Fixed-free beam

If a distributed load p = FIL is applied along the length of a fixed-free beam, as shown in Figure 2.10, the deflection is given by... 

A fixed-free cantilever beam M-Test structure fabricated in Polyl of the PolyMUMPS process can also be used as a resonator by exciting it into resonance with an AC drive signal applied to a PolyO counter-electrode defined below the end of the beam. To estimate the resonant frequency we use the spring constant for a fixed-free beam that is 20 pm wide and 150 pm long subjected to a point load at its free end ... 

Beams are often subject to different boundary conditions and forces in MEMS design. A comprehensive reference for the bending of beams in different situations is Roark s formulas for stress and strain [4]. We considered a fixed-free cantilever beam that is subjected to a point load at its free end in the spring analysis above. The fixed-free boundary condition means that one end is fixed, so that both its displacement and slope do not change under the applied force. The other end of the beam is free to both move and change its slope in response to a point load F, as shown in Figure 2.7. In that case the deflection of the beam y(j ) as a function of position x is given by... 

Figure 2.7 Bending of a fixed-free cantilever beam subjected to a point load F at the free end.

Figure 2.10 Fixed-free cantilever beam subjected to a distributed load p along the length of the beam.

Produce a solid model of a fixed-free cantilever beam in the device layer of the SOIMUMPS process using L-Edit/MEMS Pro or a similar layout tool. An example of a cross section of a cantilever beam (not to scale) is shown in Figure 1.1 of the SOIMUMPS Design Handbook. If the thickness t of the beam is x pm, the width W should be lOx pm and the length L should be lOOx pm. What are... 

Figure 5.13 Temperature distribution for a fixed-free cantilever beam.

When a load is applied, if the product is to remain in equilibrium there must be equal force acting in the opposite direction. These balancing forces, as an example, are the reactions at the supports. For purposes of structural analysis there are several supports conditions that have been defined. The free (unsupported), simply supported, and fixed supports are the most frequently encountered. The free (unsupported) condition occurs where the edge of a body is totally free to translate or rotate in any direction. The fixed (clamped or built-in) support condition at the end of a beam or plate prevents transverse displacement and rotation. The condition can... 

A zigzag configuration may be seen as a number of separate beams each with one end fixed. The top beam is loaded (F) either along its entire length or at a fixed point. This load gives rise to deflection y at its free end and moment Mat the fixed end. The second beam is then loaded by moment M (upward) and load F(the effective portion of load F, as determined by the various angles) at its free end. This moment results in deflection yi at the free end and moment Mi at the fixed end (that is, the free end of the next beam). The... 

The levitated laser dye droplet was optically pumped by a pulsed (pulse length 5 ns, repetition rate 10 Hz), frequency-doubled Nd YAG laser (2 = 532 nm) in free-space optical setup. Droplet light emission was collected by a multimode optical fiber placed at an angle of approximately 50° relative to pump laser beam. Collected light was analyzed in a fixed-grating spectrometer with a resolution of FWHM 0.15 nm. 

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