Contents lists available at ScienceDirect Composite Structures journal homepage: www.elsevier.com/locate/compstruct Vibration of a rotating composite beam with an attached point mass Tolga Aksencer, Metin Aydogdu ⁎ Department of Mechanical Engineering, Trakya University, 22030 Edirne, Turkey ARTICLE INFO Keywords: Rotating composite beams Vibration Attached mass Ritz method ABSTRACT The free vibration of a rotating laminated composite beam with an attached point mass is investigated. The Ritz method with algebraic polynomials is used in the formulation. The boundary conditions are considered as clamped-free. Different shear deformation theories (first order and third order) and classical beam theories are used in the formulation. Cross-ply lamination configurations are considered. Effects of the ratio of attached mass to the beam mass, rotation speed, hub ratio, orthotropy ratio, position of attached mass, beam theory and length to thickness ratio are analyzed in detail. Some typical mode shapes are presented in order to illustrate the effects of the attached mass. 1. Introduction Composite materials are preferred in mechanical and aerospace engineering applications (such as turbine wing, helicopter rotor blade, manipulator etc.) due to their low weight ratio and high strength. In various systems a mass is added into the system in order to increase performance. The attached point mass in rotating composites structures can be used, for example, to regulate the airflow in the wind turbine or to increase the flexibility in the car's fan and to change the vibration frequencies in the helicopter rotor. Some studies can be obtained related to vibration of rotating beams with attached mass. Hoa [1] investigated vibration of rotating beams with attached mass using finite element method. Boyce et al.[2] ob- tained vibration frequencies of rotating uniform bars with a tip mass at a constant speed. Jones [3] investigated frequencies of rotating beams with attached mass using the integral equation method for different boundary conditions. Hyun [4] examined transverse vibration of a ro- tating beam carrying tip mass with the integral equation method. Lee [5] investigated the effects of tip mass on vibration of rotating beam with a mass attached at free end. Bhat [6] studied mode shapes and natural frequencies of a uniform cantilever beam via Ritz method. Some results are given with several parameters such as root radius, the speed of rotation, tip mass and the moment of inertia of tip mass. A dynamic model of the rotating beam system with a tip mass was obtained using a finite element model considering viscous damper and drag force by Hui et al.[7]. Park and Kim [8] studied the dynamic characteristic of a curved beam attached tip mass by adding the effects of Coriolis and centrifugal force. Song and Librescu [9] have studied the vibrational and piezo characteristics of a thin-walled beam with a rotating tip mass. Craig [10] investigated the vibration of a rotating beam with a con- centrated tip mass. The vibration of a beam is studied with delamina- tion along the width and the mass at the end point by the Jafari [11]. The frequency analysis of a rotating beam with a mass at its end is studied by Ansari [12], taking into account the torsional-bending vi- brations. The coupled bending-bending vibration of an elastically con- strained and mass-added beam was investigated by Lin et al. [13]. Khulief [14] studied the vibration of a tapered beam with end mass using the finite element method. Kwok et al. [15] modeled with a blade modeled in their study. In this model, the vibration of the blade at- tached mass for arbitrary angle is examined. The vibration of rotating composite beams is a very complicated problem in general, if one considers pre-twist of the composite beam and coupling of flapwise-lagwise and axial vibrations. The effect of the Coriolis force, and coupled vibration of pre-twisted rotating composite beams has been investigated in a general manner in some of the pre- vious studies [16,17]. Vibration analysis of rotating thin-walled com- posite box beams can be obtained in [18–20]. Free vibration of composite thin-walled rotating beams with arbi- trary closed sections has been investigated by Song and Librescu [19]. Jung et al. [20] used a mixed approach in order to study the dynamics of rotating and nonrotating composite beams and blades with general geometry (open and closed cross section). Chandramani et al. [18] studied vibration of higher-order-shearable pretwisted rotating com- posite blades using the Galerkin method. In a recent work, Rafiee et al. [21]. have been investigated rotating nanocomposite thin-walled beams undergoing large deformation. In this study, a general computational model has been developed to study the nonlinear steady state static response and free vibration of thin- https://doi.org/10.1016/j.compstruct.2018.02.009 Received 11 December 2017; Received in revised form 1 February 2018; Accepted 5 February 2018 ⁎ Corresponding author. E-mail addresses: tolgaaksencer@trakya.edu.tr (T. Aksencer), metina@trakya.edu.tr (M. Aydogdu). Composite Structures 190 (2018) 1–9 Available online 08 February 2018 0263-8223/ © 2018 Elsevier Ltd. All rights reserved. T