A New Dynamic Finite Element (Dfe) Formulation for Lateral Free Vibrations of Euler–bernoulli Spinning Beams Using Trigonometric Shape Functions

Free Vibration of Centrifugally Stiffened Uniform and Tapered Beams Using the Dynamic Stiffness Method

“…The reason for this can be attributed to the fact that for higher hub-o!set ratios or angular speeds, the centrifugal force terms dominate the (mechanical) bending sti!ness terms, and noting that the centrifugal terms are better represented by stepped approximation than the bending sti!ness terms. This accords with similar "ndings of a recently published paper [24].…”

Dynamic Finite Element Analysis of Extensional-Torsional Coupled Vibration in Nonuniform Composite Beams

“…The dynamic finite element (DFE) and its application to the dynamic analysis of various homogeneous, sandwich and composite flexible structural elements, is well established (see, e.g., Refs. [26,28,29]). In a number of their earlier publications, the authors have also demonstrated the applicability of the DFE to the free vibration analysis of uniform composite circular tubes and box beams, characterized by constant coefficients k 1 , k 12 , and k 2 , and exhibiting coupled extensional-torsional behaviour.…”

“…To achieve this refined formulation, the interesting features of the DFE methodology presented in the earlier works of the first author are exploited (see, e. g., Refs. [26,28,29]). Starting with integral Eqs.…”

“…By imposing the displacement and force boundary conditions, the underlined boundary terms disappear in expressions (5) and (6) [19][20][21][26][27][28][29]. Discretization of the domain into a certain number of 2-node, four degree-of-freedom beam elements, then leads to (see Fig.…”

Free Vibration Analysis of Curved Sandwich Beams: A Dynamic Finite Element

“…Therefore, the approximation space is defined using frequency dependent trigonometric basis functions to obtain the appropriate interpolation functions with constant parameters over the length of the element. DFE theory was first developed by Hashemi (1998), and its application has ever since been extended by him and his coworkers to the vibration analysis of intact (Hashemi et al,1999, andHashemi &Richard, 2000a,b) and defective homogeneous , sandwich (Adique & Hashemi, 2007, 2010 and laminated composite beam configurations (Hashemi & Borneman, 2005, and Hashemi & Roach, 2008a exhibiting diverse geometric and material couplings. DFE follows a very similar procedure as FEM by first applying the weighted residual method to the differential equations of motion.…”