Basic displacement functions for centrifugally stiffened tapered beams

Abstract

SUMMARYIntroducing the concept of basic displacement functions (BDFs), free vibration analysis of rotating tapered beams is studied from a mechanical point of view. Holding pure structural/mechanical interpretations, BDFs are obtained by solving the governing static differential equation of flapwise motion of rotating EulerBernoulli beams and imposing appropriate boundary conditions. Following the principles of structural mechanics, it is shown that exact shape functions and consequently structural matrices could be derived in terms of BDFs. The new shape functions capture the effects of variation of both cross-sectional area and moment of inertia along the element and the stiffening effect of centrifugal force. The method is employed to determine the natural frequencies of tapered rotating beams with different variations of cross-sectional dimensions and the results are in good agreement with those in the literature. Finally, the effects of rotational speed and taper ratio on the natural frequencies are investigated.

Derivation of an Efficient Non-Prismatic Thin Curved Beam Element Using Basic Displacement Functions

“…An important point about this element is that the new shape functions capture the effects of variation of curvature and second moment of cross-sectional area along the element; hence it is expected that the element shows a high rate of convergence. The efficiency of the idea of BDFs has been recently verified for straight Euler-Bernoulli [33,34,37] and Timoshenko [38,39] beam elements and in the present paper, new types of BDFs are introduced and the idea is extended for analysis of curved members which are mechanically more complicated than the straight ones.…”

Basic Displacement Functions in Analysis of Centrifugally Stiffened Tapered Beams

“…BDFs were firstly introduced by Attarnejad [29][30][31] to analyze non-rotating tapered Euler-Bernoulli beams. Later, Attarnejad and Shahba [32] proposed new shape functions in terms of BDFs to analyze rotating tapered EulerBernoulli beams where BDFs take into account the effects of both the varying cross-sectional area and the centrifugal force, and they obtained the BDFs by solving the static part of the governing differential equation using a power-series method. BDFs have been adopted for analysis of different beam problems [33][34][35][36][37].…”

A new nine-node element for analysing plates with varying thickness using basic displacement functions

“…Unlike the stiffness method which satisfies equilibrium equations only in certain integration points inside the elements, flexibility method guarantees that equilibrium equations are satisfied at all interior points of the element. Until now many papers are devoted to implement this technique in both static and dynamic analyses of straight or curved beams [33][34][35], which shows the flexibility of BDFs to cover a broad range of mechanical phenomenon.…”