Transverse Free Vibration of Pre-stressed Heavy Columns Laminated from Two-Hybrid Materials with Circular Cross-Section

This study investigates the explicit stiffness of laminated members and their application to dynamic pre-stressed column elements. The paper focuses on two main areas. First, the stiffness of circular cross-sections laminated from two-hybrid materials is formulated in terms of axial stiffness, flexural stiffness, mass per unit length, and mass moment of inertia. Numerical examples of explicit stiffness are detailed. Second, the explicit stiffness of laminated members is applied to dynamic pre-stressed column elements related to free vibration. The governing differential equation for the transverse free vibration of laminated heavy columns, including rotary inertia and pre-stress effects due to external load and self-weight, is derived. The differential equation is solved numerically to obtain natural frequencies and mode shapes. To validate the solution, the natural frequencies are compared with those obtained from the finite element analysis. The numerical experiments present the effects of varying column parameters on the natural frequencies, which are documented in tables and figures.