A uniform, structural beam can be considered to be built-in at one end and simply supported at the other. If the beam length is L; second moment of area I; cross sectional area A; material density p; material Young's modulus E, show that the natural frequencies in bending an for the beam are given by:-tan (aL) = tanh(aL) where a4= p.A.con2/(E.1) and values of aL which satisfy this relationship are mr + K14 (n= 1,2,3 etc)(14 marks)(b) Evaluate the first 3 natural frequencies for the beam if :-L= 5m; I = 4x10-6 m4; A = 0.005 m2; p = 7800 kg/m3; E = 200GN/m2.(6 marks)
21 JAN XXXXXXXXXXJAN XXXXXXXXXXJAN 2010
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