Dynamic response analysis of the helicopter blades with non-uniform structural properties

Siami, Ali; Nitzsche, Fred; Leibbrandt, Riekert; Spieß, Christian; Hilewit, Doma

doi:10.2514/6.2021-0562

Cited by 4 publications

(7 citation statements)

References 15 publications

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“…This distinct method is based on the time marching approach, and it uses the central finite difference method to discretize the equations in time domain. It should be noted that the accuracy of the TMM has been evaluated by the author in Siami et al (2021) by comparing the outputs of the algorithm with the results obtained with the commercial program FLIGHTLAB for a blade.…”

Section: Resultsmentioning

confidence: 99%

“…Assuming uniform structural properties along each element and using the separation of variables given in equation (7), the intrinsic 1D nonlinear equations presented in equation (1) can be written as (Siami et al, 2021)where qi(t) has been defined in equation (8). It should be noted that Fextk(t) and Mextk(t) are the terms related to external loads.…”

Section: Theorymentioning

confidence: 99%

“…They will appear in the equations if external distributed loads are applied to the elements. The matrix coefficients presented in equation (10) can be found in another study by Siami et al (2021).…”

Section: Theorymentioning

confidence: 99%

“…A computational model was also developed to study the nonlinear steady-state static response and free vibration of fiber multiscale composite beams using the intrinsic 1D nonlinear equations (Rafiee et al, 2016). The structural dynamics analysis of rotating helicopter blades with non-uniform properties subjected to realistic boundary conditions using 1D nonlinear equations was presented by Siami et al (2021). Flexible joints were employed between the hub and blade, and the results were evaluated by comparing the time responses and the Campbell diagrams against the commercial package FLIGHTLAB.…”

Section: Introductionmentioning

confidence: 99%

“…The Jacobian matrix of the numerical solution part is derived analytically to increase the time efficiency of the introduced solution approach. The accuracy of the solution is evaluated by comparing the results with the outputs of a time marching method (TMM) evaluated previously by the authors (Siami et al, 2021). The harmonic balance response for the linearized system of equations about the steady-state solution is presented using analytical formulations and the outputs are compared with the solution of the nonlinear system.…”

Section: Introductionmentioning

confidence: 99%

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A harmonic balance solution for the intrinsic 1D nonlinear equations of the beams

Siami

Nitzsche

2023

Journal of Vibration and Control

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In this paper, a harmonic balance method is introduced to solve the intrinsic 1D nonlinear equations presented by Hodges for analyzing initially curved and twisted anisotropic rotating beams. First, the nonlinear first-order partial differential equations are discretized in space domain using the Galerkin approach. Then, the time response of the system of equations is approximated by using first and the second harmonic terms under the harmonic excitations applied to the structure. The harmonic balance algorithm has been developed for the linearized system of equations about the steady-state solution and for fully nonlinear equations. The differences between these two systems have been addressed under consideration of different levels of external loads. Fully analytical formulae have been presented for the HB solution of the linearized equations in this work. In the proposed approach for the nonlinear system, the Jacobian matrix utilized in the numerical solution part is obtained analytically to increase the time efficiency of the solution method. The results of the proposed approach for an initially twisted and curved blade are compared with a different algorithm based on a finite difference approach to discretize the equations and a time marching method to solve the system of equations in time domain. The comparison between the outputs of the harmonic balance method and the time marching method demonstrate high correlations between these distinct methods. It should be noted that the accuracy of the time marching method solution has been evaluated in another publication by the authors using the output of FLIGHTLAB for a blade with different types of boundary conditions. The proposed harmonic balance-based method delivers a very time-efficient approach for time analysis of twisted/curved beams and blades under harmonic loads in comparison with other employed methods. The developed approach can be a powerful computational tool for design optimization of composite blades.

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Section: Resultsmentioning

confidence: 99%