Aei

£3 (i + j - l)(i + j)(l + ; + j) (2 + ; + /)( 3 + ; + j) Similarly, the elements of the mass matrix can be found as rf

mtp i P2

where pi = 30240 + 28512(/ + j) + 9672(/2 + j2) + 1392(/3 + f) + 72(/4 + /)

+ 200400' + 4520(rj + ij2) + 320(/3j + if) + 520i2j2, P2 = /(l + 0(2 + 0(3 + Oj(l + J)(2 + /)(3 + j)( 3 + / + j) x (4 + i + j)(5 + i + j)(6 + i + j)(7 + i + j).

The fact that the governing equation is derivable from energy is reflected in the symmetry of [M] and [ÍT]. Results for free vibration (i.e., with / = 0) are given in Table 2.7. As with the Ritz method, one sees monotonie convergence from above and accuracy comparable to that achieved via the Ritz method. However, unlike the Ritz method, one does not always obtain results for free-vibration problems that converge from above.

Table 2.7. Approximate Values of co, yjm £4/(EI) for i = 1,2, and 3, for a Clamped-Free Beam Using n Polynomial Functions

n

0 0

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