A tapered flat bar with thickness t and length L is attached to rigid supports at both ends, as… 1 answer below »

A tapered flat bar with thickness t and length L is attached to rigid supports at both ends, as shown in Fig. P2.18. The bar has a mass density p per unit volume, and its modulus of elasticity is E. Determine appropriate shape functions to be used in representing the axial motion of this bar by SDOF models: (a) if ψ{x) is a simple polynomial function; and (b) if ψ(x) is sinusoidal.