Analytical Solutions to the Differential Equation of TransverseVibrations of a Piecewise Homogeneous Beam in the Frequency Domain for the BoundaryConditions of Various Types

We obtain an analytical solution for the differential equation of transverse vibrations of a piecewise homogeneous beam in the frequency domain for various types of boundary conditions. All calculations use only addition, multiplication, and inversion of square matrices of second order. The formulas are such that, when using them for layer-by-layer recalculation, the rounding error does not accumulate since the exponential functions in some expressions have exponents with nonpositive real parts.

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