Nonlinear thermo-electro-mechanical free vibrations of sandwich nanocomposite beams bonded with sensor layers considering pyroelectricity

An examination on the linear as well as nonlinear thermo-electro-mechanical free vibrations of a sandwich piezoelectric beam is performed in this research. Core layer has been strengthened with graphene platelets. Two piezoelectric layers as sensors are bonded to the bottom and top surfaces of the core layer. The formulation is developed for beams with general immovable end supports. A nonlinear integro-partial differential equation along with its nonlinear boundary conditions is discharged presuming a second order approximation for the nonlinear normal strain. The direct technique of multiple scales treats the nonlinear governing integro-partial differential equation along with its associated nonlinear boundary conditions. Subsequently, an analytical closed form relation is released for the estimation of amplitude dependent nonlinear natural frequencies. It is shown that the strengthening of a beam that is experiencing a thermal environment during its work with the graphene platelets becomes dysfunctional since it promotes the chance of static instability occurrence. On the other hand, it is seen that the pyroelectricity can postpone the static instability possibility. Furthermore, the pyroelectricity alleviates the hardening nonlinearity. Moreover, at large amplitude of vibrations, the influences of the temperature developing, the pyroelectricity, and the graphene platelet weight fraction decline.