Journal of Vibration and Control

Transverse vibration of viscoelastic Timoshenko beam-columns is investigated. The normal and the shear stress-strains are constituted by the Kelvin model with different viscosity parameters. The governing equations and the boundary conditions are derived from the generalized Hamilton principle. The exact frequency equations and the modal functions are proposed. The orthogonality conditions are established in the state space. The transverse response to arbitrary external excitation and initial conditions is determined via decoupling the governing equations based on the orthogonality. The natural frequencies and the decrement coefficients of various beam and beam-column models are numerically contrasted. The effects of the length-to-depth ratio, the axial tension, and the viscosity coefficients on the natural frequencies and the decrement coefficients are numerically demonstrated.

In this paper, we consider the problem of modal-space control for the hydraulically driven fully parallel mechanism with actuation redundancy. Firstly, the mechanical-hydraulic interaction system is transformed into modal-space model. Then, independent modal decoupled systems for the redundant mechanism are obtained. According to the eigenvalue frequency characteristics, two types of modal systems – zero eigenvalue modal systems and nonzero ones – naturally result and these systems can be treated separately. For the nonzero eigenvalue modal systems, it is convenient to employ dynamic pressure feedback control to regulate damping. For the zero eigenvalue modal systems, we give a proof to show that they just lie in the null space of the Jacobian of the mechanism, then it is more appropriate to implement force control for this type of modal system. Some simulation results further explain the proposed modal-space control method.

In this paper, a fully adaptive control design is considered for a four-degree-of-freedom aeroelastic system that has structural nonlinearities and operates in an unsteady aerodynamic incompressible flowfield. By using the flap hinge torque of a trailing-edge flap surface in combination with a leading-edge active flap, a closed-loop controller that adapts for uncertainties in the system parameters is designed. An implicit observer is implemented in the control design to compensate for lack of measurements of the lag states that model the unsteady flow. The innovative Lyapunov-based control design procedure results in a partial-state feedback adaptive controller that is globally asymptotically stable. Numerical simulation results show the effectiveness of the control strategy; comparative simulations are run to illustrate the benefit of using twin flaps as opposed to the conventional single flap control design.

In this study, the use of acoustic absorbent materials specifically felt to mitigate tire cavity resonance noise is presented. The inclusion of a trim in the tire cavity is represented by the addition of the acoustic damping loss factor into the sound pressure response function. In addition, the possible solution of using multilayer trim materials to mitigate the cavity mode effect is presented using the sound absorption coefficient values from the impedance tube experiments and by adopting other empirical models. Moreover, the sound absorption coefficient calculated from the method of electrical-analogy is compared with that from the experimental data and found to be reasonable. Experimental modal analysis was performed to show the effect of inserting an absorbent material (polyfelt) onto the inside surface of the tire where reduction in both the inside cavity sound pressure level and the wheel hub acceleration was observed. A Taguchi analysis is also done to rank the effectiveness of varying trim thickness and mass density as well as adding air gap to suppress tire cavity resonance noise.

Hilbert-Huang Transform (HHT) has been renowned for its capacity to reveal fault indicating information issue from vibration signals. It uses Empirical Mode Decomposition (EMD) to decompose a signal accordingly to its contained information into a set of Intrinsic Mode Functions (IMFs). Then, the instantaneous frequencies are performed of each IMF using Hilbert Transform (HT). However, the HHT has some disadvantages which are caused by the EMD technique. The EMD has the mode mixing problem that may occur between IMFs, it causes the End Effect phenomenon, which leads to a wrong instantaneous values at both sides of the signal. Furthermore, its lack of mathematical basis. To overcome the HHT inherent problems, we propose the use of the Empirical Wavelet Transform (EWT) which designs an appropriate wavelet filter bank fully depends on the processed signal with HT in the early detection and condition monitoring of tooth crack fault. In this paper, we develop a dynamic model describing a single stage spur gear in normal and abnormal functioning. Results of analyzing the pinion’s vibration displacement show that the proposed approach denoted (HEWT) successfully detect the tooth crack at a much earlier stage of damage development even though in noisy environment. Performance evaluation and comparison between HEWT and HHT methods show that the HEWT is better sensitive to tooth crack fault detection in gearbox systems.

This paper investigates asymmetric vibrations of non-homogeneous circular plates of parabolically varying thickness on the basis of classical plate theory. The non-homogeneity of the plate material is assumed to arise due to exponential variation in Young’s modulus as well as density along radial direction in distinct manner. First three natural frequencies of clamped, simply supported and free plates have been obtained using Ritz method. The basis functions have been chosen as polynomial co-ordinate functions satisfying the essential boundary conditions. Thereafter, the effects of taper parameter, non-homogeneity parameter, density parameter and nodal diameter have been analysed for first three modes of vibration. The results obtained are compared with those available in literature for homogeneous and non-homogeneous plates.

Inverted pendulum systems, because of highly nonlinear, coupled, and unstable dynamic behaviour, are excellent experimental platforms for testing new developed control algorithms. This study explores nonlinear modelling, simulation and sliding mode stabilizing control of a real rotary inverted pendulum in detail. For simulation purposes only, the system was modelled in a nonlinear state space form including the servomotor dynamics. In the light of the simulation results, a rotary inverted pendulum system was designed and manufactured. For a certain quality level of desired output, benefits of the sliding mode control of the system without using an equivalent control signal by selecting a proper smoothing function were shown. This model free approach can be used to satisfy a need especially for practical control applications in industry to a certain level, encouraging practical control engineers to use sliding mode control, who have no ability to model a system or no sufficient time for this, or encounter very complex nonlinear system models in many cases. Comparisons of the theoretical and experimental results demonstrate that the state equations describe the dynamics of the system satisfactorily, and that robust and accurate balancing of the pendulum can be achieved by using model free sliding mode control with sigmoid smoothing function.

To realize a broadened band gap as a potential application of vibration control in the electric vehicle powertrain system requires, a novel configuration of locally resonant (LR) beam with multi-oscillators attached is proposed, in which two types of oscillators are periodically and alternately attached at identical intervals. An analytical model is proposed based on transfer matrix method, which is validated by a finite element simulation. The band gaps in flexural vibration generated by this novel structure are investigated by the analytical model. The band gap coupling effect is observed and the influence of the intervals and oscillator parameters are discussed. The novel configuration effectively enlarges the range of band gaps in flexural vibrations.

In the present paper, viscously damped free vibrations of sectorial and annular sectorial membranes are investigated. Instead of undamped natural frequencies which are typically computed and applied in the free vibrations, viscously damped natural frequencies are done. The viscously damped natural frequency equation and the critical viscous damping equation are exactly derived. In the viscously damped free vibration, effects of viscous damping on natural frequencies are also studied.

To realize a vibration suppression of flexible structures like a membrane, our research focuses on introducing smart structures technology into the membrane structure. In this study, the membrane structure is composed of a vibration control system using a flexible Polyvinylidene fluoride (PVDF) film as an actuator. A non-contact vibration test system, which uses a high power Nd: YAG pulse laser for producing an ideal impulse excitation and laser Doppler vibrometers for measuring the response on the membrane, is employed to evaluate the vibration characteristics of the smart membrane structure. To confirm the effectiveness of the proposed method, using a flexible PVDF actuator installed on the membrane structure, control experiments with H _∞ control for reducing single mode and multiple modes vibration are conducted. In the results of the control experiments for single mode vibration suppression, a corresponding resonance peak is reduced by around 20 dB. In case of multiple modes vibration suppression, the first and second resonance peaks are reduced by 14 dB and 24 dB, respectively. This study demonstrates that the present control method using a flexible piezoelectric element and a non-contact vibration test system effectively suppress and evaluate the vibration responses of smart membrane structures.

The design of vibration controllers for flexible structures requires special attention due to the size of structural models, generally with a high number of degrees of freedom. The implementation of full order controllers for structures with high numbers of degrees of freedom often requires a high computational processing effort and advanced hardware. To avoid this, it is desirable to use reduced order controllers. The design of reduced order H _∞ controllers characterizes a nonconvex optimization problem. In this context, this work presents a direct minimization method to design reduced order H _∞ controllers in the controllable canonical form. An optimization problem is formulated to minimize the H _∞ norm with an additional constraint to consider stability of the closed-loop system. The solution of the optimization problem is obtained using genetic algorithms, exploiting the advantage of this point of view in the solution of nonconvex problems. This formulation is verified in the active vibration control of a cantilever beam. A comparison of the proposed formulation with the formulation that uses linear matrix inequalities and the Augmented Lagrangian method is presented in this work and some numerical aspects of the problem are discussed.