Vibration Control Of Beam Research Articles

A hybrid photovoltaic/flexoelectric actuation mechanism applied to precision actuation and vibration control of beams

A hybrid photovoltaic/flexoelectric actuation mechanism applied to precision actuation and vibration control of beams

Transverse Dynamic Responses and Optimization of a Flexibly Constrained Beam with Multiple Nonlinear Supports that Present Cubic Stiffness

This paper establishes a simplified model of a flexible beam with multiple nonlinear supports that present cubic stiffness to study the potential application of cubic nonlinearities in the vibration control of beams. The Lagrangian method (LM) is used to predict transverse dynamic responses of the flexible beam with multiple nonlinear supports that present cubic stiffness, whereas the harmonic balance method (HBM) and Galerkin truncation method (GTM) are utilized to study the accuracy of the LM. Against the background, the effect of nonlinear supports that present cubic stiffness on the nonlinear transverse dynamic responses of the beam is studied. For this study, the accuracy of the LM is guaranteed under the 4-term truncation number. Nonlinear transverse dynamic responses of the flexibly constrained beam with multiple nonlinear supports that present cubic stiffness are sensitively influenced by their initial calculation values. For different boundary conditions or working statuses, the maximum restoring forces at both ends of the flexible beam can be suppressed effectively by optimizing the parameters of nonlinear supports that present cubic stiffness. Appropriate parameters of nonlinear supports that present cubic stiffness are good at vibration control of the flexibly constrained beam. In addition, complicated dynamic responses of the flexible beam with multiple nonlinear supports that present cubic stiffness are motivated under some inappropriate parameters of nonlinear supports.

An experimental and numerical comparison of traditional spring DVA in parallel and shape memory alloy actuated DVA in series and parallel for fixed beam vibration control

Shape memory alloy is a desirable smart material that could be used as a stiffness adjustment component in dynamic vibration absorbers (DVA). This research provides an analytical and experimental framework for investigating a stationary beam's vibration powered by a mixture of three SMA springs in series and two in parallel. In order to reduce vibration from a stationary beam, DVA, which is supported by springs composed of shape-memory alloy, is developed. In this study, a fixed beam in the system is held in place by a nut and bolt arrangement. The shaker is used with a function generator to provide vibration in real time. After installing two conventional springs with masses 305.1 mm apart from the fixed beam's ends, the vibration amplitude was measured. Experiments were carried out at various frequencies with three SMA springs with masses in series and two in parallel in place of the conventional springs. The results were recorded using Pulse software, which interfaced with the FFT and accelerometer. According to the experimental arrangement, the system was adequately dampened. Harmonic response analysis results were compared over a range of frequencies using ANSYS Workbench R15.0 to simulate the fixed beam spring-mass mass system.

Experimental and numerical Comparison of traditional spring DVA and shape memory alloy actuated DVA for fixed beam vibration control

A desirable smart material that might be employed in dynamic vibration absorbers (DVA) as a stiffness adjustment element is shape memory alloy (SMA). This paper offers a numerical and experimental platform that examines the vibration of a stationary beam that has been operated by a SMA. In this study, a DVA is created using springs made of shape-memory alloy to eliminate vibration in a fixed beam. The system has a fixed beam secured by a C clamp. Real-time vibration was provided by the shaker with the help of a function generator. Results for the vibration's amplitude were recorded after the conventional spring with mass was mounted at a distance of 305.1 mm from the left end of the fixed beam. The SMA spring with mass was used in place of the conventional spring, and experiments were run at various frequencies. To record the results, the FFT and accelerometer were interfaced using Pulse software. The fixed beam with spring mass system is modelled in ANSYS Workbench R15.0 in accordance with the experimental setup. Over a range of frequencies, the results of a harmonic response analysis were compared. The experimental & analytical results are in good agreement when one SMA spring or two SMA springs connected in parallel or series are used to dampen the system effectively. The outcomes of this work can be utilised as a reference for designing DVA with a Nitinol spring as a stiffness tuning component in circumstances where smooth and continuous tuning of the absorber is required.

Passivity-based boundary control with the backstepping observer for the vibration suppression of the flexible beam

In engineering applications, flexible beam vibration control is an important issue. Although several researchers have discussed controlling beam vibration, there are few strategies for implementing it in actual applications. The passivity-based boundary control for suppressing flexible beam vibration was investigated in this paper. The controller was implemented using a moving base, and the beam model was an undamped shear beam. The control law was established using the storage function in the design technique. The finite-gain L2 - stability of the feedback control system was then proven. This method dealt directly with the PDE of the beam model with no model reduction. Because of the non-collocated measurement and actuation in many applications, the backstepping observer was required for state estimation. Since the controller was implemented at the end of the beam via a moving base, the beam domain remained intact. Therefore, the method is simple to apply in applications. With the use of the finite-difference approach, the PDEs were numerically solved. The controller's performance of the proposed control scheme was demonstrated using computer simulation.

Vibration control of beams under moving loads using tuned mass inerter systems

Traditional tuned mass dampers (TMDs) have been proven efficient for the moving-load-induced vibration control of beams. However, a large tuned mass is required in TMDs to adjust the structural dynamic characteristics and achieve the demanded performance targets, which leads to additional dynamic effects and inconvenience of installation. The tuned mass inerter system (TMIS) is an ungrounded lightweight passive control device, which contains a suspended mass, a parallel-connected tuned spring and an inerter-based subsystem. In this study, the application and optimization of TMISs on vibration suppression of multi-span beam models under moving load series are investigated. Using the Bubnov-Galerkin integration method, the modal-superposition generalized system for specified modes of a beam with TMIS under successive moving load series is established. Then, a design strategy for TMISs is proposed to achieve the structural target performance demand by decreasing the moving load-induced resonant responses and attached tuned mass. In the optimization algorithm, the tuned mass ratio is taken as the optimal objective, and the limited dynamic response amplitude under different speed parameters is the constraint condition. A single-span simply supported beam with the TMIS under a moving load series is analyzed. The designed TMISs are tuned to the dominating mode with the maximum mass participate factor of the main structures. TMISs show good vibration mitigation compared to TMDs with equal tuned mass. Meanwhile, under the premise of identical structural performance demands, TMISs require less tuned mass than TMDs and achieve a lightweight control effect. The corresponding dynamic amplitude vs speed curves and time history response curves of beams with TMISs and TMDs are also depicted through comparative analyses. The vertical deflection and acceleration responses apparently decrease, and the resonance is mitigated due to the designed TMISs. The sensitivity analysis results indicate that TMISs attached to beams are insensitive to the perturbance of their parameters and the input moving load excitations; thus, TMIS proves to be a robust tuning system.

Study on Tunable Band Gap of Flexural Vibration in a Phononic Crystals Beam with PBT

Low-frequency flexural vibration plays a significant role in beam vibration control. To efficiently attenuate the propagation of flexural vibration at a low-frequency range, this paper proposes a new type of a phononic crystals beam with an adjustable band gap. The governing equations of flexural vibration in a periodic beam are established based on the Euler theory and Timoshenko theory. The band structures are calculated by the plane wave expansion method, the attenuation properties and transmission response curves with a finite periodic beam are calculated by the spectral element method and finite element method. The effects of the elastic foundation and axial stress on band gaps are discussed in detail, and the regulation of the temperature field on the band gap is emphatically studied. The theoretical and numerical results show that the elastic foundation and axial stress have significant influence on the band gap, and the location and width of the band gaps can be adjusted effectively when the Young’s modulus of PBT is changed by a varying temperature. The results are very useful for understanding and optimizing the design for composite vibration isolation beams.

Vibration suppression of an elastic beam with boundary inerter-enhanced nonlinear energy sinks

Nonlinear vibration absorbers have been widely used for vibration suppression of elastic structures, but they were usually placed within the structures. However, designing such a vibration damping device within an engineering structure is possibly difficult. In this paper, an inertial nonlinear energy sinks (NES) is mounted on the boundaries of the elastic beam to suppress its vibration. Although this vibration suppression approach is more in line with engineering requirements, it introduces nonlinear oscillators at boundaries. This brings certain difficulties to the structural vibration analysis and the optimal absorber design. An approximate analytical approach for the steady-state response is developed in this work and verified by numerical solutions. The comparison with the uncontrolled system demonstrates the high-efficiency vibration suppression of the inertial NES installed on the boundary. Besides, the optimization of the NES parameters is performed. Resonance amplitude of the elastic structure can be reduced by 98% with the optimized NES. In summary, this paper proposes a novel approach to suppress the bending vibration of elastic structures through boundary NESs. The vibration reduction effect is very significant, and it is more feasible to implement. Therefore, this work is helpful to study the vibration of elastic structures with nonlinear boundaries and to promote the application of nonlinear vibration absorbers. A boundary damping strategy is proposed to solve the problem of the difficulty of installing the vibration absorber in engineering. Introduce an inertial nonlinear energy sinks (NES) to reduce the weight of the shock absorber. The nonlinear boundary is separated and merged into the elastic beam vibration control equation to realize the decoupling of the continuum model. Resonance peak of the elastic structure can be reduced by 98% with the optimized NES. This work is helpful to study the vibration of elastic structures with nonlinear boundaries and to promote the application of nonlinear vibration absorbers.

Dynamic behavior of sandwich beams with different compositions of magnetorheological fluid core

ABSTRACT Magnetorheological fluid (MRF) sandwich beams belong to a class of adaptive beams that consists of MRF sandwiched between two or more face layers and have a great prospective for use in semi-active control of beam vibrations due to their superior vibration suppression capabilities. The composition of MRF has a strong influence on the MRF properties and hence affects the vibration characteristics of the beam. In this work, six MRF samples (MRFs) composed of combination of two particle sizes and three weight fractions of carbonyl iron powder (CIP) were prepared and their viscoelastic properties were measured. The MRFs were used to fabricate different MRF core sandwich beams. Additionally, a sandwich beam with commercially available MRF 132DG fluid as core was fabricated. The modal parameters of the cantilever MRF sandwich beams were determined at different magnetic fields. Further, sinusoidal sweep excitation tests were performed on these beams at different magnetic fields to investigate their vibration suppression behavior. MRF having larger particle size and higher weight fraction of CIP resulted in higher damping ratio and vibration suppression. Finally, optimal particle size and weight fraction of CIP were determined based on the maximization of damping ratio and minimization of weight of MRF.

Vibration control of beams by shear and moment type dynamic absorber

Vibration control of beams by shear and moment type dynamic absorber

Active Vibration Control of Helicopter Maneuvering Flight Using Feedforward‐Robust Hybrid Control Based on Reference Signal Reconstruction

Current control laws for active control of helicopter structural vibration are designed for steady‐state flight conditions, while the vibration response of maneuvering flight has not been taken into consideration yet. In order to obtain full‐time vibration suppression capability, the authors propose a filtered least mean square‐mixed sensitivity robust control method based on reference signal reconstruction (LMS‐MSRC), driving piezoelectric stack actuators to suppress helicopter structural vibration response in maneuvering flight. When feedback controller designed by H∞ theory is implemented, active damping is added on the secondary path to weaken the adverse effects of its sudden changes in maneuvering flight state. Furthermore, a reference signal reconstruction scheme is given concerning equivalent secondary path. In addition, the reconstruction accuracy, the convergence speed, stability, and global validity of the hybrid controller are analysed. Compared with multichannel Fx‐LMS, numerical simulations of LMS‐MSRC for vibration suppression are undertaken with a helicopter simplified finite element model under several typical flight conditions. Further experiments of real‐time free‐free beam vibration control are performed, driven by a stacked piezoelectric actuator. The instantaneous overshoot of measured response is 42% less than the peak value and its attenuation reaches 85% within 2.5 s. Numerical and experimental results reveal that the proposed algorithm is practical for suppressing transient disturbance and multifrequency helicopter vibration response during maneuvering flight with faster convergence speed and better robustness.

Design criteria of bistable nonlinear energy sink in steady-state dynamics of beams and plates

A bistable nonlinear energy sink (BNES) conceived for the passive vibration control of beam and plate structures under harmonic excitation is investigated. By applying an Incremental Harmonic Balance (IHB) method together with an adjusted arc-length continuation technique, the frequency and amplitude responses are obtained, and their respective trends are discussed in detail from three aspects. The simplest single-mode dynamics is first considered with a special focus on the coupled effect of the cubic nonlinear stiffness and the negative linear stiffness, where an analytical treatment using complex-averaging method is also applied to obtain the slow invariant manifold for understanding the underlying dynamics. Then the multi-mode dynamics of the beam are discussed in variation of each parameter. As a result, a simple step-by-step design rule for the BNES is summarized. Finally, the obtained results and design criteria of the BNES in the beam case are extended to a 2D plate, realizing a broadband control for multi-mode plate vibration. It is found that compared to a traditional cubic one, a BNES can have a better performance both on the frequency and amplitude point of view.

Differential quadrature solution for vibration control of functionally graded beams with Terfenol-D layer

The governing differential equation of motion for vibration control of a functionally graded material (FGM) beam using magnetostrictive layers is solved using differential quadrature method(DQM). It is known that, when differential quadrature is implemented directly for the solution of governing differential equation for vibration control of beam, it is required to convert the generalised eigenvalue problem into standard eigenvalue problem. However in the present work, the original differential equation of vibration control of beam is be separated into two simpler second and fourth order differential equations using the separation of variables in conjunction with the characteristics equation of damped single degree of freedom system. Solution of corresponding two simpler differential equation also yields damped natural frequency and damped factor comparable to that of the former approach. It is to be noted that using either of the solutions using differential quadrature method δ point description of the physical domain at boundary is used to obtained the differential quadrature equations for the various boundary conditions of the beam. In order to assure the accuracy of formulation and solution using DQM, convergence behavior of natural frequencies is examined for five combinations of boundary conditions and comparison studies from the two solution approaches is presented. The effect of the location of the magnetostrictive layers, material properties and control parameters on the vibration suppression are investigated.

Reduction of structural vibrations with the piezoelectric stacks ring

It is known that piezoelectric material shunted with external circuits can convert mechanical energy to electrical energy, which is so called piezoelectric shunt damping technology. In this paper, a piezoelectric stacks ring (PSR) is designed for vibration control of beams and rotor systems. A relative simple electromechanical model of an Euler Bernoulli beam supported by two piezoelectric stacks shunted with resonant RL circuits is established. The equation of motion of such simplified system has been derived using Hamilton’s principle. A more realistic FEA model is developed. The numerical analysis is carried out using COMSOL® and the simulation results show a significant reduction of vibration amplitude at the specific natural frequencies. Using finite element method, the influence of circuit parameters on lateral vibration control is discussed. A preliminary experiment of a prototype PSR verifies the PSR’s vibration reduction effect.

Effect of the fractional foundation on the response of beam structure submitted to moving and wind loads

A particular attention is devoted to analyze the effect of the foundation having fractional order viscoelastic material on a response of a beam structure. Periodic responses are computed using the stochastic averaging method, and the effects of fractional order damping on the vibration reduction of the beam are analyzed. The analysis shows that, as the order of the derivative increases, the resonant amplitude of the beam vibration decreases. It means that high order of the fractional derivative appear to be beneficial for the beam vibration control . It is also observed that the multivalued solution only appears for the smallest order and suddenly disappears as the derivative order increases. Further, the additive and parametric wind turbulence contributes to decrease the chance for the beam to reach the resonance of the amplitude oscillations . The analytical predictions are confirmed by numerical simulations.

Experimental analysis of active–passive vibration control on thin-walled composite beam

In the study presented, active and passive vibration control techniques for a thin-walled composite beam were developed and experimentally analysed. An MFC (Macro Fibre Composite) actuator was used, together with the magnetic forces between two permanent cuboidal magnets (passive vibration control) for vibration damping applications. After the experiments conducted with active vibration control (MFC actuator), it was found that in all cases, the vibration damping of the analysed system was much higher at its resonant frequency. Nevertheless, due to the experimental results, it could be concluded that active and passive vibration control systems were efficient for thin-walled composite beam vibration amplitude control. Methodology for thin-walled composite beam vibration control analysis was developed and presented in the article.

Multi-mode optimal fuzzy active vibration control of composite beams laminated with photostrictive actuators

Firstly, a multi-field coupling finite element formulation of composited beam laminated with the photostrictive actuators is developed in this paper. Moreover, an optimal fuzzy active control algorithm is also proposed on the basis of the combination of optimal control and fuzzy one. This method opens a new avenue to resolve the contradiction between the linear system control method and nonlinear actuating characteristics of photostrictive actuators. The desired control for suppressing multi-modal vibration of photoelectric laminated beam is firstly obtained through optimal control and then the fuzzy control is used to approach the desired mechanical strain induced by photostrictive actuators. Thus, the multi-mode vibration control of beam is realized. In the design process of optimal fuzzy controller, the design of fuzzy control is independent of optimal control. The simulation results demonstrate that the proposed control method can effectively realize multi-modal vibration control of photoelectric laminated beams, and the control effect of optimal fuzzy control is better than that of optimal state feedback control.

Optimal Placement Strategy of Multiple Patches for Active Vibration Control of Cantilever Beams Based on Modal Strain

Identification of a proper location for sensor actuator pair is very important for multimode vibration control of beams. A lot of research work is carried by various researchers, for the optimization of actuators and sensors location. Various techniques and approaches have been used, but there are two broad approaches. In the first approach the placement of patches is combined with controller parameters, while in second approach, the locations are achieved independently of controller parameters. For achieving the best vibration control, the placement of the piezopatches should be in the region of maximum strain location. This paper presents, controller independent, simplified optimal patch placement strategy, on cantilever beams, based on modal strain profile. The modal strain patterns obtained from FE analysis of beams, are utilized to devise a strategy for identifying the locations of piezopatches. The effectiveness of strategy adopted for optimal location is compared with the results obtained from a controller dependent placement methodology employed by previous researchers. It is found that the proposed methodology is in agreement with the work carried out earlier.

Vibration control of beams by shear and moment-type dynamic absorber

Vibration control of beams by shear and moment-type dynamic absorber

Active vibration control of a beam instrumented with MWCNT/epoxy nanocomposite sensor and PZT-5H actuator, robust to variations in temperature

Multi walled carbon nano tube (MWCNT)/epoxy nanocomposite strain sensor and piezoelectric actuator pair are used in active vibration control (AVC) of a smart cantilevered beam. Due to different coefficients of thermal expansion of MWCNT and epoxy, the resistance of carbon nanotube/epoxy based strain sensor changes nonlinearly with change in temperature. The temperature dependence of CNT based strain sensor is modelled by fitting a polynomial curve on the experimentally obtained characterization data of CNT/epoxy strain sensor. Using augmented constitutive equations of piezoelectricity, finite element model of smart cantilevered beam instrumented with collocated nanocomposite strain sensor and PZT-5H actuator is derived. Effect of temperature on PZT-5H actuator is also considered in derivation of the control law. Active vibration control of the first mode of a smart cantilevered beam instrumented with collocated CNT based strain sensor and PZT-5H actuator is performed at ambient temperature and at temperature slightly away from the ambient temperature for two cases: (1) without considering the temperature dependence of CNT composite strain sensor in Kalman observer and (2) considering the temperature dependence of CNT composite strain sensor in Kalman observer. Simulations are also performed to visualize the behaviour of smart beam when the beam is subjected to a temperature impulse. This paper suggests a novel AVC strategy using MWCNT/epoxy strain sensor and PZT-5H actuator patch that is robust to variations in temperature.