By Gang W.
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Additional info for Analyses of Sandwich Beams and Plates with Viscoelastic Cores
The general form of the GHM method  is formed using the stiﬀness matrix, K; ¯ are given by: and damping matrix, D; and mass matrix, M α) ˆ −ˆ α1 R · · · −ˆ αn R α ˆ1 Λ 0 0 .. 0 0 0 0 α ˆn Λ Ke + K0 (1 + −ˆ α1 RT K= .. . 32) M 0 ··· 0 0 α ˆ 1 ωˆ12 Λ 0 .. .. 0 .. 0 ··· 0 1 . D= 0 α ˆ n ωˆ12 Λ n ··· 0 0 α ˆ 1 2ωˆζ11 Λ 0 .. .. 0 .. 0 ··· 0 0 0 ˆ . 34) where ¯ Λ = G0 Λ ¯ R = RΛ Finally, we obtain the constant mass, damping, and stiﬀness matrix for the structure with viscoelastic materials.
The assumed modes method and conventional ﬁnite element method are outlined as well. All the analytical results are validated by experimental data. Chapter 4 sets up the assumed mode analysis for the sandwich plate. The results of natural frequency and loss factors are presented to compare with the previous experimental data. A parametric study of temperature eﬀects on the complex shear modulus is presented. We demonstrate that the natural frequency and loss factors vary with the change of the temperature.
After the parameters are determined, the GHM method is incorporated into conventional dynamic structural analytical techniques for structures with viscoelastic components. 25) where, M is a mass matrix, Ke is a stiﬀness matrix contributed from elastic components in the structures, and G is a complex shear modulus of a viscoelastic material. We assume there is only one viscoelastic material on the structure. 30) We demonstrate the case for only one mini-oscillator, N = 1. Because K0 is usually positive semi-deﬁnite, the above mass matrix may not be positive deﬁnite.