Mechanics of Microelectromechanical Systems - N Lobontiu and E Garcia Part 9 docx

... 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...

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

... free end’s deflection by means of Castigliano’s displacement theorem, the real stiffness is: where the denominator is: It can be seen that the combined Eqs. (1. 197 ) and (1. 198 ) are not identical ... 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:...

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...

Ngày tải lên: 10/08/2014, 05:20

... 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...

Ngày tải lên: 10/08/2014, 05:20

... 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 unit. When ... (the stiffness defining the elastic properties of the U-spring when the body translates about a direction perpendicular to the main one and is contained in the plane of the microdevice) a...

Ngày tải lên: 10/08/2014, 05:20

... 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 of a thin curved member ... the deflection at point 1 depends linearly on the temperature increase and non-linearly on the geometric parameters defining the half bent beam. An example will be analyzed next that st...

Ngày tải lên: 10/08/2014, 05:20

... 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 the...

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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 ... enable achieving the level of torque needed when Answer: Problem 4.8 A microcantilever of given dimensions and is used as an electrostatic actuator. Find the gap between the microcantileve...

Ngày tải lên: 10/08/2014, 05:20

... The large-displacement theory is non- linear, and effects of different loads do combine and affect each other and, together, they affect the deformed state of a MEMS component. In many instances, ... 4 and is rewritten here for convenience: 304 Chapter 5 The sine and cosine terms appear in Eq. (5.1 09) because of the inclination of the force with respect to the local referen...

Ngày tải lên: 10/08/2014, 05:20