The natural frequency (f) of a piezoelectric cantilever beam is described by the following equation:, where E = Modulus of elasticity, I = Area moment of inertia, L = Length of the cantilever beam, and m = Mass of proof mass (or end mass). The area moment of inertia for an arbitrary shape R with respect to an arbitrary axis (for example, x-axis) is related by: (a) What is the dimension of an area moment of inertia? (b) If the thickness of a piezoelectric cantilever beam increases, does the natural frequency increase or decrease? (c) Both the thickness and width of a piezoelectric cantilever beam can change the natural frequency. Which parameter (thickness or width) will lead to the natural frequency change more significantly? Briefly explain your answer.
The natural frequency (f) of a piezoelectric cantilever beam is described by the following equation:, where E = Modulus of elasticity, I = Area moment of inertia, L = Length of the cantilever beam, and m = Mass of proof mass (or end mass). The area moment of inertia for an arbitrary shape R with respect to an arbitrary axis (for example, x-axis) is related by:
(a) What is the dimension of an area moment of inertia?
(b) If the thickness of a piezoelectric cantilever beam increases, does the natural frequency increase or decrease?
(c) Both the thickness and width of a piezoelectric cantilever beam can change the natural frequency. Which parameter (thickness or width) will lead to the natural frequency change more significantly? Briefly explain your answer.
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