Problem

Repeat Problems 8.12 and 8.13 using a three-element four-node finite element model....

Repeat Problems 8.12 and 8.13 using a three-element four-node finite element model.

REFERENCE:

8.13: Let the bar in Figure P8.13 be made of aluminum 1 m in length with h1 = 20 cm and h2 = 10 cm. Calculate the natural frequencies using the finite element model of Problem 8.12.

REFERENCE:

8.12 :As mentioned in the text, the usefulness of the finite element method rests in problems that cannot readily be solved in closed form. To this end, consider a section of an air frame sketched in Figure P8.13 and calculate a two-element finite model of this structure (i.e., find M and K) for a bar with

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