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Mechanical behavior of materials 06 problem set 1

Mechanical behavior of materials 06 problem set 1

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3.032 Problem Set 1 Fall 2006 Due: Start of lecture, 9/15/06 1. Thin-ﬁlm silicon nitride cantilevers such as the one shown in Figure 1 are used in scanning probe microscopy, resonant frequency measurements, and electrostatic ac tuation. Let us approximate this cantilever as a clamped-free beam with a length of 200 µm, a width of 30 µm, and a thickness of 0.8 µm. Take the Young’s modulus of thin-ﬁlm silicon nitride to be 210 GN/m2 . The weight of the cantilever can be neglected. Image by OpenCourseWare. Adapted from work by KristianMolhave, Wikimedia Commons. Figure 1: Thin-ﬁlm silicon nitride cantilever. (a) If the free end of the beam contacts a surface (represented by a point load in Figure 1), and is deﬂected upwards by 1.0 µm, ﬁnd the magnitude of the point load. (b) Draw a free-body diagram of the beam. Sketch the shear and bending moment in the beam along its le ...
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