By Gang W.

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**Extra resources for Analyses of Sandwich Beams and Plates with Viscoelastic Cores**

**Sample text**

Finally, the conclusions are presented in the Chapter 7. The mass and stiﬀness matrices in the assumed modes method for the sandwich plate analyses are present in the Appendix. 18 Chapter 2 Viscoelastic Materials This chapter presents dynamic characteristics of viscoelastic damping materials and outlines the diﬀerent existing mathematical models. Classical representations of viscoelastic materials include the Maxwell model, the Kelvin-Voigt model, and the Zener model (Standard Solid Model). We will show that these models cannot capture the behavior of viscoelastic damping materials.

Because both ATF and ADF methods lead to a ﬁrst order damping model, only state space forms can be used when combined with structural analytical models. An unfortunate consequence of using this method is that the global mass matrix is singular. 3 Golla-Hughes-McTavish Model The Golla-Hughes-McTavish (GHM) method is a technique for deriving viscoelstic ﬁnite elements from commonly used elastic ﬁnite elements and measurements of frequency dependent complex modulus. 6. The eﬀect of the mini-oscillator includes a second order rational function involving three parameters.

We are especially interested in developing a method that alleviates the large number of degrees of freedom needed to analyze sandwich beams using CFEM or AM coupled with internal dissipation coordinate methods such as GHM [23, 42] or ADF [38]. One possible approach was developed by Douglas [18] based on the governing equation given by Mead and Marcus [44]. The progressive wave solution was used to calculate frequency response functions using an impedance matrix. Douglas was the ﬁrst to explore wave solutions in order to implicitly account for the frequency dependent complex modulus of viscoelastic core in the solution method.

### Analyses of Sandwich Beams and Plates with Viscoelastic Cores by Gang W.

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