Download PDF by Henry M. Paynter: Analysis and design engineering systems

By Henry M. Paynter

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In this respect, the operators Φ and Ψ¯ are given by ⎛ ⎛ ⎞ D(L − z)λ p + λq ⎜ ⎟ λp ⎜ ⎟ ⎜ ⎟ −Dλ p ⎜ ⎟ ⎟ 0 Φ(λq , λ p ) = ⎜ ⎜ ⎟ ⎜ ⎟ 0 ⎜ ⎟ ⎝ ⎠ λp λq ⎞ 0 ⎜0⎟ ⎜ ⎟ ⎜λ R ⎟ ⎜ ⎟ ⎟ Ψ¯ (λ R ) = ⎜ ⎜0⎟ ⎜0⎟ ⎜ ⎟ ⎝0⎠ 0 with dom Φ = R2 and dom Ψ¯ = L 2 (0, ; R). 27) can be satisfied by selecting E˜ R = 0 and 00000 0 0 E˜ S∗ = 00000D0 E˜ C∗ F˜ R∗ = 0 0 0 0 0 −1 0 = 0D10000 0 0 00000 which is equivalent to have ⎛ ∂ ⎞ 0 − ∂z ⎜− ∂ 0 ⎟ ⎜ ∂z ⎟ ⎜ 0 −1 ⎟ ⎜ ⎟ ⎟ E¯ S = ⎜ ⎜ 0 −· |0 ⎟ ⎜−· | L 0 ⎟ ⎜ ⎟ ⎝ −· | D L ·⎠ 0 0 0 · |L ⎛ ⎜ ⎜ ⎜ ⎜ ¯ FR = ⎜ ⎜ ⎜ ⎜ ⎝− 0 1 0 0 0 ⎞ ⎟ ⎟ ⎟ ⎟ ⎟ ⎟ ⎟ ⎟ L ⎠ · 0 0 ⎛ 0 ⎜D ⎜ ⎜1 ⎜ ¯ EC = ⎜ ⎜1 ⎜0 ⎜ ⎝0 0 ⎞ 0 0⎟ ⎟ 0⎟ ⎟ 0⎟ ⎟ 1⎟ ⎟ 0⎠ 0 where · |0 and · | L denote the value of a function in z = 0 and in z = L.

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Analysis and design engineering systems by Henry M. Paynter


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