A refined dynamic theory for viscoelastic cylindrical shells and cylindrical laminated composites, Part 1: General theory

Through the use of a new technique, approximate theories are developed for the dynamic response of viscoelastic cylindrical shells and cylindrical laminated composites (CLC). The new technique eliminates the inconsistencies between the deformation shapes assumed over the thickness of the shell and the boundary or interface conditions to be satisfied on its lateral surfaces. Accordingly, the theory correctly predicts the dynamic behavior of shells or CLC without using any correction factors. Due to its length, the work is divided into two parts. The first part is devoted to the development of the approximate theories and the second part to the assessment. In this part, first the approximate equations of a single viscoelastic cylindrical shell are derived. Then, a discrete model (DM) is proposed for a composite made of viscoelastic laminae. In establishing DM, it is noted that the equations of a single shell hold also in each lamina of the composite. The equations of DM are completed by adding the interface continuity conditions to the above-mentioned equations. Finally, a continuum model (CM) is developed for a composite shell made of two alternating layers by using a smoothing operation. CM simplifies the determination of dynamic behavior of composite shells when the number of laminae is large. © 1989