Free vibration of electro-magneto-thermo sandwich Timoshenko beam made of porous core and GPLRC

In this article, free vibration behavior of electro-magneto-thermo sandwich Timoshenko beam made of porous core and Graphene Platelet Reinforced Composite (GPLRC) in a thermal environment is investigated. The governing equations of motion are derived by using the modified strain gradient theory for micro structures and Hamilton&apos;s principle. The magneto electro are under linear function along the thickness that contains magnetic and electric constant potentials and a cosine function. The effects of material length scale parameters, temperature change, various distributions of porous, different distributions of graphene platelets and thickness ratio on the natural frequency of Timoshenko beam are analyzed. The results show that an increase in aspect ratio, the temperature change, and the thickness of GPL leads to reduce the natural frequency; while vice versa for porous coefficient, volume fractions and length of GPL. Moreover, the effect of different size-dependent theories such as CT, MCST and MSGT on the natural frequency is investigated. It reveals that MSGT and CT have most and lowest values of natural frequency, respectively, because MSGT leads to increase the stiffness of micro Timoshenko sandwich beam by considering three material length scale parameters. It is seen that by increasing porosity coefficient, the natural frequency increases because both stiffness and mass matrices decreases, but the effect of reduction of mass matrix is more than stiffness matrix. Considering the piezo magneto-electric layers lead to enhance the stiffness of a micro beam, thus the natural frequency increases. It can be seen that with increasing of the value of <i>W_GPL</i>, the stiffness of microbeam increases. As a result, the value of natural frequency enhances. It is shown that in <i>h_c/h</i> = 0.7, the natural frequency for <i>W_GPL</i> = 0.05 is 8% and 14% less than its for <i>W_GPL</i> = 0.06 and <i>W_GPL</i> = 0.07, respectively. The results show that with an increment in the length and width of GPLs, the natural frequency increases because the stiffness of micro structures enhances and vice versa for thickness of GPLs. It can be seen that the natural frequency for <i>a_GPL</i> = 25 &micro;m and <i>h_c/h</i> = 0.6 is 0.3% and 1% more than the one for <i>a_GPL</i> = 5 &micro;m and <i>a_GPL</i> = 1 &micro;m, respectively.