Amplitude Of Excitation Force Research Articles

An harmonic equivalent excitation method for random vibration response

Many loads on engineering structures had obvious randomness, such as earthquakes, wind, sea waves, uneven pavement, etc. The calculation and analysis of random vibration were complicated and inefficient, which has perplexed the development of engineering technology for a long time. To solve the above problems, this paper proposed a harmonic equivalent excitation method for structural random vibration analysis. The excitation force of multi-frequency action in continuous time interval was converted into harmonic excitation force with the same effect as superposition excitation in each discrete time interval by a harmonic equivalent method. The frequency and amplitude of harmonic excitation force in discrete-time intervals were calculated, which were then taken as the deterministic load input of the structure. The response of the structure was calculated by the conventional structural dynamic analysis method. Finally, the harmonic equivalent excitation method was used to analyze random pavement excitation and its application in the control of time-delay vibration reduction. The results show that the harmonic equivalent excitation method simplifies the calculation form of random vibration analysis without reducing the accuracy, and provides an effective method for analyzing random vibration in the engineering field.

An abnormal vibration diagnosis and control method for internal combustion power plant

Abstract Focusing on the difficulty in vibration control of internal combustion power plant because of its diverse substructures and complex excitation, an abnormal vibration diagnosis and attenuation method based on the system’s whole-body vibration signals is proposed. The characteristics of the exciting forces, such as toppling torque, inertia force (or moment) and coupling centrifugal force, are analyzed. The resonance frequency distribution of the power unit is obtained by modal analysis. Then an expression that could reveal the relationship between the whole-body vibration intensity and the exciting force amplitude is established, and conclusion is drawn that different excitations would drive the system to vibrate at different frequencies. Based on this basic relation, a fault diagnosis method relying on comprehensive analysis of vibration signals in both time and frequency domain is proposed. Vibration attenuation methods targeted at specific faults are also put forward. Finally, the validity of the proposed method is verified by applying it to a 12V280 diesel generator set.

Study on excitation force characteristics in a coupled shaker-structure system considering structure modes coupling

The interaction between an elastic structure and electrodynamic shakers commonly exists in Ground Flutter Simulation Tests (GFST) with multi-point excitations, causing a considerable discrepancy between the practical excitation forces and desired ones. To investigate the excitation force characteristics on a cantilever beam excited by a voltage-sourced electrodynamic shaker, the coupled shaker-beam system is modeled to derive the excitation force formula using Hamilton’s principle and Galerkin’s approach. Simulation results using the multi-mode beam model coupled with the shaker model are in good agreement with experimental results, verifying that the proposed multi-mode method can accurately predict the excitation force. Furthermore, parametric studies show that the influence of system parameters on the excitation force is related to the shaker's operating mode. Unlike in current mode of shaker, when the beam resonant frequency approaches the suspension frequency of shaker armature, the variation of excitation force amplitude in voltage mode is no longer minimal. Meanwhile, if the exciting point in the GFST is located far away from the modal node, it is essential to compensate the force because the accuracy of tests can be reduced dramatically. The coupled shaker-beam model proposed in this paper can provide the basis for compensation measures.

Numerical identification of the dynamic characteristics of a nonlinear foil bearing structure: Effect of the excitation force amplitude and the assembly preload

Modelling and identification of the dynamic characteristics of foil bearings under varying loads pose a great challenge and require the use of advanced numerical models. Although simple models can represent the structural characteristics of foil bearings with a certain degree of approximation, they are not able to reliably predict the properties of such a system over a wide range of external and internal loads. This is why the authors of this paper have undertaken to develop a model of the foil bearing structure, which would take into account all the most important phenomena affecting its dynamic properties. The model was developed using the finite element method, making it possible to represent the complex shape of the foil assembly and its geometric nonlinearity as well as the contact phenomena and friction, using static and kinetic friction coefficients. This model was verified experimentally and then used to identify the dynamic characteristics of the foil bearing over a wide range of loads, including different radial clearance and assembly interference. An original method of modelling the assembly preload is also proposed. The results confirmed that the parameters analysed have an enormous impact on the stiffness and damping coefficients. The presented methods can help other researchers assess the dynamic characteristics of a bump-type foil bearing structure. The presented structural model provides dynamic parameters that are necessary for a thorough analysis of the entire foil bearing.

Dynamical analysis of series hybrid electric vehicle powertrain with torsional vibration: Antimonotonicity and coexisting attractors

In this paper, nonlinear dynamics of the torsional vibrations of the Series Hybrid Electric Vehicle (SHEV) powertrain are explored. The mathematical equation of the SHEV is obtained by considering both internal and external excitations. We examine the effects of rotational speed, load fluctuation, and road fluctuation on the dynamics of the proposed model. Preliminary analysis based on Hamiltonian energy shows that there is sufficient energy to maintain continuous oscillation behaviors. Our study shows that the interaction between internal and external perturbations originates an important set of phenomena, including chaos, when varying system parameters. More interestingly, the exciting phenomenon of multistability is investigated for the first time on the proposed SHEV model. Furthermore, when increasing excitation force amplitude in some specific regions, an interesting scenario of antimonotonicity is found. • Nonlinear dynamics of the torsional vibrations of the Series Hybrid Electric Vehicle (SHEV) powertrain are explored. • Both internal and external excitations are considered in the mathematical model. • The Hamiltonian energy shows that there is sufficient energy to maintain continuous oscillation behaviors. • The exciting phenomenon of multi-stability is investigated on the proposed SHEV model. • Anti-monotonicity and period-doubling bifurcations are also reported when adjusting the excitation force amplitude of the system.

Micro windmill piezoelectric energy harvester based on vortex-induced vibration in tunnel

A micro windmill piezoelectric energy harvester is proposed to explore the wind energy translation based on vortex-induced vibration(VIV). The novel power takeoff is composed of a wind turbine with three blades, an air blast blower, an ancillary wind tunnel, and a circular PVDF piezoelectric converter. The air blower improves the airflow speed in the wind tunnel. A bluff body is fixed in the flow field to induce vortex and excite the circular PVDF piezoelectric film vibration. Theory and experiments are conducted to investigate the energy translation. Based on the blade element momentum method(BEM), the theoretical model of the air blast blower is derived. The calculation results show that the axial fan blasts the air into the wind tunnel, and the airflow speeds range from 1.37 m/s to 18.78 m/s. Furthermore, the theoretical model of the VIV is developed to decorated the airflow aerodynamic characteristics around the bluff body. The vortex-induced high-frequency resonance consequently improves the piezoelectric energy harvesting efficiency and promotes the excitation force amplitudes. Correspondingly, the output electric power on the piezoelectric plate is numerically investigated based on the theoretical model and experiment. The optimal output power matches the load resistance and the wind velocity on the bluff body. The maximal output power arrived at 8.97 μW on the external load resistance of 650 KΩ with a wind velocity of 19 m/s. Furthermore, experimental results validate the theoretical dynamic model and show that a windmill piezoelectric energy harvester based on vortex-induced vibration (VIV-WPEH) can increase the output power over either range of the low natural airflow speed and the optimizing bluff body individually.

Development of a model for predicting dynamic response of a sphere at viscoelastic interface: A dynamic Hertz model

A model for predicting the dynamic response of a sphere at viscoelastic interface is presented. The model is based on Hertz contact model and the model for a sphere in a medium. In addition to the elastic properties of medium and the size of sphere, the model considers the density of sphere, the density and viscosity of medium, and damping of oscillations of sphere due to radiation of shear waves. The model can predict not only the effects of the mechanical properties of medium, the physical properties of sphere, and the amplitude of excitation force on sphere displacement, but also the effects of these parameters on shift of resonance frequency. The proposed model can be used to identify the elastic and damping properties of materials, and to understand the dynamic responses of spherical objects at viscoelastic interfaces in practical applications.

Adaptive versus Conventional Positive Position Feedback Controller to Suppress a Nonlinear System Vibrations

The nonlinear vibration control of a nonlinear dynamical system modeled as the well-known Duffing oscillators is investigated within this article. The conventional Positive Position Feedback (PPF) controller is proposed to mitigate the considered system nonlinear vibrations. The whole system mathematical model is analyzed by applying the multiple time scales perturbation method. The slow-flow modulation equations that govern the oscillation amplitudes of both the main system and controller are derived. The stability analysis is investigated based on Lyapunov’s first method. The effects of the different control parameters on both the main system and controller are explored. The obtained analytical and numerical results illustrated that the PPF controller can eliminate the main system nonlinear vibrations once the controller natural frequency is tuned to be the same value as the external excitation frequency, otherwise, the controller adds excessive vibrational energy to the main system rather than suppressing it. In addition, the PPF controller can destabilize the main system motion when excited by strong excitation force. Therefore, a modified version of the PPF controller named the Adaptive Positive Position Feedback (APPF) controller is proposed to overcome the main drawbacks of the conventional PPF controller. The idea is to track the external excitation frequency using an adaptive frequency measurement technique to update continuously the PPF controller natural frequency to become the same value of the excitation frequency. Based on this strategy, the system mathematical model is analyzed again by making the controller’s natural frequency equal to the external excitation frequency. The obtained analytical and numerical simulations showed that the adaptive positive position feedback controller can suppress the main system nonlinear vibration close to zero regardless of the excitation force amplitude and excitation frequency.

Identification of nonlinear normal modes for a highly flexible beam

In this paper, a new approach is used to obtain the nonlinear mode for a flexible cantilever beam. The dependency of resonance of the beam on the exciting force amplitude is observed experimentally and theoretically. In this regard, the end response of a cantilever beam under the base excitation is measured for various force amplitudes. Then, by using the nonlinear normal modes, the reduced-order governing equation is obtained. The discrete model obtained according to identification of nonlinear terms can predict the frequency response of the beam and jump phenomenon properly. Comparison between experimental data and theoretical outputs show acceptable agreement.

Development of a mathematical model of a vibrating polyfrequency screen as a dynamic system with distributed parameters

A mathematical model of a vibrating polyfrequency screen as a dynamic system with distributed parameters has been developed. The dynamic system of solids of finite sizes was chosen as the design scheme for the screen: framework, sieves with bulk material and impactors, the contact interaction of which occurs through two-side bonds and collisions on surface areas that have elastic-damping coverings. It is shown that a change in the amplitude of the exciting force has a significant effect on the dynamics of vibration impactors of a polyfrequency vibrating. There is an amplitude value at which the impactor passes from the mode without interacting with elastic bonds to the vibro-impact mode. The impactor movements begin to change disproportionately altered by the exciting force amplitude. It is shown that the start of the impactors in the screen substantially depends on the exciting force. Changes in the amplitude of the exciting force make it possible to achieve chaotic oscillations of impactors, which in turn leads to oscillations of screen surfaces with a continuous frequency spectrum, i.e. to the operation mode of the screen, which is most appropriate for dehydration and separation of fine mineral fractions.

Measurement of multivalued response curves of a strongly nonlinear system by exploiting exciter dynamics

A strongly nonlinear system often has multiple solutions under harmonic excitation. However, measuring all of these multiple responses in structural dynamics is challenging because often one solution is unstable and difficult to obtain. The standard stepped sine approach is to fix the harmonic excitation force amplitude, and step the excitation frequency up or down. This leads to the well-known jump phenomenon, and captures at most two stable solutions. Alternatively, the excitation frequency can be fixed and the amplitude swept up or down, although this also leads to jumps in the response. Recently, experimental continuation methods have successfully measured all solutions, including the unstable solutions, via active control. This paper takes a different approach and exploits the dynamics of the electromagnetic exciter to both stabilize the unstable solution, and also to track the solutions continuously, without any jumps. This is achieved by monotonically increasing or decreasing the voltage applied to the exciter at a fixed frequency, and using the force drop-out phenomenon through the resonance to control the force applied to the structure. In these tests, the input voltage then defines the continuation parameter, rather than force amplitude or frequency in the standard tests. The obvious advantage of this method is that there is no feedback control of the excitation and it is easy to implement. A strongly nonlinear single degree of freedom system is used to demonstrate this method.

Stress-constrained topology optimization of continuum structures subjected to harmonic force excitation using sequential quadratic programming

In this paper, we propose a method for stress-constrained topology optimization of continuum structure sustaining harmonic load excitation using the reciprocal variables. In the optimization formulation, the total volume is minimized with a given stress amplitude constraint. The p-norm aggregation function is adopted to treat the vast number of local constraints imposed on all elements. In contrast to previous studies, the optimization problem is well posed as a quadratic program with second-order sensitivities, which can be solved efficiently by sequential quadratic programming. Several numerical examples demonstrate the validity of the presented method, in which the stress constrained designs are compared with traditional stiffness-based designs to illustrate the merit of considering stress constraints. It is observed that the proposed approach produces solutions that reduce stress concentration at the critical stress areas. The influences of varying excitation frequencies, damping coefficient and force amplitude on the optimized results are investigated, and also demonstrate that the consideration of stress-amplitude constraints in resonant structures is indispensable.

The effects of structural parameters on excitation force of airflow vibration piezoelectric generator

In order to meet the requirements of airflow vibration piezoelectric generator, and solve the critical issue of stable excitation force, the key is to effectively control structure sensitive parameters. The range of structural parameters of airflow excitation device are optimized by simplified orthogonal test. The result shows that corresponding to different resonator lengths, it approximates a linear increasing trend between the amplitude of excitation force and airflow velocity, and the greater length owns the smaller slope, and vice versa. It is relatively complex for the space and ring gaps, too big or too small gap would make the amplitude smaller or even no waveform formed. The length of resonator is the main factor impacting on the frequency of excitation sound pressure, and the frequency decreases with the increase of the length, presenting an inverse relationship, and the space and ring gaps have less effect on the frequency. Therefore, for high airflow velocity, the stable excitation force of high amplitude and frequency can be obtained by short resonator. In addition, reasonable space and ring gaps are also important for ensuring bigger amplitude of excitation sound pressure. The resulting sensitive parameter values of sound excitation device can be used as references for engineering design.

Field Tests for Investigating the Extraction Rate of Piles Using a Vibratory Technique

Factors directly affecting the extraction rate of the piles pulled out by a vibratory pulling system are summarized and classified into five categories (excitation force, resistance, vibration amplitude, pile plumbness keeping, and slowing down at the later stage) from the mechanics and engineering practice. Field tests on steel sheet piles extracted by vibratory technique in different soil conditions are conducted to ascertain how these factors affect the extraction rate of a pile with regard to three major actors of vibratory pile pulling: the pile to be extracted, the selected pulling system, and the imposed soil conditions. The extraction rates of three different sheet pile types (having up to four different lengths) pulled out by two different vibratory pulling systems are documented. The piles with different lengths and types, pulled out with or without a clutch, have different extraction rates. The working parameters governing the vibratory hammer, such as excitation force and vibration amplitude, exert significant influences on the rate of pile extraction, especially in the early stages of up-lift process. The extraction rate of the piles driven in different soil conditions is uniform because different extraction resistances mainly refer to shaft friction. The properties of the pile-soil interface influence the extraction rate of the piles, and the extraction rate decreases with the time for which the piles have been buried in the earth.

Principal-internal resonance of an axially moving current-carrying beam in magnetic field

The magneto-elastic 1:3 principal-internal resonance of axially moving current-carrying beams in a magnetic field is investigated. With the elastic theory of Euler–Bernoulli beam and the basic theory of electromagnetic field taken into account, the magneto-elastic vibration equation of an axially moving beam in a magnetic field is therefore developed by the Hamiltonian principle. On the basis of the hypothetical two-order modal shape function satisfying the fixed-hinged boundary condition, amplitude–frequency response equations of the 1:3 principal-internal resonance are obtained by Galerkin and multi-scale method. Calculation results based on relevant MATLAB programming, show that: When the system first-order primary resonance occurs, the second-order modal amplitude that should be disappeared excited by internal resonance, but its value is smaller than the first-order modal amplitude. It has only two changing stages and lacks a small single-value area in the curve of amplitude and external excitation force amplitude for the first-order primary resonance of the system; the curves of amplitude versus magnetic field strength, influenced by applied current, exhibit an asymmetric distribution property along the longitudinal line where the value of the magnetic field strength is zero; the response can be dominated by the first mode in the second-order primary-internal resonance of the system, in which the amplitude of the external excitation must exceed a critical value before the first mode can be excited. In addition, such as the axial velocity, the magnetic field strength, the excitation amplitude and the tuning parameters have a significant effect on the amplitude of the system, especially the magnetic field has an obvious inhibitory effect on the vibration.

Magneto-elastic dynamics and bifurcation of rotating annular plate**Project supported by the National Natural Science Foundation of China (Grant No. 11472239), the Hebei Provincial Natural Science Foundation of China (Grant No. A2015203023), and the Key Project of Science and Technology Research of Higher Education of Hebei Province of China (Grant No. ZD20131055)

In this paper, magneto-elastic dynamic behavior, bifurcation, and chaos of a rotating annular thin plate with various boundary conditions are investigated. Based on the thin plate theory and the Maxwell equations, the magneto-elastic dynamic equations of rotating annular plate are derived by means of Hamilton’s principle. Bessel function as a mode shape function and the Galerkin method are used to achieve the transverse vibration differential equation of the rotating annular plate with different boundary conditions. By numerical analysis, the bifurcation diagrams with magnetic induction, amplitude and frequency of transverse excitation force as the control parameters are respectively plotted under different boundary conditions such as clamped supported sides, simply supported sides, and clamped-one-side combined with simply-anotherside. Poincaré maps, time history charts, power spectrum charts, and phase diagrams are obtained under certain conditions, and the influence of the bifurcation parameters on the bifurcation and chaos of the system is discussed. The results show that the motion of the system is a complicated and repeated process from multi-periodic motion to quasi-period motion to chaotic motion, which is accompanied by intermittent chaos, when the bifurcation parameters change. If the amplitude of transverse excitation force is bigger or magnetic induction intensity is smaller or boundary constraints level is lower, the system can be more prone to chaos.

Optimum LCVA for suppressing harmonic vibration of damped structures

Explicit design formulae of liquid column vibration absorber (LCVA) for suppressing harmonic vibration of structures with small inherent structural damping are developed in this study. The developed design formulae are also applicable to the design of a tuned mass damper (TMD) and a tuned liquid column damper (TLCD) for damped structures under harmonic force excitation. The optimum parameters of LCVA for suppressing harmonic vibration of undamped structures are first derived. Numerical searching of the optimum parameters of tuned vibration absorber system for suppressing harmonic vibration of damped structure is conducted. Explicit formulae for these optimum parameters are then obtained by a series of curve fitting techniques. The analytical result shows that the control performance of TLCD for reducing harmonic vibration of undamped structure is always better than that of non-uniform LCVA for same mass and length ratios. As for the effects of structural damping on the optimum parameters, it is found that the optimum tuning ratio decreases and the optimum damping ratio increases as the structural damping is increased. Furthermore, the optimum head loss coefficient is inversely proportional to the amplitude of excitation force and increases as the structural damping is increased. Numerical verification of the developed explicit design expressions is also conducted and the developed expressions are demonstrated to be reasonably accurate for design purposes.

A multi-frequency fatigue testing method for wind turbine rotor blades

Rotor blades are among the most delicate components of modern wind turbines. Reliability is a crucial aspect, since blades shall ideally remain free of failure under ultra-high cycle loading conditions throughout their designated lifetime of 20–25 years. Full-scale blade tests are the most accurate means to experimentally simulate damage evolution under operating conditions, and are therefore used to demonstrate that a blade type fulfils the reliability requirements to an acceptable degree of confidence. The state-of-the-art testing method for rotor blades in industry is based on resonance excitation where typically a rotating mass excites the blade close to its first natural frequency. During operation the blade response due to external forcing is governed by a weighted combination of its eigenmodes. Current test methodologies which only utilise the lowest eigenfrequency induce a fictitious damage where additional tuning masses are required to recover the desired damage distribution. Even with the commonly adopted amplitude upscaling technique fatigue tests remain a time-consuming and costly endeavour. The application of tuning masses increases the complexity of the problem by lowering the natural frequency of the blade and therefore increasing the testing time. The novel method presented in this paper aims at shortening the duration of the state-of-the-art fatigue testing method by simultaneously exciting the blade with a combination of two or more eigenfrequencies. Taking advantage of the different shapes of the excited eigenmodes, the actual spatial damage distribution can be more realistically simulated in the tests by tuning the excitation force amplitudes rather than adding tuning masses. This implies that in portions of the blade the lowest mode is governing the damage whereas in others higher modes contribute more significantly due to their higher cycle count. A numerical feasibility study based on a publicly available large utility rotor blade is used to demonstrate the ability of the proposed approach to outperform the state-of-the-art testing method without compromising fatigue test requirements. It will be shown that the novel method shortens the testing time and renders the damage evolution with a higher degree of fidelity.

Passive targeted energy transfer in the steady state dynamics of a nonlinear plate with nonlinear absorber

In this work, the inducement of passive nonlinear sink for vibration control of nonlinear plate model was studied. The considered system was composed of simply supported thin plate under harmonic excitation with a nonlinear attachment. By varying parameters and locations of the nonlinear energy (NES), an optimized passive targeted energy transfers (TETs) from the plate to the attachments was performed. Moreover, comparative studies of the performance of NESs and linear tuned mass dampers (TMDs) are given. By performing complex averaging and arclength continuations techniques, semi-analytical approximations for nonlinear steady-state response was developed. To justify the averaging method, numerical simulation was also performed. The obtained results show that the NES designed for specific amplitude of excitation has better performance with respect to TMD, but with increase in amplitude of excitation force, NES has lower robustness with respect to TMD. The obtained results show that, if the phase differences of plate and NES with exciting force are ±π2 and ±π respectively, then the best condition for energy transfer from plate to NES will occurs, but if both the plate and NES have π with exciting force, the amplitude of vibration for both of them are considerably high.

Stability analysis of a composite laminated piezoelectric plate subjected to combined excitations

The aim of this paper is to discuss the stability of a symmetric cross-ply composite laminated piezoelectric plate subject to combined excitations. Multiple timescale perturbation method is implemented to solve the nonlinear governing equations including the second-order approximation. The case of 1:1:3 internal resonance and primary resonance case is investigated. The stability of the system is discussed using frequency, force response curves. A bifurcation analysis was performed using the amplitude of parametric excitation force as the bifurcation parameter. It is found that there are two Hopf bifurcation points: the first one is at \(f_{11}=5.592\), and the other one is at \(f_{11}=13.96\). It is observed that the system is dominated by the periodic attractor in the ranges of \((5.592< f_{11 }< 7.21)\) and \((13.31< f_{11 }< 13.96)\). The system is enriched with period doublings which are the main way leading to chaotic behavior. Some recommendations regarding the parameters limit of the dynamic system are reported.