Vibration Of Beam Research Articles

Enhancing Vibration Control in Smart Beams: A Comparative Study of Piezoelectric-Based Controllers Under Fluid-Induced Vibrations

Smart structures with integrated piezoelectric elements play a pivotal role in mitigating vibrations across diverse applications, by safeguarding against structural damage and performance degradation. This study delves into the active control of vibrations in beams, particularly in fluid-immersed environments where hydrodynamic forces induce complex beam oscillations. The dynamic behavior of geometrically nonlinear, simply supported beams integrated with piezoelectric elements was examined. The position of the piezoelectric patch was optimized through the GA algorithm to minimize the settling time. The optimal location for the piezoelectric patch was determined in the middle of the beam. The investigation encompasses harmonic excitation forces spanning frequencies from 10[Formula: see text]Hz to 200[Formula: see text]Hz. Our study evaluates the system’s response under two critical conditions: one with the presence of external hydrodynamic forces and the other without. To achieve effective vibration control, we employ both Proportional-Derivative (PD) and Sliding Mode Controllers (SMC), optimizing their parameters for minimum settling time as an objective function. The results underscore the remarkable superiority of the SMC, reducing settling times by an impressive 50% when compared to the PD controller. Additionally, the SMC demonstrates the ability to significantly reduce control efforts, as evidenced by actuator voltage. In the context of forced vibrations, the SMC maintains its superior performance, especially at lower frequencies. However, at higher frequencies, the emergence of chattering affects the SMC’s performance, although it remains more effective than the PD controller in low-frequency scenarios. This study sheds light on the effectiveness of piezoelectric-based control strategies for smart beams, offering valuable insights into their performance under various vibration conditions. These findings hold significant promise for practical applications where vibration control is critical.

An Analytical Solution of Piezoelectric Energy Harvesting from Vibrations in Steel-Concrete Composite Beams subjected to Moving Harmonic Load

An Analytical Solution of Piezoelectric Energy Harvesting from Vibrations in Steel-Concrete Composite Beams subjected to Moving Harmonic Load

A Novel Approach of the Viscoelasticity of Axially Functional Graded Bar and Application of Harmonic Vibration Analysis of an Isotropic Beam as Support

The use of smart materials and passive controllers in modern technologies has stimulated the study of vibration in elastic systems with viscoelastic damping. It is also possible to create components with precise material distribution coefficients and distinct properties, such as Functionally Graded Materials. This work investigates the resonant frequency characteristics of a beam supported at its ends by Axially Functionally Graded (AFG) viscoelastic bars using the finite element method. The set of equations governing motion is obtained by assuming Euler–Bernoulli beam theory for the beam and bar theory for the bars using Lagrange’s equations. The material properties of the functionally graded bar is assumed to vary through the length according to the power law distribution. The longitudinal loss factor values are used to define the internal damping coefficient, which is also dependent on the Young’s modulus value varying along the bar. The effects of the length-varying material properties and internal damping of the FG support bars on the force transmission TR and frequency parameters λ are examined in detail. No study has been found in the literature on the vibration of viscoelastic FG bar-supported beams subjected to a harmonic force at the centre point. It is shown that using bars formed with combinations of different materials considering material damping will be useful to keep the vibration level and force transmission at a certain value and control the frequency parameters.

Nonlinear free vibrations of a structurally tailored anisotropic pre-twisted thin-walled beam subjected to large deformations

It is essential to understand the nonlinear free vibration behaviour of a thin-walled composite structure as they find their applications in harsher environments prone to large deformations. Further, these structures made of fibrous materials, have directional properties for different fibre orientations resulting in a diversified and a complex nonlinear behaviour. In this regard, present work provides a comprehensive mathematical formulation on nonlinear vibration of pre-twisted thin-walled anisotropic box beam. The mathematical model is derived as coupled (flap-lag-extension-torsion) model considering shear deformation and green's strain tensor for large displacements in order to study the influence of nonlinear couplings on the dynamic behaviour. The derived energy equations are presented depending on degree of nonlinearity. These nonlinear equations those derived are nondimensionalized and solved with in the frame work of energy method using classical Ritz approximation. An iterative method is used to solve the nonlinear equations pertaining displacement terms. This nonlinear behaviour is evaluated for two important types of structural tailoring techniques available for thin-walled composite beams namely Circumferentially Asymmetric Stiffness (CAS) and Circumferentially Uniform Stiffness (CUS). It is found that CAS layup experiences significantly severe nonlinear effects compared to CUS due to the presence of 3rd degree nonlinear coupling terms. The variation of nonlinear frequency ratios over different ply angles showing the influence of nonlinearity on fibres orientation is presented for the first time for the two ply lay ups. The influence of degree of nonlinearity on the accuracy of the nonlinear frequencies is evaluated and presented. Moreover, the impact of nonlinearity on the pre-twisted beam is presented for different pre-twist angles.

Numerical analysis of energy dissipation due to eddy currents in a vibrating beam

Vibration attenuation is a key aspect of mechanical engineering. One method to achieve this is through eddy currents, which can be generated in a vibrating system when a magnetic field is present, creating forces that oppose motion. This study examines a mechanical system consisting of a thin cantilever beam vibrating in a uniform and time-invariant magnetic field under steady-state conditions to understand the nature of energy dissipation and the relationship between motion, eddy currents, and damping forces. The calculation of eddy currents generally requires the use of complex numerical procedures. However, for systems with simple geometry, such as a cantilever beam, a recent numerical procedure based on the finite difference method, known for its simplicity in implementation, has been adapted and expanded to determine eddy currents under motional induction. A numerical application has been developed in which the vibration of a specific beam is characterised by its bending or torsional mode shapes, and the nature of the corresponding dissipative forces is analysed. Results indicate that the eddy currents are an effective means of dissipating energy at lower-order modes. Additionally, the direction of the applied magnetic field can induce coupling between bending and torsional vibrations.

IRC controller for suppressing the vibrations of cantilever beam excited by an external force

IRC controller for suppressing the vibrations of cantilever beam excited by an external force

Broadband and robust vibration reduction in lattice-core sandwich beam with 3D-printed QZS resonators

The demand for lightweight lattice-core sandwich structures that exhibit superior mechanical and dynamic properties is widespread in many devices. This paper presents a lattice-core sandwich beam (LSB) with an embedded array of quasi-zero-stiffness (QZS) resonators, referred to as Q-LSB. This research distinguishes itself from existing studies on metamaterial structures with QZS resonators by investigating the nonlinear stiffness of QZS resonators and the damping of a soft three-dimensional (3D) printing material. The objective is to achieve efficient and robust vibration reduction beyond the band gap of its linear counterpart. We investigate the beam vibration using both experimental and numerical methods. The experimental results demonstrate that the resonators can entail significant vibration reduction in a wide frequency range, covering the first three eigenmodes of the host LSB. Furthermore, the reduction effect improves as the excitation level increases within the tested excitation range, highlighting the structure’s robustness against the excitation amplitude. A numerical model based on a dynamically equivalent homogenization method and the finite element method is established and experimentally validated. Subsequently, the numerical parametric results reveal that the broadband vibration reduction is due to the damping effect, while the robust vibration reduction effect is attributed to the nonlinear stiffness of the resonators.

Analysis of the effect of nonlocal factors on the vibration of nanobeams

Abstract Currently, the Eluer-Bernoulli beam nonlocal theory does not fully consider the effects of foundation deformation and axial force on the beams, and cannot accurately reflect the real mechanical properties of nanobeams. The primary objective of this study is to introduce a novel computational method designed for an enhanced characterization of the vibrational behavior of nano beams. Initially, this method incorporates the influence of foundation deformation on beam bending, accounts for the effects of axial forces, integrates Eringen's nonlocal theory, and establishes a modified Euler-Bernoulli beam theory model for the first time, accompanied by a degradation validation of the model. Subsequently, the Laplace transform and Hasselman's complex mode synthesis method are utilized to solve the model, providing the first derivation of the state-space transfer function for the nano beam vibration model based on the modified Euler-Bernoulli beam theory that includes axial force effects. Lastly, the study elucidates the impact of nonlocal factors and various parameters on the vibration characteristics of nanobeams. The results show that the order n increases, and the peak frequency value moves in the direction where the nonlocal factor tends to zero. When the order n is less than 6, the frequency peak is mainly concentrated in the interval where the nonlocal factor is greater than 0 and less than 0.1. At the same order, the beam length increases, and the peak frequency moves in the direction of increasing non-local factor. The modified geometric parameters and the foundation beam stiffness parameters have a greater effect on the peak of the beam's vibration mode in the higher order case and a lesser effect in the lower order case. The larger the nonlocal factor, the larger the peak of the vibration mode. The foundation beam stiffness parameter also has an effect on the direction of the peak vibration mode at the 1st and 2nd orders. The research results will help to predict the vibration behavior of nano beams under different conditions more accurately and provide an important reference for related applications.

Hybrid piezo-triboelectric wind energy harvesting mechanism with flag-dragging the cantilever beam vibration

Hybrid power generators will improve the extraction of electrical energy from the wind to develop sustainable and eco-friendly self-powered wireless sensors. A novel piezo-triboelectric flag wind energy harvesting nanogenerator (P-FTENG) is proposed that consists of a piezoelectric cantilever beam and a triboelectric flag. The flag flutters in the wind, inducing vibration in the cantilever beam, thereby converting wind energy into electrical power with piezo and triboelectric effects. Based on the aerodynamic mechanism, a nonlinear flutter theoretical model is derived to evaluate the drag force and pressure of fluid separation on the piezo-triboelectric structure. Furthermore, this paper comprehensively elaborates on the transverse motion of the flag flutter caused by the airflow. The force from the transverse motion excites the cantilever beam. The power output of P-FTENG generation depends on various factors. The optimized flag-shaped configuration may activate the piezoelectric cantilever beam vibration and decrease the crucial flutter wind speed, according to test results. P-FTENG generates a voltage of around 17.8 V when the wind speed is 8.5 m/s. The cantilever beam energy harvester's PEH reaches 32 mW/m2, while Flag-TENG's output power density reaches 37 μW/m2, which charges capacitors and lights the array of LEDs. The hybrid piezo-triboelectric flag nanogenerator fluttering in the wind is promising for powering the function of a calculator or electronic thermometer/hygrometer sensor.

Fuzzy PI vibration suppression control strategy for space double flexible telescopic manipulator with fractional disturbance observer

The space double flexible telescopic manipulator (SDFTM) with time-varying length, is called the space flexible manipulator and can carry out reciprocating linear telescopic motion along its axis. It possesses characteristics such as lightweight flexibility, small space occupation, large turning radius, and a wide working range. These features can assist astronauts in performing complex tasks in dangerous outer space environments and offer broad application prospects. However, due to the highly nonlinear and time-varying length characteristics of the space flexible manipulator, its dynamic modeling becomes more complex and challenging. Moreover, during the rotation of the space flexible manipulator, its inherent flexible behavior can trigger vibration phenomena, significantly impacting the execution accuracy of on-orbit tasks. Therefore, proposing control methods to address vibration issues is an effective approach. Thus, achieving stable and precise operation of the space flexible manipulator necessitates the precise establishment of its dynamic model and the development of high-precision control algorithms, which have become key research directions. Firstly, a time-varying dynamic modeling method of the space manipulator is proposed by combining the Lagrange principle and flexible beam vibration theory. Unlike the traditional method, which only considers the limit length of the space manipulator under static conditions, the dynamic process of the space manipulator presented during actual operation is fully considered, which greatly improves the modeling accuracy. Then, a time-varying model based on the fuzzy PI real-time control strategy (FD-FZPI) with fractional order disturbance observer (FO-DOB) is proposed. Based on the robust stability principle, a more accurate FO-DOB is proposed based on integer order DOB, coupled with a fuzzy PI controller to compensate for the external disturbance and modeling error of the space manipulator. Finally, numerical simulation analysis is carried out, and the results show that the average parameter difference between the time-varying dynamic model and the static dynamic model can reach about 5.2 %, which indicates the accuracy of the proposed dynamic modeling method. At the same time, the proposed FD-FZPI control strategy achieves about 14.6 % performance improvement over the traditional DOB-PI control method, indicating that the proposed control strategy can effectively suppress the flutter fluctuation of the space manipulator and achieve accurate and stable dynamic tracking.

Analytical Solution for Dynamic Response of a Reinforced Concrete Beam with Viscoelastic Bearings Subjected to Moving Loads.

To provide a theoretical basis for eliminating resonance and optimizing the design of viscoelastically supported bridges, this paper investigates the analytical solutions of train-induced vibrations in railway bridges with low-stiffness and high-damping rubber bearings. First, the shape function of the viscoelastic bearing reinforced concrete (RC) beam is derived for the dynamic response of the viscoelastic bearing RC beam subjected to a single moving load. Furthermore, based on the simplified shape function, the dynamic response of the viscoelastic bearing RC beam under equidistant moving loads is studied. The results show that the stiffness and damping effect on the dynamic response of the supports cannot be neglected. The support stiffness might adversely increase the dynamic response. Further, due to the effect of support damping, the free vibration response of RC beams in resonance may be significantly suppressed. Finally, when the moving loads leave the bridge, the displacement amplitude of the viscoelastic support beam in free vibration is significantly larger than that of the rigid support beam.

Experimental and theoretical evaluation of axial forces in short steel ropes

AbstractAssessing rope force in bridge structural health monitoring, particularly for shorter lengths, poses challenges. The vibration method, commonly utilized for taut strings, yields inaccurate results for short ropes due to neglecting bending stiffness. To address this, the differential equation of lateral vibration of a prismatic beam possessing bending stiffness EI, evenly distributed mass m under the tension force N is solved approximately and numerically using FEM for greater accuracy. Nonlinear fitting via the Gauss‐Newton aids in refining results. Laboratory experiments, varying axial forces and rope characteristics, validated these methods, offering recommendations for improved accuracy.

Analysis of the transverse vibration of a multistepped FGM beam resting on a Winkler foundation in a thermal environment and carrying concentrated masses

This paper examines a novel case study involving the free vibration of a stepped FGM beam-mass system resting on elastic foundations and subjected to a nonlinear or uniform thermal load. The present study examines the complex interaction of thermal effects on dynamic behavior by varying the cross-section and length ratios, material parameters and mass magnitudes. After adopting Euler-Bernoulli's theory, the dynamic behavior of non-uniform FGM beams was investigated using the generalized finite element method (GFEM) and the Rayleigh quotient finite element method (RQFEM). In line with the objective set, relevant results derived from parametric studies, showcasing accentuated variation in dimensional frequency curves and bending moments, have been highlighted and discussed.

Asymptotic analysis of geometrically nonlinear beam vibrations: Kirchhoff and Bolotin equations

AbstractThe paper analyzes various approximate models of geometrically nonlinear vibrations of a beam. In practice, simplified equations are often based on the quasi‐static Kirchhoff hypothesis—neglecting axial inertia. This hypothesis is justified with the prescribed end‐displacements of the beam in the axial direction. Under dead loading, quasi‐static Kirchhoff hypothesis results in a linear equation. The corresponding approximate equations obtained in this paper are based on the asymptotic procedure. The ratio of bending stiffness to reduced tensile/compressive stiffness is taken as a small parameter. Axial inertia is taken into account in the equation of the first approximation. Introduced by V.V. Bolotin concept “nonlinear inertia” is discussed. The most common errors in using the quasi‐static Kirchhoff hypothesis are analyzed.

Bifurcations and Chaos in a Cantilever Beam Vibration Model with Small Damping and Periodic Forced Terms

Bifurcations and Chaos in a Cantilever Beam Vibration Model with Small Damping and Periodic Forced Terms

Optimal control problem governed by a kind of Kirchhoff-type equation

In this paper, we consider an optimal control problem governed by a kind of Kirchhoff-type equation, which plays an important role in the phenomenon of beam vibration. Firstly, the existence of solution to the state equation is proved by the variational method. Secondly, for the given cost functional, we get that there exists at least an optimal state-control pair via the Sobolev’s embedding theorem under the constraint of the state equation. Next, the necessary optimality condition for the optimal solution is derived by using the cone method. Finally, we give the pointwise variational inequality, minimum principles and an equivalent necessary condition for the optimal control problem according to the discussion of the variational inequality.

Impact of porosity distribution and grading parameters on free vibration of functionally graded beams

This study focuses on investigating the free vibration of porous functionally graded (FG) beams based on neutral surface position and the impact of porosity distribution on the properties and performance of materials. To achieve this, the study assumes that the beam’s material characteristics vary continuously along its thickness direction. The volume fraction of constituents is specified using the modified rule of the mixture, which includes porosity volume fraction with changed porosity patterns across the cross-section. The study uses the parabolic shear deformation theory without shear correction factors to derive the equations of motion by applying Hamilton’s principle. The study employs Navier’s method to obtain analytical results for the free vibration of porous FG beams. To verify the proposed formulation, the study compares the results with relevant findings from the literature. The study also examines the relationship between frequency of vibration and grading parameter in homogeneous porosity distributions, as well as the frequency of vibration in beam structures with different porosity patterns. Additionally, numerical examples are provided to investigate the impact of parameters like power-law index, span to depth ratio, porosity distribution pattern, and porosity volume fraction on the natural frequencies of FG beams.

The analysis for fatigue caused by vibration of railway composite beam considering time-dependent effect

The time-dependent effects in steel-concrete composite beam bridges can intensify track irregularities, subsequently leading to amplified train-bridge coupling vibrations. This phenomenon may increase the stress amplitudes in the bridge steel, thereby impacting the fatigue performance of the composite structures. This paper employs multiple rigid body dynamics to construct a high-speed train model and utilizes the finite element method to develop a steel-concrete composite beam element model that accounts for time-dependent effects, interfacial slip, and shear hysteresis. This approach enables the computational analysis of the train-bridge coupling system, facilitating an investigation into the influence of concrete’s time-dependent effects on the fatigue performance of railway steel-concrete composite bridges. Focusing on a 40-m simply supported composite bridge, the train-bridge coupling dynamic responses were computed for each operational year within a decade of the completion of construction. Applying the P-M linear fatigue damage accumulation theory, statistical analysis of stress history data across various operational periods was conducted to quantify the fatigue damage induced by a single eight-car high-speed train on the lower flange of the mid-span steel beam and the beam-end studs. The findings reveal that the beam-end studs sustain greater damage than the mid-span steel beam. Moreover, the detrimental impact of time-dependent effects diminishes with the increase of operational years. Notably, compared to the initial year, the fatigue damage to the lower flange of the mid-span steel beam by an eight-car train in the tenth year has surged by 39.3%. Conversely, the damage to the beam-end studs has decreased by 47.5%.

Energy generation from friction-induced vibration of a piezoelectric beam

The primary challenge in harnessing vibration energy with piezoelectric materials is the discrepancy in frequency between the energy source and the energy generator, which lowers the efficiency of energy harvesting. To address the challenge, a piezoelectric beam under friction-induced vibration (FIV) is designed, modeled, and studied for the first time to realize the pronounced FIV contributing to energy generation by adapting the vibrations of the continuum structure to align close to its resonant frequencies. The Stribeck friction model is applied to characterize the variation of friction based on the relative sliding velocity vr between contacting objects. The analytical solution is derived to solve the dynamic responses, and transient charging simulation validated by the experiment is utilized to assess energy output. Furthermore, parameter studies are conducted based on the validated model with regard to the material properties of the beam and piezoelectric material, electrode connections of piezoelectric patches, and friction model parameters to investigate their influences on energy output. Considering the same dimensional properties, materials with low Young's modulus E and density ρ are desired for the host structure to facilitate large dynamic strain in piezoelectric materials. With an exponential decay factor C = 8, representing optimal material contact interface, pronounced higher FIV mode can be induced leading to higher output power. A root mean square charging power PeRMS of 42.4 mW and a peak instant charging power Pe − peak of 263 mW can be achieved. In the current study, the model is implemented on a beam coupled with one piezoelectric patch, which has potential applicability to non-uniform beams with various layouts of piezoelectric patches. The presented model enables efficient optimization of continuum structural design for higher piezoelectric energy generation under friction.

Discrete variational method for partial differential equations of functionally gradient beam vibration

Discrete variational method for partial differential equations of functionally gradient beam vibration