106
edits
Changes
Jump to navigation
Jump to search
Line 17:
Line 17: − + Line 32:
Line 32: + +
Analysis of Diamond Cantilever Vibration (view source)
Revision as of 18:44, 16 January 2013
, 18:44, 16 January 2013→Model
<math>\frac{d^4y}{dx^4}=-(\frac{\rho}{ET^2})\frac{d^2y}{dt^2}</math>
<math>\frac{d^4y}{dx^4}=-(\frac{\rho}{ET^2})\frac{d^2y}{dt^2}</math>
Knowing that the motion of the beam will be oscillatory let's us assume that the solution can be divided into two parts, one representing the maximum amplitude of the motion and the other representing the periodic nature of the motion.
Knowing that the motion of the beam will be oscillatory let's assume that the solution can be divided into two parts, one representing the maximum amplitude of the motion and the other representing the periodic nature of the motion.
<math>\frac{y(x,t)}{}=y_a(x)e^{i \omega t}</math>
<math>\frac{y(x,t)}{}=y_a(x)e^{i \omega t}</math>
<math>y_n = \sum_m{c_{nm}f_m}</math>
<math>y_n = \sum_m{c_{nm}f_m}</math>
We know that the solutions to the uniform case, as the eigenfunctions of a Hermitian matrix operation, are orthogonal. This means that taking the inner product of
[[Media:NonuniformAnalysisNew.pdf|Nonuniform-Width Analytical Model]]
[[Media:NonuniformAnalysisNew.pdf|Nonuniform-Width Analytical Model]]