An Analytical Solution for Natural Frequencies of Elastically Supported Stepped Beams with Rigid Segments
Özet
In this work, an analytical solution for the natural frequencies of elastically supported stepped beams with rigid segments is presented. The elastic end boundary conditions are modeled with a translational stiffness element, a rotational stiffness element, and an end-concentrated mass. This model is of great significance in machine construction studies. Under the assumption of Euler-Bernoulli beam theory, the non-dimensional equations of the motion and main equations that can give all of the boundary conditions were obtained by using Hamilton's principle. After deriving the transverse displacement functions by means of using the separation-of-variables technique, the frequency equation was found by setting the determinant of the coefficient matrix to zero. The natural frequencies of the transverse vibrations were found according to physical and geometric parameters. The method was validated by using FEM results and findings from the literature. This study indicates that the physical and geometric parameters of the elastic supports and rigid segments affect the natural frequencies of the beam. The revealed analytical method can be used to calculate the natural frequencies and mode shapes of all beam types, such as elastically supported uniform beams and single-step beams with or without concentrated mass and/or rigid segments.
Açıklama
Anahtar Kelimeler
rigid segment, stepped beam, elastic support, end masses, natural frequencies, Euler-Bernoulli beam
Kaynak
APPL MECH-BASEL
WoS Q Değeri
Scopus Q Değeri
Cilt
6
Sayı
1
