Refined Structural Dynamics Model for Composite Rotor Blades

Composites Engineering, 1992

The structural behavior of coupled, thin-walled, composite beams of open as well as closed section was analyzed using Vlasov theory and then the results were validated by experiment. The analysis modeled the walls of beams as general composite laminates and accounted for the transverse shear deformation of the cross-section. The out-of-plane warping deformation of the cross-section was included implicitly in this formulation. In order to validate the analysis, graphite-epoxy beams of various cross-sections such as solid rectangular, I-section, single-cell rectangular and two-cell airfoil were fabricated and tested for their structural response under tip bending, torsional and extensional loads. Specialized bending-torsion and extension-torsion couplings were introduced in these beams using proper ply lay-ups. Good correlation between theoretical and experimental results was achieved. Transverse-shear-related couplings were found to influence the structural response of open-as well as closed-section beams. For blades with hygrothermally stable lay-ups, bending-transverse shear coupling increased the bending flexibility by about 50%. The in-plane-bending coupling stiffness [B] of the walls of the beam generally influenced the structural response of the beams quite significantly; this effect was expecially large for I-beams. The influence of constraining the warping deformation was found to be substantial on the structural response of open-section beams as compared to closed-section beams. A 630% increase in the torsional stiffness due to constrained warping was noticed for graphite-epoxy I-beams of slenderness ratio 30. The feasibility of achieving the desired levels of bending-torsion and extension-torsion couplings in two-cell rotor blades was demonstrated. NOTATION chord and thickness of two-cell composite rotor blade length of beam coordinate system for plate segment coordinate system for beam displacements in the n, s, z directions, referring to the plate segment displacements in the x, y, z directions, referring to the beam membrane strains referring to the plate segment bending curvature referring to the plate segment rotations about the x, y, z axes, referring to the beam transverse shear strains for the beam in the xz and yz planes, respectively warping function constrained warping parameter stress field referring to the plate segment stress resultants referring to the plate segment moment results referring to the plate segment axial force referring to the beam bending moments referring to the beam shear forces in the x, y directions, referring to the beam torsion moment referring to the beam bimoment (or warping moment) referring to the beam stiffness matrix for the beam applied torsion at the tip of the beam applied force at the tip of the beam axial force at the tip of the beam Young's moduli of the plies in the principal directions Poisson's ratio of the plies in the principal plane shear modulus of the plies in the principal plane differentiation with respect to the z coordinate of the beam

2012

Composite beams and columns are analyzed and designed either with explicit beam expressions or with numerical (e.g. FE) methods, both require the knowledge of the cross sectional properties, i.e. the bending-, the shear-, the torsional-, warping-, axial stiffnesses and the coupling terms. These properties are calculated either by using kinematical relationships (e.g. cross sections remain-plane after the deformation of the beam) or by asymptotic methods, however in both cases the accuracy depends on the assumed degree of freedom of the model. These assumptions may lead to inaccurate or contradictory results. In this paper a new theory is presented in which no kinematical assumption is applied, rather the properties are derived from the accurate (three dimensional) equations of beams using limit transition. The theory includes both the in-plane and the torsional-warping shear deformations. As a result of the analysis the stiffness matrix of the beam is obtained which is needed for either analytical or numerical (FE) solutions.

Composite Structures, 2004

Vibration analysis of a rotating composite blade is the main purpose of this study. A general formulation is derived for an initially twisted rotating shell structures including the effect of centrifugal force and Coriolis acceleration. In this work, the blade is assumed to be a moderately thick open cylindrical shell that includes the transverse shear deformation and rotary inertia, and is oriented arbitrarily with respect to the axis of rotation to consider the effects of disc radius and setting angle. For a thick shell, we must consider the transverse shear deformation as well as rotary inertia. Thus, based on the concept of the degenerated shell element with the Reissner-Mindlin's assumptions, the finite element method is used for solving the governing equations. In the numerical study, effects of various parameters are investigated: initial twisting angles, thickness to radius ratios, layer lamination and fiber orientation of composite blades. Also, they are compared with the previous works and experimental data.

Materials Today: Proceedings, 2021

The dynamic behaviour of rotating flexible bodies, such as turbine blades/exhaust fan blades are significantly different from those of stationary bodies as centrifugal force come into effect in addition to gravity. Such rotating blades may be modelled as cantilever beam / plate / panel. A finite element formulation for vibration analysis of rotating laminated composite panels is employed in this article; based on the first order shear deformation theory, an accurate relationship between strains and displacements of pre-twisted panels are derived. The governing equations of motion are derived considering centrifugal force. Here studied the effect of rotation speed (x), setting angle (u), twist angle (w), fibre orientation angle (h) and variable thickness of panels on the vibration behaviour of cantilever composite panels. Also noticed the loci veering and loci crossing phenomena occurs between symmetric and skewsymmetric modes, respectively at different rotation speeds.

Composite Structures, 2018

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.

Advances in Composite Materials - Analysis of Natural and Man-Made Materials, 2011

A structural element having one dimension many times greater than its other dimensions can be a rod, a bar, a column, or a beam. The definition actually depends on the loading conditions. A beam is a member mainly subjected to bending. The terms rod (or bar) and column are for those members that are mainly subjected to axial tension and compression, respectively. Beams are one of the fundamental structural or machine components. Composite beams are lightweight structures that can be found in many diverse applications including aerospace, submarine, medical equipment, automotive and construction industries. Buildings, steel framed structures and bridges are examples of beam applications in civil engineering. In these applications, beams exist as structural elements or components supporting the whole structure. In addition, the whole structure can be modeled at a preliminary level as a beam. For example, a high rise building can be modeled as a cantilever beam, or a bridge modeled as a simply supported beam. In mechanical engineering, rotating shafts carrying pulleys and gears are examples of beams. In addition, frames in machines (e.g. a truck) are beams. Robotic arms in manufacturing are modeled as beams as well. In aerospace engineering, beams (curved and straight) are found in many areas of the plane or space vehicle. In addition, the whole wing of a plane is often modeled as a beam for some preliminary analysis. Innumerable other examples in these and other industries of beams exist. This chapter is concerned with the development of the fundamental equations for the mechanics of laminated composite beams. Two classes of theories are developed for laminated beams. In the first class of theories, effects of shear deformation and rotary inertia are neglected. This class of theories will be referred to as thin beam theories or classical beam theories (CBT). This is typically accurate for thin beams and is less accurate for thicker beams. In the second class of theories, shear deformation and rotary inertia effects are considered. This class of theories will be referred to as thick beam theory or shear deformation beam theory (SDBT). This chapter can be mainly divided into two sections. First, static analysis where deflection and stress analysis for composite beams are performed and second dynamic analysis where natural frequencies of them are assessed. In many applications deflection of the beam plays a key role in the structure. For example, if an aircraft wig tip deflection becomes high, in addition to potential structural failure, it may deteriorate the wing aerodynamic performance. In this and other applications, beams can be subjected to dynamic loads. Imbalance in driveline shafts, combustion in crank shaft applications, wind on a bridge or a www.intechopen.com

Aiaa Journal, 2002

A re ned structural model based on a mixed force and displacement method is proposed for the analysis of composite rotor blades with elastic couplings. The present formulation allows the modeling of either open-section or closed-section blades of arbitrary section shape, stacking sequence, and end restraint effects. The theory accounts for the effect of elastic couplings, shell wall thickness, section warping, warping restraint, and transverse shear deformations. A semicomplementary energy functional is used to derive, in a variationally consistent manner, the beam force-displacement relations. Bending and torsion related warpings and shear correction factors are obtained in closed form as part of the analysis. The resulting rst-order shear deformation theory (Timoshenko) describes the beam kinematics in terms of the axial, ap and lag bending, ap and lag shear, twist, and torsion-warping deformations. The theory is validated against experimental data and other nite element results for graphite-epoxy composite beams of various cross sections such as I sections, box sections, and two-cell airfoils. Good correlation is achieved for all of the test examples. The in uence of wall thickness and transverse shear on the static beam response is also investigated. Wall thickness effects are shown to become signi cant when the thickness-to-depth ratio of the beam reaches around 20%. The slenderness ratio has a signi cant effect on the transverse shear behavior of the beam, especially for beams with low slenderness ratios. It is also shown that the layup angle has a nonnegligible effect on the transverse shear behavior of the beam.

Composite Structures, 2019

The mechanics of a laminated composite beam attached to inside of a rotating rim and directed to the inward direction is investigated. The Ritz method is utilized in the solution of the problem. Simple algebraic polynomials are used in the displacement field. Clamped-free boundary conditions are considered. First, Reddy (third order) and classical beam theories are used in the formulation. Cross-ply lamination configurations are considered. Effects of rotation speed, hub ratio, orthotropy ratio, beam theory and length to thickness ratio are analyzed in detail. Mode shapes of composite rotating beams are given. It is obtained that composite beams may buckle due to compressive centrifugal force for the some combinations of rotation speed and hub ratio.

The turbine, propeller, helicopter blades are idealized as rotating cantilever beams in the analysis of its different characteristics. The motive of this paper is to find the natural frequency of rotating composite beams. In the present work a rotating composite beam is considered and the natural frequencies of the beam are determined using dynamic stiffness matrix method. The Dynamic Stiffness matrix method developed for the homogeneous cantilever beams is implemented to composite cantilever beams. First the effective young's modulus is determined for the composite material. The effective young's modulus is used to predict the frequency of rotating composite beam for various parameters. The results obtained, indicates how the natural frequency is influenced by various parameters such as speed, hub radius and number of layers in composite.