Frequencies of rotating tapered timoshenko beams with different boundary conditions

Khulief, Y. A.; Bazoune, Abdelaziz

doi:10.1016/0045-7949(92)90189-7

Cited by 31 publications

(23 citation statements)

References 14 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…Centrifugal force K Flexural stiffness matrix K G Geometric stiffness matrix K II , K JJ Nodal stiffness matrices of nodes (1) and (2) Rotating beams are widely used in the aerospace and mechanical engineering structures such as helicopter rotor blades, spacecraft with flexible appendages and windmills; thus, they have been extensively studied [1][2][3][4][5][6][7]. Understanding the response of these elements to both static and dynamic loads provides designers with important information to evaluate the performance of rotating machinery.…”

Section: A(x)mentioning

confidence: 99%

Basic Displacement Functions in Analysis of Centrifugally Stiffened Tapered Beams

Attarnejad

Shahba

2011

Arab J Sci Eng

View full text Add to dashboard Cite

Introducing the concept of basic displacement functions (BDFs), a new beam element is presented for the analysis of rotating tapered beams. BDFs are obtained using the energy method; i.e., the unit-load method. Following the basic principles of structural mechanics, it is shown that the shape functions and consequently the structural matrices can be derived in terms of BDFs. The method is a combination of flexibility and stiffness methods and is considered as the logical extension of the conventional finite element method. The method is employed for both static and free vibration analyses of different types of tapered beams, and the results compare well with those in the literature. Finally, the effects of the taper ratio, hub radius and rotating speed parameter on the natural frequencies and static deflection are investigated. The results obtained are satisfactory even for only a few elements.

show abstract

Section: A(x)mentioning

confidence: 99%

Basic Displacement Functions in Analysis of Centrifugally Stiffened Tapered Beams

Attarnejad

Shahba

2011

Arab J Sci Eng

View full text Add to dashboard Cite

show abstract

“…(19)(20)(21)(22)(23)(24)(25)(26)(27) at x 0 = 0, and using the correlations defined in Table 2, the following equations are obtained Table 3 DTM theorems adopted for boundary conditions…”

Section: Solutionmentioning

confidence: 99%

“…Yokoyama [26] used the finite element method to calculate the natural frequency of rotating uniform Timoshenko beams. Khulief and Bazoune [27] developed finite element method for different deformation, rotary inertia and centrifugal stiffening and solved rotating tapered Timoshenko beams for different combinations of the fixed, hinged and free boundary conditions. The free vibration characteristics of rotating Timoshenko beams have been subject to extensive studies by Lee and Lin [28], Du et al [29], Nagaraj [30] and Lin and Hsiao [31].…”

mentioning

confidence: 99%

Vibration analysis of a rotating Timoshenko beam with internal and external flexible connections

Talebi

Ariaei

2014

Arch Appl Mech

View full text Add to dashboard Cite

An analytical method is presented to determine the vibration characteristics of a rotating Timoshenko beam with variable cross section and intermediate flexible connections using the differential transform method. Based on the application of Timoshenko beam theory on separate beams and the compatibility requirements on each connection point, the correlations between every two adjacent spans are obtained. The formulation is extended to a point where it would be able to evaluate the cases with internal and external flexible connections. The results will be validated against those reported in the literature and compared with the ones from the modal test. A number of parametric studies are conducted to assess the stiffness of elastic connections, rotating speed, hub radius and tapered ratio effects on the beam natural frequencies and mode shapes. It is observed that by changing the stiffness of the intermediate springs, the general formulation developed here can cover a large array of problems such as cracked or intermediately constrained beams.

show abstract

“…Bazoune and Khulief [3] developed a finite beam element for vibration analysis of a rotating double-tapered Timoshenko beam. Khulief and Bazoune [9] extended the work in Bazoune and Khulief [3] to account for different combinations of the fixed, hinged, and free end conditions. In this study, as an extension of the authors' previous works [8,17,18], free vibration analysis of a rotating, double-tapered, cantilever Timoshenko beam that undergoes flapwise bending vibration is performed using the differential transform method (DTM), which is an iterative procedure to obtain analytic Taylor series solutions of differential equations.…”

Section: Introductionmentioning

confidence: 97%

Flapwise bending vibration analysis of a rotating double-tapered Timoshenko beam

Őzdemir

Kaya

2007

Arch Appl Mech

View full text Add to dashboard Cite

In this study, free vibration analysis of a rotating, double-tapered Timoshenko beam that undergoes flapwise bending vibration is performed. At the beginning of the study, the kinetic-and potential energy expressions of this beam model are derived using several explanatory tables and figures. In the following section, Hamilton's principle is applied to the derived energy expressions to obtain the governing differential equations of motion and the boundary conditions. The parameters for the hub radius, rotational speed, shear deformation, slenderness ratio, and taper ratios are incorporated into the equations of motion. In the solution, an efficient mathematical technique, called the differential transform method (DTM), is used to solve the governing differential equations of motion. Using the computer package Mathematica the effects of the incorporated parameters on the natural frequencies are investigated and the results are tabulated in several tables and graphics.

show abstract

Frequencies of rotating tapered timoshenko beams with different boundary conditions

Cited by 31 publications

References 14 publications

Basic Displacement Functions in Analysis of Centrifugally Stiffened Tapered Beams

Basic Displacement Functions in Analysis of Centrifugally Stiffened Tapered Beams

Vibration analysis of a rotating Timoshenko beam with internal and external flexible connections

Flapwise bending vibration analysis of a rotating double-tapered Timoshenko beam

Contact Info

Product

Resources

About