{'fraction_non_alphanumeric': 0.021986970684039087, 'fraction_numerical': 0.0, 'mean_word_length': 5.145, '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}}
A new simplified method for anti-symmetric mode in-plane vibrations of frame structures with column cracks

This paper is on the natural frequency and mode shape computation of frame structures with column cracks. First, a model of intact frame structures is built to perform vibration analysis. Beam elements are considered as lumped masses and rotational springs at the storey levels of frames. Equivalent model of columns and lumped mass-stiffness effects of beams have been combined to carry out continuous solution for the anti-symmetric mode in-plane vibrations of frames. In addition, frame systems with multiple column cracks are analyzed in terms of anti-symmetric mode vibration characteristics. Cracks are considered as massless rotational springs in compliance with the local flexibility model. Compatibility and continuity conditions are satisfied at crack and storey locations of the equivalent column, modeled using the Euler–Bernoulli beam theory. The proposed method is tested for single-storey single- and multi-bay, H-type and double-storey single-bay frame systems with intact and cracked columns. Results are validated by those given in the current literature and/or obtained by the finite element analyses.