ABSTRACT
This chapter investigates the combined impacts of the foundation's parameters, distribution pattern of the GPLs, and content of the reinforcing phase on the natural frequency of the multilayered beam-type elements resting on a visco-Pasternak medium. The equivalent material properties of each of the beam's layers will be obtained using the micromechanical procedure expressed in Part 1 (see Sections 2.3.2 and 2.3.4). The kinematic relations of the beam-type elements used in the analysis can be derived based on Reddy's TSDT of beams. After extracting suitable relations for the components of valid strains in terms of the displacement field of the problem, the governing equations will be derived by expanding the dynamic form of the principle of virtual work for the beams simulated with the beam hypothesis. The coupled set of the governing equations can be found in Eqs. (2.133)–(2.135). In the following section, a numerical illustrative study will be provided to discuss the influences of various terms on the damped dynamic behaviors of GPLR nanocomposite beams. It can be seen that increasing the content of the GPLs available in the polymeric matrix results in a remarkable increase in the dimensionless frequency of the system. Also, the dynamic response of the system can be easily damped using a greater damping coefficient for the visco-Pasternak medium.
