Calculation of the Natural Frequencies of a Beam–Mass System Using Finite Element Method

In this study, the natural frequencies of an Euler-Bernoulli type beam with a mass are calculated. The beam is supported with different end conditions. The mass is located on different locations. The linear natural frequencies are calculated by using finite element method for the first five modes. Results are compared with those of exact and other approximate methods

Linear forced in-plane and out-of-plane vibrations of frames having a curved member

The forced, in-plane and out-of-plane vibrations of frames comprised of straight and curved members are investigated using Finite Element Methods. The straight and curved beams are assumed as Euler-Bernoulli type and they have circular cross-sections. The frame lies in a single plane. In the analysis, elongation, bending and rotary inertia effects are included. Four degrees of freedom for in-plane vibrations and three degrees of freedom for out-of-plane vibrations are assumed. The in-plane and out-of-plane point and transfer receptances are obtained in order to determine the sensitive and non-sensitive frequency interval of the frame system

Non-linear transverse vibrations and 3:1 internal resonances of a tensioned beam on multiple supports

In this study, nonlinear transverse vibrations of a tensioned Euler-Bernoulli beam resting on multiple supports are investigated. The immovable end conditions due to simple supports cause stretching of neutral axis and introduce cubic nonlinearity to the equations of motion. Forcing and damping effects are included in the analysis. The general arbitrary number of support case is investigated and 3, 4, and 5 support cases analyzed in detail. A perturbation technique (the method of multiple scales) is applied to the equations of motion to obtain approximate analytical solutions. 3:1 internal resonance case is also considered. Natural frequencies and mode shapes for the linear problem are found for the tensioned beam. Nonlinear frequencies are calculated; amplitude and phase modulation figures are presented for different forcing and damping cases. Frequency-response and force-response curves are drawn. Different internal resonance cases between modes are investigated. © Association for Scientific Research