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A substructure procedure which includes the foundation effects in the motion equations and the application of the dynamic solver of a commercial package is addressed.
First order shear deformation theory of shells accompanied with the Donnell type of kinematic assumptions are used to establish the general motion equations and the associated boundary conditions.
The thermal effects are also included in the motion equations and the material properties of CNTRCs are assumed to be temperature-dependent.
Analytical solutions for rotational motion equations and torque-free motion are discussed in terms of the elliptic functions and by the application of some simplification to get an approximated solution.
The first is a slightly modified Mindlin theory, including a shear correction factor, while in the second the use of the shear correction factor is replaced by stress components that exactly satisfy elasticity motion equations and plate face boundary conditions.
The classical linear and angular momentum theorems are suitably extended for higher order inertia, from which the local motion equations and the moment equilibrium equations (stress symmetry) can be derived.
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Modifying the continuity equation and motion equation and adding the scalar potential of initial flow help to derive the analytical wave vectors of the P- and S waves.
The elastic wave vector in seepage media can be derived by improving the motion equation and the continuity equation, as well as considering the initial seepage potential.
Based on the elastic theory of transient flow, the motion equation and continuity equation of the transient flow are established, and the transient flow model of long-distance pipeline is derived.
However agreement between TPPinsp-P and TPPinsp calculated from respiratory motion equation and chest wall elastance (TPPinsp-E) was weak with Band-Altman bias (TPPinsp-E - TPPinsp-P) = 4.5 ± 8.9 [95%CI −13 22].
Analysis of the nonlinear behavior of the double clamped silicon nanowire resonator with the consideration of the nonlocal effect has been made based on the Duffing motion equation and the Galerkin's method.
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Justyna Jupowicz-Kozak
CEO of Professional Science Editing for Scientists @ prosciediting.com