So, the relations between the five mentioned dynamic equations (FxFx, FyFy, FzFz, MθMθ, MαMα) and the produced deformations (δxδx, δyδy, δzδz, θ, α) can be expressed by a 5×5 stiffness matrix, as follows:equation(16)[FxFyFzMθMα]=[AEL000003EI′L300000EIL302EIL2000Cwt3GL0002EIL20EIL][δxδyδzθα]
In the above equations, L, w and t gamma-Secretase inhibitor IX the cantilever?s geometrical parameters, representing the cantilever length, width and thickness, and E, G and ν are the mechanical properties of the cantilever, representing its modulus of elasticity, shear modulus and Poisson?s ratio, respectively. Also, A is the cross-sectional area and I′I′ is the moment of inertia about the cantilever?s vertical axis. In wood equation, when w « L, we will have C=1/3. The values of these geometrical and mechanical specifications have been listed in Table 3.
Geometrical parameters and mechanical properties of cantilever (Tafazzoli et al., 2004).Cantilever length L(μm)Cantilever width w(μm)Cantilever thickness t(μm)Probe tip height H(μm)Young?s modulus E(Gpa)Shear modulus G(Gpa)Poisson?s ratio (ν)2254811216966.540.27Full-size tableTable optionsView in workspaceDownload as CSV