðòèíà − Ìóðäîõà, ìåòîä êîíå÷íûõ ýëåìåíòîâ, êâàçèîïðåäåëåííûå ìàòðèöû. * Âûïîëíåíî ïðè ïîääåðaeêå ÐÍÔ (ïðîåêò ¹ 15-19-10008) â ÷àñòè ðàçðàáîòêè îáùåé ìîäåëè è ÐÔÔÈ (ãðàíò ¹ 16-01-00785) â ÷àñòè êîíå÷íî-ýëåìåíòíîé ðåàëèçàöèè.

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Section: êîíå÷íî-ýëåìåíòíûå àïïðîêñèìàöèèunclassified

Section: ×èñëåííûå ýêñïåðèìåíòûunclassified