Free vibration and bifurcation buckling analysis of folded-plate structures using the harmonic-coupled finite strip method

Abstract

© Civil-Comp Press, 2014. Basic dynamic features of the folded-plate structures are determined by free vibration, which is measured by natural frequencies and mode shapes of vibration. This is of great importance in defining of the response of structures to dynamic loading. Stability and instability of a statically equilibrium state are conventionally defined in terms of the free motions of the system following an infinitesimal and once-and-for-all disturbance from the equilibrium state. Static bifurcation buckling behavior of the folded-plate structures can be obtained from linear equations, solving the standard characteristic-value problem by a matrix of initial stress instead of the mass matrix in free vibration. This paper discusses alternative solvers for the characteristic equations of the basic functions (or eigenfunctions) for various boundary conditions, where the characteristic equations are derived from the beam vibration equation. It analyzes the effect of alternative solvers on the accuracy of basic functions and their integrals, whilst comparing the results to the original (semi-)analytical solution. A hybrid method for accurately solving characteristic equations and obtaining the required integrals is presented, along with its reference Open Source implementation. An extensive test suite has been developed to verify the method and its implementation for the first one hundred modes of all presented edge boundary conditions.