Nonlinear high-order dynamic stability of AL-foam flexible cored sandwich beam with variable mechanical properties and carbon nanotubes-reinforced composite face sheets in thermal environment

In this paper, the nonlinear dynamic stability analysis of sandwich beam including AL-foam flexible core and carbon nanotubes-reinforced composite face sheets subjected to axial periodic load are investigated by using generalized differential quadrature method. The flexible core of sandwich beam is made of Aluminum alloy foam with variable mechanical properties in the thickness direction. With considering the high-order geometrical nonlinearity in the core and face sheets, the high-order sandwich panel theory and modified couple stress theory are employed for AL-foam flexible core and face sheets, respectively. The governing nonlinear partial differential equations of dynamic stability are derived from the Hamilton’s principle and then discretized by using generalized differential quadrature method to convert them into a linear system of Mathieu–Hill equations. These formulations lead to nine partial differential equations which are coupled in axial and transverse deformations. The boundaries of the instability region are achieved by Bolotin’s method and are illustrated in the dimensionless nonlinear excitation frequency (Ω NL) and excitation frequency ratio (Ω NL/Ω L) to load amplitude plane. A parametric study is carried out to investigate the influence of some important parameters such as slenderness ratio, face sheet thickness, temperature rise, carbon nanotube volume fraction, static load factor, coefficients of Pasternak foundation, and end supports on the nonlinear dynamic instability characteristics of AL-foam core sandwich beam. The numerical results show that with temperature increasing, the nonlinear excitation frequency (Ω NL) and width of corresponding unstable zone decrease, but dynamic frequency ratio (Ω NL/Ω L) and associated unstable region increase. With an increase in the application of sandwich structures for compressible core in advanced industries such as spacecraft, high-speed aircraft, naval vessels, transportation, and automobiles, a further interest in the problem-involving dynamic instability of structures has resulted. Because of their applications, sandwich structures are frequently exposed to periodic axial compressive forces and so the dynamic instability has been a very important topic in structural dynamics and is of practical importance in different engineering industries.