Single Harmonic Excitation Research Articles

A resonant single-wing bionic piezoelectric motor based on a biasing self-clamping mechanism.

In this study, a resonant single-wing bionic piezoelectric motor based on a biasing self-clamping mechanism inspired by dragonfly flight was designed, assembled, and tested. The main mechanism of the designed piezoelectric motor includes a mover (including a vibrator, clamping foot, bionic pedestal, etc.), a stator, and other auxiliary components. The clamping foot of the mover contacts the side of the stator to form a biasing self-clamping mechanism, which can achieve a clamping effect within half a cycle of the vibrator's resonant vibration. The piezoelectric plate on the vibrator receives a single harmonic excitation from the signal generator, causing the base plate to bend and distort. The base plate drives the clamping foot to move regularly, causing the mover to perform a linear motion. Moreover, repeated single harmonic excitations can realize the continuous movement of the mover. The structure of the piezoelectric motor was optimized using COMSOL6.0, which is a finite element analysis software. The first-order bending vibration of the vibrator was chosen as the working mode through finite element simulation, and an experimental platform was built. The performance of the prototype piezoelectric motor was tested and verified on the experimental platform. The final experimental data show that under the conditions of 300Vp-p excitation voltage and 109Hz driving frequency, the maximum no-load speed of the prototype reaches 6.184 mm/s, and the maximum load of the motor is 4g.

Modelling and vibration response of a magnetically suspended flexible rotor considering base motion

Active magnetic bearings can provide no-friction support, high operating speed, and active vibration control for rotating machinery. The magnetically suspended rotor will inevitably be excited by the base motion when working on the moving carrier, causing the rotor vibration, and even instability. The main purpose of this study is to model a magnetically suspended flexible rotor under base motion and predict the vibration response. A general model of the magnetically suspended flexible rotor under base motion is established based on the finite element method and Lagrange's equation, considering the rotor shrinkage fit and AMB sensor/actuator being not collocated. The accuracy of the rotor model in free-free state is verified in terms of modal frequencies and mode shapes through the modal test. The vibration response of magnetically suspended rotor is experimentally validated using an AMB-rotor test rig mounted on the shaker. The time-domain response of the rotor under base single harmonic and shock excitation in the experiments is close to that predicted by numerical simulation. Finally, the influence of the frequency and amplitude of the base single harmonic excitation, the amplitude and pulse width of the base shock excitation, and the AMB controller parameters on the vibration response of the magnetically suspended rotor are investigated.

A novel sensitivity-based finite element model updating and damage detection using time domain response

This paper presents an innovative explicit sensitivity equation for structural parameters estimation using the time domain data. The proposed exact sensitivity equation provides a linear relation between the time history response and variation of structural parameters. In order to achieve an accurate sensitivity equation, the incomplete measured responses of the damaged structure are incorporated into the mathematical formulation. The accuracy of the method is numerically examined in several damage scenarios. The crucial issues such as the weighting of the equation, measurement, and modeling errors are investigated. The proposed method is used to identify structural parameters subjected to impact and single harmonic excitation loads. The parameter estimation results show the robustness and accuracy of the proposed method. Moreover, the advantages of the proposed method are explained than the derivation-based method and the Direct Differentiation Method (DDM).

Phase resonance nonlinear modes of mechanical systems

The resonances of forced dynamical systems occur when either the amplitude of the frequency response undergoes a local maximum (amplitude resonance) or phase lag quadrature takes places (phase resonance). This study focuses on the phase resonance of nonlinear mechanical systems subjected to single-point, single-harmonic excitation. In this context, the main contribution of this paper is to develop a computational framework which can predict the mode shapes and oscillation frequencies at phase resonance. The resulting nonlinear modes are termed phase resonance nonlinear modes (PRNMs). A key property of PRNMs is that, besides primary resonances, they can accurately characterize superharmonic, subharmonic and ultra-subharmonic resonances for which, as shall be shown in this paper, phase lags at resonance may be different from π∕2. The proposed developments are demonstrated using one- and two-degree-of-freedom systems featuring a cubic nonlinearity.

Toward Wideband Piezoelectric Harvesters Through Self-Powered Transitions to High-Energy Response

Abstract Convergence to low-energy responses arising from coexistence of multiple stable nodes is the main drawback of a nonlinear energy harvester preventing it from efficient wideband operation. A switching circuit with a boost-like topology has been proposed in this paper to overcome this substantial challenge. The circuit uses the energy harvested by the device to trigger it to jump from the low- to high-energy response. The performance of the proposed harvesting system when subjected to single harmonic excitations covering a wide range of frequencies is verified through both analytical and numerical investigations. Results indicate that by proper selection of timing parameters of the circuit including ON-time period of the switches together with the phase differences between the switching signals and the mechanical excitation, the applied electrical perturbation will be able to trigger the nonlinear resonating beam to jump from a low-energy response to the basin of attraction of the high-energy one within the whole frequency band in which a multivalued solution exists. Also, a probabilistic study is performed on a system with random phases of switching signals which shows that a successful switching from low- to high-energy response is achievable with a probability more than 80% by just controlling the ON-time period of the switch within the proper ranges with respect to the excitation frequency.

Frequency domain modeling of nonlinear end stop behavior in Tuned Mass Damper systems under single- and multi-harmonic excitations

Nonsmooth dynamics of a Tuned Mass Damper system with lateral stops are studied using an alternating frequency/time harmonic balancing (AFT-HB) method. To this end, an extremely stiff end stop nonlinearity is considered. The application range of AFT-HB is investigated by including up to 250 harmonics in the external force, as well as in the motion description. Numerical simulations are performed by making use of a Newmark time integration algorithm for numerical verification of the results. The results for single harmonic excitations are further verified with an existing pseudo-arclength path-following tool. Two excitation scenarios are considered: single harmonic- and a wide-spectrum excitation with uniform distribution and random phase correlation between the harmonics. The AFT-HB algorithm is found to accurately reproduce the time integration results, for all considered cases. Finally, insights are gained into the differences between the system responses to single- and multi-harmonic excitations.

Dynamic Analysis of Vehicle Track Coupling Based on Double Beam Track Model

The rail was considered as double Timoshenko beam in this paper, applied to the vehicle track coupling dynamics model; the Hertz nonlinear method is used to calculate the wheel rail contact force. Wheel rail vertical force and response of vehicle are calculated by using the model under random irregularity and single harmonic excitation; at the same time, wheel rail force and vertical acceleration response of 3‐order, 10‐order, and 19‐order wheel polygon were calculated. The results show that, under the excitation of random irregularity, the wheel rail vertical force of two models was very close in the low frequency band, and the response of the double beam model in the high frequency band of 200–1000 Hz is larger than the single beam model, and the acceleration and displacement responses of the double beam model are relatively close. Under a single harmonic excitation, the double beam model has a shorter wheel rail force attenuation time than that of the single beam model. And wheel rail force peak value of double beam model is 9% larger than that of single beam model. Similarly, the vertical displacement of the double beam model increased by 2.6%. Under the 3‐order and 10‐order wheel polygon excitation, vertical wheel rail peak force of double beam is, respectively, 37.5% and 50% larger than single beam model; the vertical frame acceleration amplitude is 1 g and 1.7 g; under the 19‐order polygon wheel excitation, the difference of the wheel rail force between two models is very small, and the amplitude of acceleration of bogie is 2.3 g. And double beam model has more advantage in analyzing high frequency problems such as wheel polygonization.

Efficient swept sine chirp excitation in the non-linear vibro-acoustic wave modulation technique used for damage detection

In this article, the non-linear vibro-acoustic modulation technique is used for structural damage detection. A new experimental configuration and data processing strategy are proposed to improve the damage detection capability of the technique. The swept sine chirp excitation is used for both low-frequency vibration/modal and high-frequency ultrasonic excitations. The adaptive resampling procedure is then applied to extract information about modulation intensity that relates to damage. The proposed method is illustrated using numerical simulations and experimental tests. The latter involves crack detection in an aluminium beam. The results of the proposed method are compared with the classical approach based on single harmonic excitation, demonstrating that similar damage detection information can be extracted. However, the major advantage of the proposed method is simplicity and robustness since no a priori selection of excitation frequencies is needed. As a result, crack detection is more reliable and unambiguous.

Power Conserving Bond Graph Based Modal Representations and Model Reduction of Lumped Parameter Systems

Dynamic analysis is extensively used to study the behavior of continuous and lumped parameter linear systems. In addition to the physical space, analyses can also be performed in the modal space where very useful frequency information of the system can be extracted. More specifically, modal analysis can be used for the analysis and controller design of dynamic systems, where reduction of model complexity without degrading its accuracy is often required. The reduction of modal models has been extensively studied and many reduction techniques are available. The majority of these techniques use frequency as the metric to determine the reduced model. This paper describes a new method for calculating modal decompositions of lumped parameter systems with the use of the bond graph formulation. The modal decomposition is developed through a power conserving coordinate transformation. The generated modal decomposition model is then used as the basis for reducing its size and complexity. The model reduction approach is based on the previously developed model order reduction algorithm (MORA), which uses the energy-based activity metric in order to generate a series of reduced models. The activity metric was originally developed for the generic case of nonlinear systems; however, in this work, the activity metric is adapted for the case of linear systems with single harmonic excitation. In this case closed form expressions are derived for the calculation of activity. An example is provided to demonstrate the power conserving transformation, calculation of the modal power and the elimination of unimportant modes or modal elements.

A New Design of Vibration Absorber for Periodic Excitation

The authors designed a novel type of dynamic vibration absorber, called periodic vibration absorber (PVA), for mechanical systems subjected to periodic excitation. Since the periodic rather than single harmonic excitation is themost occurring case in mechanical systems, the design of PVA is hence of engineering significance. The PVA designed in this paper is composed of a dual-beam interconnected with a discrete spring in between. By appropriately choosing the design parameters, the PVA can be of resonance frequencies in integer multiples of the base frequency such that the PVA can absorb significant amount of higher harmonics in addition to the base harmonic. The designed PVA was first experimentally verified for its resonance frequencies. The PVA implemented onto a mechanical system was then tested for its absorption ability. From both tests, satisfying agreement between experiments and numerical calculations has been obtained. The sensitivities of the design variables, such as the discrete spring’s stiffness and location, were discussed as well. The parameters’ sensitivities provided us with the PVA’s adjustable room for excitation frequency’s mismatch. Numerical results showed that within 3% of frequency mismatch, the PVA still performed better than a single DVA via adjusting the spring’s constant and location. All the results proved that the novel type of PVA could be a very effective device for vibration reduction of mechanical systems subjected to periodic excitation.

Micro/macro-slip damping in beams with frictional contact interface

Friction in contact interfaces of assembled structures is the prime source of nonlinearity and energy dissipation. Determination of the dissipated energy in an assembled structure requires accurate modeling of joint interfaces in stick, micro-slip and macro-slip states. The present paper proposes an analytical model to evaluate frictional energy loss in surface-to-surface contacts. The goal is to develop a continuous contact model capable of predicting the dynamics of friction interface and dissipation energy due to partial slips. To achieve this goal, the governing equations of a frictional contact interface are derived for two distinct contact states of stick and partial slip. A solution procedure to determine stick–slip transition under single-harmonic excitations is derived. The analytical model is verified using experimental vibration test responses performed on a free-frictionally supported beam under lateral loading. The theoretical and experimental responses are compared and the results show good agreements between the two sets of responses.

The effective damping approach to design a dynamic vibration absorber using Coriolis force

In this paper, the vibration reduction of a pendulum structure with dynamic vibration absorber (DVA) using Coriolis force is investigated. When the pendulum structure is subjected to a single harmonic excitation, the effective damping of Coriolis force is used with the second-order approximations to obtain the closed forms of optimal parameters of the DVA. The closed forms obtained show that the natural frequency of the absorber should be tuned to twice that of the pendulum. The closed forms of optimal parameters are verified by numerical optimization. The modified forms of optimal parameters are proposed to be used in case of general excitation. Base on this modified form, the design procedure is demonstrated by the numerical calculation of the free vibration and wind-induced vibration of a ropeway gondola.

Multiharmonic excitation for nonlinear system identification

Parametric identification of nonlinear systems is done using a hybrid time/frequency-domain-based Fourier series identification method. A multiharmonic force excitation is proposed to overcome identification problems encountered with a single harmonic excitation for certain classes of nonlinear systems. A Duffing oscillator and a system with quadratic damping are considered in detail for illustration of the proposed identification scheme using multiharmonic excitation. It is demonstrated that for most situations a multiharmonic excitation leads to significantly better identification results than a single harmonic excitation-based method.

Testing of nonlinear interaction effects of sinusoidal and noise excitation on rubber isolator stiffness

The nonlinear excitation effects on dynamic stiffness and damping of a filled rubber isolator are investigated through measurements. For a single harmonic excitation they are found to exhibit a strong amplitude dependence, following the well-known Payne effect where stiffness is high for small excitation amplitudes and low for large amplitudes while damping displays a maximum at intermediate amplitudes. However, expanding the measurements to a multiple harmonic excitation, the commonly applied superimposition principle of single harmonic responses due to this excitation is shown to be non-valid. On the contrary, it is found that reference stiffness at a small excitation amplitude and high frequency is reduced and damping increased while superimposing a large amplitude low frequency excitation component. Superimposition of low frequency noise signals displays essentially the same influence on the reference characteristics. As a rule of thumb, the largest excitation amplitude over the isolator normally determines the stiffness at the reference frequency while the influence of envelope amplitude is increased as its frequency approaches that of the component of interest.

MULTIPLE DELAYED RESONATOR VIBRATION ABSORBERS FOR MULTI-DEGREE-OF-FREEDOM MECHANICAL STRUCTURES

This study is on the use of multiple Delayed Resonators (DR) in suppressing tonal vibrations of multi-degree-of-freedom mechanical structures. The DR is a recently introduced, actively tunable vibration absorber which converts a conventional passive absorber into a maringally stable resonator. This structure absorbs all the vibratory energy at its point of attachment. Control forces in the form of proportional acceleration feedback with variable gains and time delays are considered here. Attractive features of DR have already been demonstrated for single DR absorber cases. When excitation has multiple harmonics, multiple DRs can be used, each DR suppressing one of the harmonics. The stability assessment, however, becomes very complex in this case, due to the presence of unrelated time delays in the system. Therefore, a simpler situation is considered here; single harmonic excitation and multiple identical DRs acting on the system. A strategy called “stability charts” is used not only to resolve the stability but also to find out the tuning speed of the absorption. An example case of two identical DRs on a 3-DOF system is presented. The results demonstrate the feasibility of using multiple DR absorbers.

Dynamics of a piecewise non-linear system subject to dual harmonic excitation using parametric continuation

The dynamic behavior of piecewise linear and/or non-linear vibratory systems subject to a single harmonic excitation has been recently analyzed by using a one- or multi-term harmonic balance (or Galerkin’s) method, piecewise linear techniques, analog simulation and direct numerical integration (digital simulation). Instead, this paper proposes to utilize the technique of parametric continuationto study the steady state response and global dynamics of a two-degree-of-freedom piecewise non-linear system with backlash or multi-valued springs and impact damping. The physical system is under the influence of a mean load and is subject to a dual harmonic external excitation, where the second frequency is either twice or three times the fundamental excitation frequency. The effects of various parameters such as impact damping, mean and alternating loads, the piecewise stiffness ratios and the relative phase between the excitation harmonics on the system response are thoroughly examined. System or excitation parameter regimes that exhibit sub-harmonic, super-harmonic quasi-periodic and chaotic solutions are obtained efficiently and systematically by using the proposed scheme. This investigation also clarifies the differences between viscous and non-linear impact damping models, which have been proposed earlier in the literature for studying clearance non-linearities. Limited experimental data validate our modelling strategy. Finally, selected predictions from this technique match very well with a multi-term harmonic balance method and with direct numerical integration, wherever applicable.

The Forced Oscillation of the Centrifugal Pendulum With Wide Angles

Abstract The simple pendulum mounted to a rotor suffering torsional oscillation is used as an effective dynamic damper which may be tuned to any one harmonic order of vibration. The nonlinear equations of motion are here developed to investigate whether wider angles of swing, or whether larger or smaller sizes of pendulum relative to its carrier, are more effective. Resonance-type curves are drawn by assuming a single harmonic excitation and hyperelliptic pendulum motion without damping; it is shown that theoretically oscillations up to 90 deg may be used which are predictable, and that in all cases the tuning must be higher than that indicated by small-angle theory.