Archive | 2019
Effect of Axial Stresses of the Core on the Free Vibration Response of a Sandwich Beam with FG Carbon Nanotube Faces and Stiff and Flexible Cores
Abstract
In this article, a vibrational behavior of sandwich beams with stiff and flexible\xa0cores and face sheets reinforced with carbon nanotubes is investigated. Carbon\xa0nanotubes are used as materials with properties varying along the thickness. In\xa0order to model the behavior of faces, the Timoshenko beam’s theory is employed\xa0and also for modeling the behavior of the core, three-dimensional elasticity is\xa0used. The axial stresses of the core are considered in this model and therefore\xa0it is suitable for modelling two types of stiff and flexible cores. The equations\xa0of motion are derived using the variations of energy, and the Navier method\xa0is used to solve the equations of motion. Results are presented for different\xa0volumes of carbon nanotubes with different distributions along the thickness\xa0of the faces. In the case of stiff core, results show that the FG-V distribution\xa0has the highest natural frequency and the FG-Λ distribution has the lowest\xa0natural frequency in all cases. For flexible core, the FG-X distribution leads to\xa0the highest natural frequency and also the FG-O distribution has the\xa0 lowest\xa0natural frequency. Furthermore, results indicate that an extended high-order\xa0sandwich panel theory is a suitable model for analysis of stiff and flexible core\xa0sandwich panels. It must be mentioned for the cores made of stiff materials,\xa0the normal stress along the length of the core must be considered. It is due to\xa0the fact that the obtained results show that ignoring the normal stress along\xa0the length of the core leads to the large difference in the natural frequency\xa0of the system. In this article, due to the high order displacement field of the\xa0core, the flexibility of the core can be seen in the modeling. Additionally,\xa0since the term σc\xa0xx of the core is considered in the strain energy, a stiff core\xa0can be modeled. In many works the axial stresses of the core is removed from\xa0equations, therefore according to the results of sandwich beam with stiff core,\xa0lots of errors will be observed. Therefore, a proposed theory in this research\xa0can easily model a sandwich beam with two types of stiff and flexible cores.\xa0Since the Timoshenko beam theory is also implemented for modeling faces,\xa0different pattern of CNTs can be investigated accurately.