36 Real-Time Theoretical and Experimental Dynamic Mode Shapes for Structural Analysis Using Augmented Reality 353 Fig. 36.2 Aluminum beam reduced to 10 nodes for theoretical calculations Fig. 36.3 Experimental setup Where n=1,2,3, . . . C is an arbitrary constant, chosen to be 1 in this calculation. λn values are calculated numerically from characteristic equation. kn = cosh(λnL) −cos(λnL) sinh(λnL) −sin(λnL) (36.3) Equation 36.3 determines the stiffness factor associated with each mode shape. Using these equations, the mode shapes can be determined for the beam. 36.2.3 Experimental Analysis The experimental data uses a displacement laser sensor. The setup involves a beam attached to a shake table, a laser for displacement, a data acquisition system, cables, a power source and a computer to collect recorded data (Fig. 36.3). Data was
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