The Dynamic Stability of Quasi-Periodic and Aperiodic Multi-Segment Columns

In this work, Bernoulli–Euler columns, freely supported and loaded by a longitudinal force variable over time, are considered. The problem of dynamic stability is solved using the mode summation method. The applied research procedure allows the dynamics of the tested system to be described using the Mathieu equation. The influence of stiffness distribution in the Bernoulli–Euler beam on the value of coefficient b in the Mathieu equation is investigated. Structures are created using deterministic rules such as substitution rule, generation rule, recursion or inflation rule. The quasi-periodic structures that are taken into account are: the Fibonacci chain, the silver Fibonacci chain, the bronze Fibonacci chain, the octagonal chain, and the dodecagonal chain. The aperiodic structures that are taken into account are: the Severin chain, the Thue–Morse chain, the copper Fibonacci chain, the nickel Fibonacci chain, and the circular chain. The results obtained on the basis of numerical tests for structures with variable stiffness of the considered columns will be analyzed in order to compare and distinguish the factors that have the greatest impact on the change of natural frequencies and on the dynamic stability of the columns under consideration.