Flexural wave dispersion characteristics of imperfect Ti-6Al-4V foam circular cylindrical shells in a thermal environment

The present paper is mainly focused on analyzing the flexural wave dispersion of imperfect Ti-6Al-4V foam circular cylindrical shells in a thermal environment. The pores were supposed to be distributed across the thickness (z-direction) in the form of three different patterns as follows: symmetric porosity distribution (SPD), asymmetric porosity distribution (ASPD) and uniform porosity distribution (UPD). Besides, various kinds of temperature variations, including sinusoidal, linear and uniform temperature variations, were studied. The strain-displacement relationship of the shell was derived based on the first-order shear deformable theory (FSDT) of shells. Hamilton's principle was also applied to obtain the governing equations of metal foam shells which were then solved using an analytical method. Finally, influences of different parameters including circumferential wave number, different kinds of temperature variation, temperature change, radius to thickness ratio R/h, types of porosity distribution across the thickness, porosity coefficient and mode number on the variations of phase velocity and wave frequency were investigated and the results were illustrated and discussed.