Abstract
The dynamic response of lattice-type structures, assuming small displacements, may be described by the following set of four matrix equations: (1) Equation of consistent displacements; (2) joint equation of equilibrium; (3) force displacement equation; and (4) equation of support. The response function or indicial flexibility matrix is formed of terms that are solutions of the partial differential equations describing the transverse, torsional, and longitudinal vibrations of uniform, slender beams. The set of matrix equations becomes a set of linear, algebraic equations when transformed to the Laplace domain. Solutions that are carried out in the Laplace domain yield expressions for displacements, rotations, end moments, and forces in terms of the transform variable. Inversions are carried out in terms of series expansions of orthogonal functions. External damping, together with forcing function cut-off, is introduced to assure the uniform convergence of the series for all values of time. The application of the equations to the externally damped cantilever beam and to the unsymmetrical portal verifies the validity of the method.
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