The Buckling of a Thick Circular Plate Using a Non Linear Theory
The Buckling of a Thick Circular Plate Using a Non Linear Theory
Chester B Sensenig
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For this to be possible it is sufficient that y'l +(1/1*) Yl - (l/r )y » Y, and 5' are loropertional and also that S"^ + (l/'r)Y'> S, and y' + (l/r)Yj- are proportional. These proportionality conditions are satis- fied if Y = J^(k r) and 5 = J (k r) vjhere k is an arbitrary constant and J is the Bessel function of the first kind of order n. Since a wide class of functions can be expanded in series of the functions J^(k r) or J (k r), and since we can easily satisfy (5. 9) terra by term for such... series, xve look for solutions of the form CO f = . Er +2_. A^(^3)Ji(V^ n=l -^ 00 and S = (3, (X3) +^P, (x3)J^(k^r) vjhere k is chosen so that k R is the nth positive zero J-, . Using the identity Jq = - J-i ^^'^ the differential equation for J we obtain (d/dr)J (k r) = - k Jt (k r) and o ' on nln et-ip. F' 12 + k J (k r) • Viflth these results we obtain 'n o^ n and Thus and f^ = - e -.
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