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The governing differential equation of the actuator is forth order and highly non-linear.
Linear up to forth order expansion for in-plane and out-of-plane displacements, in the thickness plate direction, has been compared.
Theories with forth order displacement fields in the thickness layer/plate direction z are implemented by referring to the Unified Formulation by Carrera.
They had shown that the backward mapping is achievable via a forth order equation while we have employed a sixth order one due to a tight integration with the caustic geometry.
The main idea is to construct the reproducing kernel space satisfying the conditions for determining solution of the new type of Emden Fowler equations stated in the third and forth order.
To derive the Emden Fowler type equations of third and forth order, we use the sense of Eq. (2) and set textstylebegin{cases} x^{-beta},frac{mathrm{d}^{p}}{mathrm{d}x^{p}}(x^{beta},frac{mathrm{d}^{q}}{mathrm{d}x^{q}})u=H( x,u(x)), u(0)=u_{0},qquad u'(0)=0.
Similar(53)
Alexis then sallies forth, ordering Heather to stop talking, and at long last, Tamra has had "enough".
But, this summer, that decision was reversed by the E.E.O.C., which, after some procedural back-and-forth, ordered the agency to investigate the matter.
d Forth-order modal shapes of catenary.
The resulting model was solved by a forth-order Runge-Kutta algorithm.
In the mathematical model, differential equations were solved with forth-order Runge Kutta method.
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