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

... indeterminate, the reactions and need to be first determined, by using the corresponding boundary conditions: which can be expressed as: The bending moment is: The unknown reactions are: The horizontal ... microbridges 67 in the oscillating mode – when the modal frequencies are actually monitored and determined. They can operate in a contact mode or in a non-contact mode (when a pre-desig...

Ngày tải lên: 10/08/2014, 05:20

... more generic case where the area is variable, to: where it has been taken into account that the elementary volume can be expressed in terms of the cross-sectional area A and the elementary length ... stiffnesses or compliances, namely: two direct (linear and rotary) and one crossed, define the elastic response at the free end of a cantilever. More details on the spring characterizat...

Ngày tải lên: 10/08/2014, 05:20

... set of experimental measurements, for instance the deflection at a point placed at a distance from the free end, is needed. In this case, the deflection at the experimental point of detection is: Equations ... microcantilever to the performance of a right elliptically-filleted one when and is the friction force between the microcantilever tip and the investigated three- dimensional...

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... series connection of several base units. Figure 3. 27 is a three-dimensional model of a serpentine unit with the local reference frame. The in-plane compliances can be found based on Fig. 3. 24, ... the springs. A serpentine spring is formed of one or several series-connected units, as the one shown in Fig. 3. 24, where also indicated are the defining geometric parameters of the un...

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... the analytic model developed herein, as well as an independent finite element simulation. Solution: The Ansys software has been used to run the finite element analysis, with two-dimensional elements ... materials also extends in the modeling domain where the magneto-elastic equations replicate the electro- elastic ones describing the piezoelectric effect. In essence, the equations that descri...

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... three-dimensional state of stress is the state of plane stresses where the only non-zero stresses are the normal stress and the tangential stress case where Eq. (5.190) reduces to: The Tresca ... resist and of enhancing the resolution. The exposed and unexposed areas of the resist have different solubilities and the exposed 33 8 Chapter 5 Problem 5.6 The microdevice in Fig. 5...

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... end deflection and slope can be found and expressed in the known manner: The equations of the three global compliances entering Eqs. (2.166) are quite complex and are not given explicitly here. ... determined with respect to the free end. Example 2.18 Find the bending-related compliances connected to the midpoint of a microcantilever of length l and of constant cross-section i...

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... will be analyzed next that studies the free displacement in terms of the defining geometry. 172 Chapter 3 where is the out -of- the-plane stiffness of one curved spring. The six out -of- the-plane compliances ... loading and having all other geometrical and material properties identical to the ones of the bent beam serpentine spring. Answer: Stiffness of bent beam serpentine spr...

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... function of the fraction c and the distance x, in the case where The relative force difference of Eq. (4.26) increases non-linearly with c increasing and decreases quasi-linearly when x increases. ... calculating the interaction force between the coil and the magnet of Fig. 4 .38 (a) is by expressing the magnetic-electromagnetic energy in a different fashion, namely: where R is th...

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... the compliances above define any of the flexure microhinges that have been analyzed in Chapter 2. The inertia force and moment are: The unknown acceleration a can be determined when either the ... time, the stiffness of each of the inclined-beam springs are known – given in Eq. (3. 18) of Chapter 3. As a consequence, the nominal point of operation is determined, as given by Eqs....

Ngày tải lên: 10/08/2014, 05:20