A multiple-leaf spring used in automobiles is shown in Fig. 12.17. It consists of five leaves, each of thickness \(t=0.65 \mathrm{~cm}\) and width \(w=3.8 \mathrm{~cm}\). For the multiple-leaf spring described in Fig. 12.17, derive the assembled stiffness and mass matrices. Consider only one-half of the spring for modeling using five beam elements of equal length.

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Y U U3 U Joint 1 Joint 2 U6 Us UA FIGURE 12.16 A frame element in global system. X