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Mechanics of Microelectromechanical Systems - N.Lobontiu and E.Garcia Part 3

Tham khảo tài liệu 'mechanics of microelectromechanical systems - n.lobontiu and e.garcia part 3', kỹ thuật - công nghệ, cơ khí - chế tạo máy phục vụ nhu cầu học tập, nghiên cứu và làm việc hiệu quả | 48 Chapter 1 Solution The position of the neutral axis is given by Eq. 1.177 . It can be shown that this equation reduces to zw ỉ cEct 2 c Ị 2 ỉ cEct tị 1.188 The equivalent rigidity in bending is calculated by means of Eq. 1.180 and an equivalent homogeneous cross-section beam can be found whose bending rigidity is EIy e Exw t eb f m 1.189 By equating Eqs. 1.180 and 1.189 the equivalent thickness is The rigidity that corresponds to axial equivalence is determined by using Eq. 1.184 and by considering that the same axial rigidity should be produced by an equivalent homogeneous bar namely EA e Ewt ea 1.191 and the axial-related thickness for this problem is t ea cECl tx 1.192 which results from equating Eqs. 1.184 and 1.191 . 1.5 08 Figure 1.26 Thickness ratio r in terms of thickness factor C and elastic factor CE 1. Stiffness basics 49 It is clear that the thicknesses produced by Eqs. 1.190 and 1.192 are equal only for one relationship between the two factors Ct and CE. Expressing one of the factors in terms of the other implies solving a third degree equation resulting from equating the right hand sides of Eqs. 1.190 and 1.192 which will have one real solution. Figure 1.26 is the plot of the thickness ratio rt t eb t ea 1.193 and it can be seen that this ratio spans the 0.8 - 1.2 range. It can also be seen that due to its monotonic variation the ratio can only be equal to 1 for one ct CE pair and the two thicknesses are identical solely for that unique combination. 6.2 Serially-Connected Members A problem directly resulting from the previous one addresses the case where two or more different structural members are connected serially as depicted in the structure sketched in Fig. 1.27. The case studied in the previous subsection 6.1 offers the explanation with respect to the necessity of approaching the topic of serially-connected components. When the two different components that are sandwiched together do not have identical lengths the equivalent rigidities can be