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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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Aeroelasticity of Axially Loaded Aerodynamic Structures for Truss-Braced Wing Aircraft

TL;DR: In this article, an aeroelastic finite-element formulation for axially loaded aerodynamic structures is presented to analyze the effect of geometric nonlinear effect of tension stiffening on the flutter speed of truss-braced wing aircraft.
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Free vibration characteristics of multiple load path blades by the transfer matrix method

TL;DR: In this paper, the transfer matrix method is extended to treat multiple-load-path blades, without resorting to an equivalent single-loadpath approximation, and the axial degree-of-freedom is introduced to account for the differential axial displacements of the different load paths.
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Aerodynamic Load Analysis of a Variable Camber Continuous Trailing Edge Flap System on a Flexible Wing Aircraft

TL;DR: An investigative aerodynamic analysis conducted on the novel control surface known as a Variable Camber Continuous Trailing Edge Flap shows that the VCCTEF offers greater control authority than conventional ailerons at cruise, and nominal flap settings are determined for a low-speed take-off condition.
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Vibration Control in a Helicopter with Semi-Active Hydraulic Lag Dampers

TL;DR: In this paper, a semi-active operation of the hydraulic lag damper is achieved via periodic flow restrictor modulation, and the influence of the modulations and constraints on the nonrotating hub loads of a five-bladed main rotor is evaluated.

Aeroelastic effects in multi-rotor vehicles with application to a hybrid heavy lift system. Part 1: Formulation of equations of motion

TL;DR: In this article, a set of governing coupled differential equations for a model of a hybrid aircraft is presented, consisting of multiple rotor systems connected by an elastic interconnecting structure, with options to add any combination of or all of the following components; i.e., thrusters, a buoyant hull and an underslung weight.
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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