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The blades of helicopters and wind turbines undergo pitch motion in hygrothermal environments. Few works have studied the effect of this movement on blade frequencies. This paper focuses on the bending characteristics of a pitching thin-walled beam, including the effects of hygrothermal environments, rotor speeds, and composite materials. The harmonic pitch function is introduced into the dynamics model of a rotating beam. The method of multiple scales and the Galerkin method are used to solve these equations. Results indicate that the pitch amplitude A dramatically influences natural frequencies. Conclusions are obtained: (1) The flapping frequency varies periodically with pitch amplitude A, and monotonically changes every 2/$\pi$. The pitch amplitude A significantly impacts frequencies, while the pitch frequency ${\omega }_p$ and pitch phase C don’t influence frequencies. (2) An increase in temperature or humidity will decrease the flapping frequencies of a pitching beam. (3) The ply angle, coupled with the dynamic pitching angle, dramatically influences the flapping frequencies of the composite beam. The larger the ply angle, the greater the effect of pitch amplitude A on frequencies.

The problem considered in this paper is one of damped vibrations of the beam in transportation. The dynamical analysis of systems in motion is a very well-known issue, but many detailed cases have not been published yet. The considered case is applied with the double-sided fixed beams placed on a rotational disk. The disk treated as a rigid one is rotated with a constant angular velocity in the stationary reference frame. An application of vibrations of the beam is transformed from a local to global reference frame, damping forces and forces arising from the rotational motion of a local reference center are also taken into consideration. The beam is assumed as a homogenous one with symmetric cross-sections. This work is the dynamical analysis of such a type of vibrations, which is a mathematical one based on considering transient response and dynamical flexibility of this type of systems.

The free vibration of rotating tapered Timoshenko beams (TBs) made of the axially functionally graded materials (FGMs) is studied. The Chebyshev polynomials multiplied by the boundary functions are selected as the admissible functions in the Ritz minimization procedure, which is called the Chebyshev–Ritz method. As such, the geometric boundary conditions are satisfied, while the numerical robustness is guaranteed through use of the Chebyshev polynomials. The Ritz approach provides an upper bound of the exact frequencies. The effectiveness of the method is confirmed in the convergence and comparison studies. The effects of hub radius ratio, rotational speed ratio, taper ratios, rotary inertia and material gradient on the natural frequencies of the TBs for six different sets of boundary conditions are studied in detail.

In this paper, the effectiveness of a saturation control strategy in suppressing vibration of a rotating composite thin walled beam is studied. The mathematical model of the flexible beam takes into account a shear deformation effect, a warping function, a centrifugal force and the Coriolis acceleration. To extend the generality of the proposed formulation an inertia of the hub is also considered. Adaptive capability of the beam is achieved through the implementation of the saturation control algorithm.

Within the performed tests, the discussed control strategy is applied for different magnitudes of flexural–torsional vibration modes resulting from different orientations of beam laminate-reinforcing fiber’s. The obtained results prove the applied nonlinear control to be the effective method for beam vibration suppression in near-by resonance zones for all studied cases. Parametric studies considered different rotating speeds of the system. It is shown that the vibration of the beam can be suppressed to similar levels independently of the transportation motion rotating speed. However, significant differences in the width of vibration suppression zones are observed.

In this paper, the free vibration analysis of non-uniform rotating Euler–Bernoulli beam is carried out. It is assumed that the beam has exponentially decaying circular cross-section. In order to solve the problem, the differential transform method (DTM) is utilized. Based on our knowledge, we claim that the recurrence relation presented herein is an elaborate recurrence relation which has been obtained for ordinary differential equations. Non-dimensional natural frequencies of the beam are obtained and tabulated for different values of the beam parameters such as taper ratio and rotating speed. Furthermore, the finite element method (FEM) is employed to solve the problem. Comparison of the results obtained by DTM and FEM indicates the accuracy of proposed solutions.

Rotating beams are often encountered in the wind turbines and the rotors, and detection of the damages in rotating beams as earlier as possible is central to ensuring the safety and serviceability of practical structures. To this end, a modal sensitivity approach in conjunction with the sparse regularization is proposed in this paper. First, the eigen equations for the flap-wise and chord-wise vibrations of a rotating beam are established upon Hamilton’s principle. Then, damage detection is formulated as a nonlinear least-squares problem that finds the damage coefficients to minimize the error between the measured and calculated data. To solve the nonlinear least-squares problem, the sensitivity method that requires the modal sensitivity analysis is developed. In real applications, damage detection is usually an ill-posed problem and to circumvent the ill-posedness, the sparse regularization is introduced due to the fact that the numbers of actual damage locations are often scarce. Numerical examples are studied and results show that the proposed approach is more accurate than the enhanced sensitivity approach and the flap-wise modal data outperforms the chord-wise modal data in damage detection of rotating beams.

In this study, the optimum position and minimum diameter of damping wire were investigated to maximize the fundamental frequencies of a rotating blade. The blade was modeled as an isotropic, homogenous and constant cross-sectional cantilever rotating beam. The damping wire was modeled as an intermediate elastic support. In most rotating-beam applications, such as turbine blades, the slenderness ratio is low; therefore, Timoshenko beam theory was selected to analyze the model. The optimal position and minimum stiffness of elastic support were determined to maximize the natural frequencies of the beam using the finite element method. Minimum diameter of the damping wire was calculated by determining the minimum stiffness. Parameter sensitivity analysis showed that the angular velocity of the blade has no remarkable effect on the optimal position and minimum diameter of damping wire.

The Homotopy Perturbation Method (HPM) is applied to investigate the nonlinear free and forced vibration behavior of the rotating cracked beam. Nonlinear governing equations considering the two-dimensional (2D) large flexible structure in a rotating reference frame considering centrifugal forces are obtained by the Lagrangian approach and the Assumed Mode Method (AMM). The crack is modeled as an elastic nonlinear massless rotational spring, which divides the beam into two parts. The Rayleigh–Ritz method is used to discretize the governing system of equations of the motion. Stability analysis along with bifurcation and phase portrait represents the different behavior of the system, depending on the variations of base angular velocity, crack location, and stiffness. Moreover, it is shown that as the rotational speed increases, a tensile force appears along the neutral axis, stiffening the cracked structure, which results in shifting the backbone to the right and highly affects the nonlinear features of the system. The results obtained through a comparative study of the HPM with first-order approximation and numerical simulations (Runge–Kutta algorithm) demonstrate an accurate and effective solution for structures with nonlinear dynamics.

This paper aims at investigating 1/2 and 1/3 subharmonic resonances of a rotating functionally graded carbon nanotube-reinforced composite (FG-CNTRC) beam in the presence of geometric imperfections. A general function is introduced to denote three types of imperfections containing sine, global, and local modes. At first, based on the von-Kármán geometric nonlinearity assumption, the forced vibration equation is set up. Then, the Galerkin method and multiple scale method are utilized to study subharmonic resonance behaviors. Finally, coupled effects of FG-CNTRCs, rotating motion, and geometric imperfections on subharmonic resonance responses are investigated. It is found that a specific range of the excitation amplitude and frequency motivates the subharmonic resonance behavior. The coupling of geometric imperfections and geometric nonlinearities generates the 1/2 resonance phenomena, and geometric nonlinearities result in the 1/3 resonance behavior. Both the imperfection mode and amplitude can affect the resonance response and resonance regions. Moreover, in contrast with the 1/3 subharmonic resonance, geometric imperfections produce greater influence on the 1/2 subharmonic resonance.