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Differential equations of motion for combined flapwise bending, chordwise bending, and torsion of twisted nonuniform rotor blades

TLDR
In this article, the differential equations of motion for the lateral and torsional deformations of twisted rotating beams are developed for application to helicopter rotor and propeller blades, and the generality is such that previous theories involving various simplifications are contained as subcases to the theory presented in this paper.
Abstract
The differential equations of motion for the lateral and torsional deformations of twisted rotating beams are developed for application to helicopter rotor and propeller blades. No assumption is made regarding the coincidence of the neutral, elastic, and mass axes, and the generality is such that previous theories involving various simplifications are contained as subcases to the theory presented in this paper. Special attention is given the terms which are not included in previous theories. These terms are largely coupling-type terms associated with the centrifugal forces. Methods of solution of the equations of motion are indicated by selected examples.

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Modelling and analysis of coupled flap-lag-torsion vibration characteristics helicopter rotor blades:

TL;DR: In this paper, a mathematical approach targeting the modelling and analysis of coupled flap-lag-torsion vibration characteristics of non-uniform continuous rotor blades is presented, which is used for the analysis of nonuniform rotor blades.
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Integration of Hydraulic Lag-Damper Models with Helicopter Rotor Simulations

TL;DR: In this article, the authors describe the design and integration of a generic hydraulic lag-damper model into an industrial helicopter rotor simulation code, in order to allow physically consistent improvements to helicopter performance studies.
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Vibratory characteristics of pretwisted cantilever trapezoids of unsymmetric laminates

TL;DR: In this paper, an approach based on the global energy principle is developed to examine the effects of initial twist upon the vibration response of cantilevered unsymmetric laminates of a trapezoidal planform.

Wind Turbine Blade Stress Analysis And Natural Frequencies

TL;DR: In this paper, the problem of wind turbine blades has been investigated and the following requirements for a wind turbine blade system have been defined: 1) aerodynamic performance, a t l e a s t i n t h e steady s t a t e cond i t i on, and 2) the requirement that the blades must be able to handle both static and dynamic loads.
References
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Book

Theory of elasticity

TL;DR: The theory of the slipline field is used in this article to solve the problem of stable and non-stressed problems in plane strains in a plane-strain scenario.

Simplified Procedures and Charts for the Rapid Estimation of Bending Frequencies of Rotating Beams

TL;DR: In this paper, a Rayleigh energy approach utilizing the bending mode of the nonrotating beam in the determination of the bending frequency of the rotating beam was presented, which is evaluated and is found to give good practical results for helicopter blades.
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