Family of non-rotating beams isospectral to rotating beams: A discrete approach

Ramachandran, N and Ganguli, R (2019) Family of non-rotating beams isospectral to rotating beams: A discrete approach. In: AIAA Scitech 2019 Forum, 7-11 January 2019, San Diego, California.

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Abstract

A new methodology adaptable for computer implementation and based on matrix-factorization techniques is introduced to construct a family of realistic non-rotating cantilever beams that are isospectral to a given Euler-Bernoulli clamped-free rotating beam (CFRB) with non-homogeneous cross-section. The given CFRB is discretized into idealized point masses, mass-less rigid links and rotational springs. Matrix-based equations governing the kinematics of transverse vibration of this discrete model are derived and the mass reduced stiffness matrix (MRSM) is formulated. The MRSM is factorized into families of mass, length and stiffness matrices, each family defining the discrete model of a non-rotating cantilever beam isospectral to the given CFRB. Characteristics of these isospectral discrete models are governed by three transformation parameters which can be suitably tailored to obtain desired characteristics. From the isospectral discrete model, real beams with rectangular cross-sections varying in width and depth are constructed. As part of numerical studies to demonstrate practical utility of techniques presented here, transverse vibration of rotating uniform beams and beams with general polynomial variation in stiffness and mass (typical of helicopter and wind turbine rotor blades) is analyzed using the discrete model. Frequency parameters of such beams computed using the discrete model concur with published results. Using optimum values for the transformation parameters, physically realizable non-rotating cantilever beams, isospectral to example CFRBs, are constructed. Natural frequencies of these cantilever beams computed using the Finite Element Method (FEM) match well with those of the corresponding CFRB, hence confirming isospectrality. Since modal experiments on rotating beams can have practical limitations, isospectral non-rotating beams, constructed based on methods presented here, can be used as substitutes.

Item Type:	Conference Paper
Publication:	AIAA Scitech 2019 Forum
Publisher:	American Institute of Aeronautics and Astronautics Inc, AIAA
Additional Information:	cited By 0; Conference of AIAA Scitech Forum, 2019 ; Conference Date: 7 January 2019 Through 11 January 2019; Conference Code:225819
Keywords:	Aviation; Cantilever beams; Factorization; Nanocantilevers; Stiffness; Turbomachine blades; Vibration analysis, Computer implementations; Frequency parameters; Matrix factorizations; Rectangular cross-sections; Rotating cantilever beams; Transformation parameters; Transverse vibrations; Wind turbine rotors, Stiffness matrix
Department/Centre:	Division of Mechanical Sciences > Aerospace Engineering(Formerly Aeronautical Engineering)
Date Deposited:	24 Sep 2020 05:51
Last Modified:	24 Sep 2020 05:51
URI:	http://eprints.iisc.ac.in/id/eprint/65395

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