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Matrices were formulated, which contained hydroxypropyl methylcellulose (HPMC) as a matrix-forming agent, together with lactose monohydrate and microcrystalline cellulose as filler.
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Meanwhile, wave reflection and transmission matrices are formulated for cross section area discontinuity condition.
Wave reflection and transmission matrices are formulated, accounting for general support conditions.
The generalized internal nodal and gravity forces for super elements as well as the accurate tangential stiffness matrices are formulated.
Stiffness and mass matrices are formulated via the conventional displacement method and the eigenequation is then solved.
The fuzzy comparison judgment matrices are formulated according to the suggestions of the maintenance staff, which is included in Additional file 1: Annexure A. Fig. 5 Hierarchy structure.
Based on the sufficient conditions, the explicit expression of the desired filter gain matrices is formulated in terms of linear matrix inequalities.
Nonlinear Green Lagrange axial strains are introduced in the governing equations of a viscoelastic composite and new nonlinear damping and stiffness matrices are formulated including initial stress effects.
As a prerequisite for the wave propagation analysis, dispersion equations are solved, Green's matrices are formulated and Somigliana's identities are derived for an isolated curved segment.
As a result of expanding the dynamic orthogonality conditions, mass and stiffness perturbation matrices are formulated by the initial information of undamaged structures as well as the structure's modal parameters before and after the occurrence of damages.
General compliance and stiffness matrices are formulated for the virtual hinge under in-plane and out-of-plane loads by combining the transformed compliances of the individual hinge segments.
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