{'fraction_non_alphanumeric': 0.012605042016806723, 'fraction_numerical': 0.0, 'mean_word_length': 5.572413793103448, 'pattern_counts': {'":': 0, '<': 0, '<?xml version=': 0, '>': 0, 'https://': 0, 'lorem ipsum': 0, 'www.': 0, 'xml': 0}, 'pii_count': 0, 'substrings_counts': 0, 'word_list_counts': {'cursed_substrings.json': 0, 'profanity_word_list.json': 0, 'sexual_word_list.json': 0, 'zh_pornsignals.json': 0}}
Free vibrations of Timoshenko beam-columns on Pasternak foundations

In this paper the free vibration and the stability of axially loaded Timoshenko beams on elastic foundation are analyzed through the dynamic stiffness matrix method. The study is carried out considering a two–parameter elastic soil which contains the characteristics of both the Winkler and the Pasternak foundations. The equation of motion and the exact dynamic stiffness matrix of a beam–column including the effect of shear deformation and rotatory inertia is derived. The eigenproblem of the beam–column is therefore solved through the application of the general Wittrick and Williams algorithm. The effects of soil characteristics as well as shear deformations and rotatory inertia on the natural frequencies of the beam-column are investigated. An extensive parametric study highlights the main parameters that characterize the dynamical behavior of the considered beam–column.