By Min-hang Bao, S. Middelhoek
A few years in the past, silicon-based mechanical sensors, like strain sensors, accelerometers and gyroscopes, all started their winning improve. each year, enormous quantities of thousands of those units are offered, customarily for scientific and car purposes. The airbag sensor on which learn already all started numerous a long time in the past at Stanford college are available in each new automobile and has stored already a variety of lives. strain sensors also are utilized in glossy digital blood strain gear. Many different mechanical sensors, generally invisible to the general public, practice invaluable features in numerous commercial and purchaser items.
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Additional resources for Micro Mechanical Transducers - Pressure Sensors, Accelerometers and Gyroscopes
The result is applicable to many micro structures with some minor modifications. First, we consider the energy stored in an element section, dx, at a position x on the beam as shown in Fig. 14. The coordinate system is taken as before with the x-axis at the centroidal line of the beam and the z-axis in the thickness direction and downwards. The displacement of the beam in the zdirection is a function of x and t, w(x,t). (1) The potential energy As discussed in w for a pure bending in the x-z plane, the stress and strain in the beam are: e = - z w " ( x , t ) and T = - E z w " ( x , t ) , respectively.
Bao, H. Yang, S. Shen, D. Lu, A micromachined piezoresistive angular rate sensor with a composite beam structure, Sensors and Actuators, Vol. A72 (1999) 217223  K. Tanaka, Y. Mochida, M. Sugimoto, K. Moriya, T. Hasegawa, K. Atsuchi, K. Ohwada, A micromachined vibrating gyroscope, Sensors and Actuators A50 (1995) 111115 w Stress and strain 23 Chapter 2 Basic mechanics of beam and diaphragm structures It is well known that silicon is an excellent solid state material. Therefore, the mechanical properties of silicon mechanical structures are ideally governed by the theory of elasticity in a large temperature range.
The same is true for Trr and Tzz. 2) This means that the stress tensor matrix T is symmetric. Therefore, it has only six independent components. 3) w Strain According to the theory of elasticity, deformation inside the material will be produced by the stresses. Let the components of a displacement for point P(x,y,z) be u(x,y,z), v(x,y,z) and w(x,y,z) in the x-, y- and z-directions respectively. The incremental displacement between point P(x,y,z) and P'(x+Ax, y+Ay, z+Az) can be expressed as: r 0u 0u ~u "~ Av = A Ov bv ~w Ow Ov Oz Oz ~u Tx 0 0 \ g o 0 ~v 2 0y 1(~9u -2 0y 0 + Ov) Ox l(~gu+Ow) ,-2 /gz l (~u ~w) -m(a + 0x 0x 0 l(0u+0w) -2 ~gz Oz+Ox l (Ov -20z /gy + 0 Ow) Oy ax" l Azj Chapter 2.