{'fraction_non_alphanumeric': 0.012453300124533, 'fraction_numerical': 0.0, 'mean_word_length': 5.756302521008403, '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 vibration analysis of elastically restrained functionally graded curved beams based on the Mori–Tanaka scheme

ABSTRACT In this paper, free vibration analysis of elastically restrained functionally graded curved beams are presented based on the Mori–Tanaka scheme and modified Fourier series method. The effective material properties of the beam are evaluated by using the Mori–Tanaka scheme. The functions of displacements and rotation are represented in the form of a basic Fourier cosine series plus two auxiliary functions. By submitting modified Fourier series to governing equations and boundary conditions, the natural frequencies can be obtained through a generalized eigenvalue problem. A great deal of new results for elastically restrained functionally graded curved beams are presented.