Analysis of the Vibrations of an Elastic Beam - VtsjkR$R BP Y z$As$BtR BP st ejsR$ s8 V 3BZY!I e$t%sjZ\\e$tPZt{$Bt_BAj8 =R$t{BtT}R PB8 Y YBk BP jsR${$k

Analysis of the Vibrations of an Elastic Beam - VtsjkR$R BP...

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VtsjkR$R BP ±Y z$A s±$BtR BP st ejsR±${ s8 V 3BZ ±Y ! I e$² t%sjZ \e$² tPZt{±$Bt _ BAj 8 =R$t± {BtT { }²R P B8 ²Y ²Y B k BP jsR²${$²k $² {st A RYBbt ²Ys² ²Y js² sj I 4 {²$Bt³ j w ?, 0 D³ BP s Zt$PB 8³ ²Y$t jsR²${ A s8 BP j t±²Y U ³ R ² $t²B %$A s²$Bt³ BA kR ²Y }s ²$sj I$& t²$sj JZs²$Bt ' ( j (0 L ± (j (0 L o{ ( j (? ) W w ?, 0 D , bY W w ?, 0 D } R t²R st s}}j$ I tsj PB { ³ ' $R ²Y 8sRR } Zt$² j t±²Y³ ± $R ²Y {B ^{$ t± BP %$R{BZR P ${±$Bt w j %st²³ ´±´³ $P ²Y A s8 $R %$A s²$t± $t s 4Z$I RZ{Y sR s$ D stI o{ $R ²Y R²stIs I Rk8ABj PB ²Y A tI$t² 8BIZjZR BP ²Y A s8´ G I ht ²Y I$& t²$sj B} s²B 6 Ak w 6 j Dw ? D ) Q j Q? w ? D Bt s IB8s$t ? $t hg >( , U H ²B A PZ ²Y R} {$h I Ak $8}BR$t± ABZtIs k {BtI$²$BtR bY${Y b b$jj I R{ $A RYB ²jk´ qB A ±$t ²Y } B{ RR BP $I t²$Pk$t± ²YBR ABZtIs k {BtI$²$BtR b tB² ²Ys² b$²Y ²Y R²stIs I $tt } BIZ{² ± j, F X # $ j w ? D F w ? D Q? b Ys% ³ PB j w ? D stI F w ? D $t ? ³ ±6 j, F X ) 8 Q j Q? F w ? D Q? ) Q j Q? F w ? D e e e ² 8 Q j Q? QF Q? Q? ) X Q j Q? F w ? D ² Q j Q? QF Q? ~ e e e L 8 Q j Q? Q F Q? Q? d
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) X Q j Q? F w ? D ² Q j Q? QF Q? L Qj Q? Q F Q? ~ e e e ² 8 Qj Q? Q F Q? Q? ) X Q j Q? F w ? D ² Q j Q? QF Q? L Qj Q? Q F Q? ² j w ? D Q F Q? ~ e e e L 8 j w ? D Q F Q? Q? ) X Q j Q? F w ? D ² Q j Q? QF Q? L Qj Q? Q F Q? ² j w ? D Q F Q? ~ e e e L ? j, 6 F # 3 qY Xts²Z sj" ABZtIs k {BtI$²$BtR s I ht I sR ²YBR bY${Y {sZR ²Y ABZtIs k ² 8R X Q j Q? F w ? D ² Q j Q? QF Q? L Qj Q? Q F Q? ² j w ? D Q F Q? ~ e e e ²B IZ{ ²B 9 B´ qY s s js ± tZ8A BP ²Y R ³ {B R}BtI$t± ²B %s $BZR bskR $t bY${Y ²Y A s8 {st A 8BZt² I B {BtR² s$t I´ e-s8}j R $t{jZI ²Y {js8} I A s8 U j w(D ) Qj Q? w(D ) j w U D ) Qj Q? w U D ) (µ ²Y R$8}jk RZ}}B ± I A s8 U j w(D ) Q j Q? w(D ) j w U D ) Q j Q? w U D ) (µ ²Y P A s8 U Q j Q? w(D ) Q j Q? w(D ) Q j Q? w U D ) Q j Q? w U D ) ( stI ²Y {st±$j % A s8 U j w(D ) Qj Q? w(D ) Q j Q? w U D ) Q j Q? w U D ) ( 3 yt ²Y jsR² {sR ²Y A s8 $R {js8} I s² ? ) ( stI P ? ) U ´ yt sjj {sR R ²Y ABZtIs k {BtI$²$BtR s s}}j$ I ²B F w ? D sR b jj sR ²B j w ? D sR RYBbt´ 1
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es{Y BP ²Y R {B R}BtIR ²B s I$& t² I ht$²$Bt BP ²Y IB8s$t ? ´ qY s 8stk³ $tI I $tht$² jk 8stk³ B²Y }BRR$A$j$²$ R´ G b$jj ZR ²Y {st²$j % A s8 sR ²Y R²stIs I -s8}j $t BZ bB , Y A {sZR $² {B R}BtIR ²B bYs² $R 8BR² sR$jk I 8BtR² s² I $t ²Y jsAB s²B k´ 3B stk BP ²Y R ABZtIs k {BtI$²$BtR ²Y PBZ ²Y B I B} s²B b$jj A R jPTsI`B$t² A {sZR b Ys% ±6 j, F X ) ± j, 6 F X ´ qY B} s²B $R sjRB tBtT t ±s²$% PB stk ABZtIs k {BtI$²$BtR RZ{Y ²Ys² ²Y ABZtIs k ² 8R s $R$t± sP² ²Y h R² ²bB $t² ± s²$BtR Ak }s ²R³ $´ ´³ X Q j Q? F w ? D ² Q j Q? QF Q? ~ e e e , IZ{ ²B 9 B A {sZR ³ $t ²Y$R {sR b Ys% ³ PB F w ? D ) j w ? ±6 j, j X ) 8 Q j Q?
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