EQUATIONS of motionAn efficient method has been developed to analyze the natural frequencies of a Timoshenko-Ehrenfest beam with variable cross-sections undergoing free flexural vibration. The method uses a single element to discretize the beam and combines polynomial and trigonometric...
A simplified method,which may be called modal perturbation method,for solving the longitudinal free vibration of complicated beams with variable cross sections is introduced in the paper,In the method,the lower analytical longitudinal modal functions of the uniform beam are used to form an approximate...
In this paper, using the similarity between the longitudinal free vibration of a bar with variable cross section and the beam bending the longitudinal vibration function is obtained from the moment on the cross section of the bending beam. For some specified variation of cross section area of the...
varying rectangular cross-section of depth and breadth proportional to xs and xt, respectively, where both s and t are arbitrary real numbers for a truncated beam and arbitrary positive numbers for a sharp ended beam and x is the axial co-ordinate measured from the sharp end of the beam. ...
A two-noded curved beam element is employed based on a mixed finite element formulation based on Timoshenko beam theory by considering cross-sectional warping and the tests are performed over free vibration analyses. The new formulation of orthotropic Pasternak foundation for straight beam interaction ...
Moreover, the cross-section with variable thickness offers an advantageous degree of freedom for optimal structural design. Thermal gradient due to one-dimensional through-thickness steady heat conduction is considered. The theoretical formulations are based on Timoshenko beam theory and include the ...
the free vibration characteristics of a ship beam are predicted from Timoshenko's theory of elasticbeam of variable cross section by use of Galerkin's method. The results are evaluated by use of those obtained recently from Euler's theory [e.g., S. Abrate, J. Sound. Vib. 185 (4), 703...
Finally, the effectiveness of a proposed transfer matrix on the calculation of natural frequencies for a multi-step beam was verified. It is believed that the current method could help in the design of various structures, including beams with variable cross section.Boiangiu Mihail...
Spline-Method for Numerical Calculation of Natural-Vibration Frequency of Beam with Variable Cross-SectionSpline-Method for Numerical Calculation of Natural-Vibration Frequency of Beam with Variable Cross-SectionSplinemathematical modelingvibrations of beams with constantvariable...
Transient analysis of axially functionally graded Timoshenko beams with variable cross-section 2016, Composites Part B: Engineering Citation Excerpt : The fixed-end forces and element stiffness matrix are obtained from the CFM in Laplace domain (for elaborate explanation, please look Refs. [25–29])...