Abstract:Natural frequencies and free vibration are important characteristics of beams with non-uniform cross section. Hence, the solution for free vibrations of non-uniform beams is presented using a Laguerre collocation method. The elastically restrained beam model is based on the Euler-Bernoulli theory. Also, the non-uniform beam is rested on a non-uniform foundation (Winkler type). The Laguerre collocation method is introduced for solving the differential equation. This approach reduces the governing differential e… Show more
“…Celik [10] used Chebyshev Wavelet Collocation Method to consider vibration of non-uniform beams with various boundary conditions and with flexible end conditions. Ghannadiasl et al [11] studied the elastically restrained non-uniform beam modeled based on the Euler-Bernoulli theory using a Laguerre collocation method. The third group: Huang and Li [12] presented a novel approach based on transforming the differential equation of motion for transverse vibration of non-uniform Euler-Bernoulli beams into a Freed Holm integral equation.…”
The exact characteristic equation of frequency and mode shape for transverse vibrations of non-uniform and nonhomogeneous Euler Bernoulli beam with general non-classical boundary conditions at both ends.
“…Celik [10] used Chebyshev Wavelet Collocation Method to consider vibration of non-uniform beams with various boundary conditions and with flexible end conditions. Ghannadiasl et al [11] studied the elastically restrained non-uniform beam modeled based on the Euler-Bernoulli theory using a Laguerre collocation method. The third group: Huang and Li [12] presented a novel approach based on transforming the differential equation of motion for transverse vibration of non-uniform Euler-Bernoulli beams into a Freed Holm integral equation.…”
The exact characteristic equation of frequency and mode shape for transverse vibrations of non-uniform and nonhomogeneous Euler Bernoulli beam with general non-classical boundary conditions at both ends.
“…The vibration of non-uniform beams with different boundary conditions and flexible ends has studied by Selik [6] using the Chebyshev wavelet collocation method. The free vibration of beams with a nonuniform cross-section and placed on a fixed and linear Winkler bed based on the Euler-Bernoulli beam theory and using the Lager collocation method has been studied by Qanadiasl et al [7]. 3 rd groups: A new approach based on the transformation of the differential equation of transverse vibration of Euler-Bernoulli beams with non-uniform cross-section to Fredholm integral equations has introduced by Huang and Lee [8] Liu et al [9] have created new simple models for studying the free vibrations of Euler-Bernoulli FG conical beams using the spline finite point method.…”
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