Mechanics of Microelectromechanical Systems - N Lobontiu and E Garcia Part 5 pot

... boundary conditions: Having found these unknown reactions, the free end deflection and slope can be found and expressed in the known manner: The equations of the three global compliances entering ... 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 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

... 4. 25 as a 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 ... 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...

Ngày tải lên: 10/08/2014, 05:20

... 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 ... slope or the deflection of Eqs. (5. 10) can be measured directly (experimentally), namely: or: Example 5. 2 Determine the external acceleration by means of a flexure-hinge microacceleromete...

Ngày tải lên: 10/08/2014, 05:20

... 4 and is rewritten here for convenience: 304 Chapter 5 The sine and cosine terms appear in Eq. (5. 109) because of the inclination of the force with respect to the local reference frame xy of ... 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....

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

... 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

... produced by the combined action of the forces and and is: whereas the tip deflection is: Equations (2 .54 ), (2 .55 ) and (2 .56 ) enable finding the tip force components when and are available experimentally. 94 Chapter ... 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...

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 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