Free and forced vibrations of trusses by Fourier decomposition, and homotopy methods for nonlinear matrix eigenvalue problems (I) Methods

AbstractVibrations of elastic frames or trusses are investigated by use of Fourier/frequency domain methods, using classical solutions of linear hyperbolic PDEs with constant coefficients and angle-preserving connections of beams (by clamping). Separation of variables is used, e.g., A(x,μ)eμt. For free vibrations, eigensolutions (in particular their values μ=α+iβ) are determined homotopically and individually, employing systems of quasilinear ODEs, usually explicit. Additionally to the methods in Part (I), properties and supplements are presented in Part (II)