Original Article Vibration analysis of a rotating variable thickness bladed disk for aircraft gas turbine engine using generalized differential quadrature method B Shahriari 1 , Mohammadhadi Jalali 2 and MR Karamooz Ravari 3 Abstract In this paper, free vibration analysis of rotating variable thickness annular bladed disk suitable to be used in aircraft gas turbine engine is investigated. The numerical generalized differential quadrature method is introduced in this paper as a fast and efficient numerical method to be used for vibration analysis of bladed disks of real gas turbine engines. The boundary conditions are supposed to be similar to those of the real bladed disk used in the aircraft engines i.e. clamped for the inner edge and free for the outer edge. Considering the thickness of the disk to vary as a power function and the blades of the bladed disk to be rigid, the numerical solution is performed and the effects of thickness variation, geometric parameters, angular velocity, and number of blades on the natural frequencies and critical speeds are inves- tigated. The obtained numerical results are compared with those reported in the literature indicating a good agreement. Keywords Aircraft gas turbine engine, rotating variable thickness bladed disk, vibration, natural frequencies, critical speeds, general- ized differential quadrature method Date received: 20 April 2016; accepted: 24 August 2016 Introduction Rotating bladed disks are one of the most fundamental components of engineering devices such as aero-gas turbine engines. An undesired vibration of these rotat- ing systems in the operating conditions may cause cata- strophic failures of the parts or even the whole engine. According to what is mentioned above, a careful design of the rotating systems is of crucial importance. The dynamic characteristics of circular disks have been studied for several decades. Lamb et al. 1 inves- tigated the vibration of spinning uniform disk, for the first time. They obtained an exact solution for natural frequencies of rotating, homogenous, constant thick- ness circular disk. Southwell 2 extended the Lamb’s work and analyzed the effects of rotation on the vibra- tion of uniform homogeneous circular disk, more deeply. Deshpande et al. 3 presented a model for in-plane vibration of rotating thin disk accounting for the stiffening of the disk due to the radial expan- sion resulting from its rotation. Considering that the thickness of the plate to be varied linearly and expo- nentially, Lee et al. 4 used the assumed modes method to formulate the equations of motion of rotating homogeneous circular annular plates. They obtained the natural frequencies and critical speeds for vibration modes consisting of radial nodal lines with- out any nodal circle. Al-bedoor 5 presented a dynamic model for a typical elastic blade attached to a disk driven by a shaft, which is flexible in torsion. He employed the Lagrangian approach in conjunction with the finite element method in deriving the equa- tions of motion, within the assumption of small deformation theory. Yang and Huang 6 studied the effects of disk flexibility, blade’s stagger angle, and rotational speed on the natural frequencies and mode shapes of a shaft–disk–blade system. They derived the equations of motion using energy approach in conjunc- tion with the assumed modes method. Yang and Huang 7 analyzed the dynamic behavior of a coupled Proc IMechE Part G: J Aerospace Engineering 0(0) 1–11 ! IMechE 2017 Reprints and permissions: sagepub.co.uk/journalsPermissions.nav DOI: 10.1177/0954410016684360 journals.sagepub.com/home/pig 1 Department of Mechanical and Aerospace Engineering, Malek-Ashtar University of Technology, Iran 2 Department of Mechanical Engineering, Isfahan University of Technology, Isfahan, Iran 3 Department of Mechanical Engineering, Graduate University of Advanced Technology, Kerman, Iran Corresponding author: B Shahriari, Department of Mechanical and Aerospace Engineering, Malek-Ashtar University of Technology, Isfahan, P.O. 83145-115, Iran. Email: shahriari@mut-es.ac.ir