(9)–(11), becomes a polynomials for f i (i = 0, 1, 2, 3) and f j g(j = 0, 1, 2), setting the coefficients of the polynomials to zero yields a set of algebraic equations.
Step 3: Substituting (44), (45) and (46) into (43) and setting the coefficients of the powers of i to be zero, one can obtain an over-determined nonlinear algebraic system in a i ( i = 1, …, n ) and c.
For the assumed superposition modulation (7), this can be easily achieved by setting the coefficients as (L_{A,n}^{s}=2^{n}) and (L_{B,n}^{s}=operatorname {j}cdot 2^{n}).
The governing equilibrium equations can be derived from Eq. 26, by integrating the displacement gradients by parts and setting the coefficients of δu 0, δv 0, δw 0, and δθ x,y to zero (Ferreira and Roque 2007, 2009).
where satisfiy (4.5), with the aid of Mathematica software; substituting (5.5) along with (4.5) into (5.2) and (5.4) yields a set of algebraic equations for setting the coefficients of these terms to zero yields a set of overdetermined algebraic equations with respect to, and.
Substituting Equations (9), (10), and (13) into the above equation, using variation technique and setting the coefficients of δu i, δw i, and δθ i equal to zero results into the following differential equations of motion for a DWNT ∂ N xi ∂ x = ρ A i ∂ 2 u i ∂ t 2, Open image in new window (15a).
