Derive the element matrices for an axisymmetric, linear quadrilateral element. Figure 5.14 shows the cross-section of a circular disc which is fixed at the inner radius and free at the outer radius....



Derive the element matrices for an axisymmetric, linear quadrilateral element.


Figure 5.14 shows the cross-section of a circular disc which is fixed at the inner


radius and free at the outer radius. Use the idealisation shown in Figure P5.7 to


calculate the frequencies of the modes having 0, 1 and 2 nodal diameters and no


nodal circles, other than the inner radius. Take E = 196 × 109 N/m2, ν = 0.3 and


ρ = 7800 kg/m3. Compare these frequencies with the analytical values [5.13] 312.2,


276.3 and 322.5 Hz.

Nov 24, 2021
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