Moment Excitation Research Articles

Resonance regulation on a hydraulic pipe via boundary excitations

Resonance of a hydraulic pipe is the standing wave brought by the excitation in fact. This provides a new idea of vibration control of the hydraulic pipe, which means the resonance can be regulated by combination of excitations. Inspired by this opinion, the current work studies the multi-modal resonance regulation of a hydraulic pipe by multiple boundary excitations for the first time. The system considers the pump installed at the pipe's end as the fixed boundary with a displacement excitation. To minimize the multi-modal resonance, a force excitation and a moment excitation are acted on the right end. These three excitations have different phase angles and different amplitudes. But they have the same frequency to avoid combination resonance or even beat phenomenon and chaos. Combined responses subject to these three excitations are derived via the analytical method, and verified by a numerical simulation method. To find out the regulating mechanism, nonlinearities of the system are neglected for calculating the exact analytical solution first. The discussion clarifies that, the phase angle of the moment excitation has the same effect on different modal resonances. It is an advantage for the multi-modal resonance reduction. On the contrary, the phase angle of the force excitation has different effects on different modal resonances. By optimizing phase angles and amplitudes of excitations, both the first-two resonances are reduced by 50% comparing with the system suffered to the displacement excitation only. The optimized conclusion is also real for the nonlinear system. The potential energy and dissipation work are reduced by over 70% for the first-two resonances. This work proposes a potential boundary control technique for the hydraulic pipe system. Multi-modal resonance control can be realized by adjusting the phase angle or the amplitude of boundary excitations.

Planar Swirl-shaped Acoustic Black Hole Absorbers for Multi-directional Vibration Suppression

A planar swirl-shaped Acoustic Black Hole (ABH) absorber is proposed and investigated in this paper. In addition to the well-known bending wave retarding phenomena, the speed of torsional waves in the curved ABH with a rectangular cross section is also shown to decrease with the thickness thinning. Alongside the enhanced bending-twisting coupling brought about by the planar and curvilinear configuration, the curved ABH absorber exhibits reduced orientation-dependent properties to cope with multi-directional rotational moment excitations, and meanwhile generates enriched dynamics and enhanced energy trapping and dissipation. As a result, the absorber enables broadband multi-directional vibration suppression when added on a primary thin structure. Experimental studies demonstrate that deploying multiple distributed ABH absorbers can entail effective, robust and broadband vibration reduction for an arbitrarily selected polygon plate. Analyses also confirm the dual vibration reduction mechanisms in terms of structural interaction and damping enhancement, both being fully played out through the proposed curvilinear ABH design.

Generalised round-trip identity—For the determination of structural dynamic properties at locations inaccessible or too distant for direct measurement

In noise and vibration engineering, a structure’s passive dynamic properties are often quantified by frequency response functions (FRFs). This paper focuses on acquiring FRFs from experimental tests, considering both, translational (x, y, z) and rotational (e.g. moments around these axes) terms. In practical applications, test structures may not allow FRFs to be measured directly due to the impracticality of applying a controlled excitation in a particular direction (e.g. in-plane), the inability to measure rotational dynamics (e.g. moment excitation), insufficient signal-to-noise ratio (SNR) between excitation and response degrees of freedom, or simply due to restricted access. Methods exist to resolve some of the mentioned issues using indirect experimental techniques, such as the round-trip identity. However, these methods are limited to cases in which the driving-point FRFs are sought-after. The present paper extends previous work into a more generalised formulation of the round-trip identity feasible for reconstructing driving-point and transfer mobilities from in-situ measurements conducted in coupled assemblies. By using the round-trip identity, the excitation of moments and/or inaccessible points is avoided altogether and instead replaced by a number of applied forces remote to the points of interest. Manipulation of this round-trip identity yields a formulation for long distance transfer FRFs, expressed in terms of multiple shorter transfer path elements, which are less prone to insufficient SNR. These practical applications of the generalised round-trip concept are experimentally validated for multi-input multi-output assemblies.

Parameter identification of ship roll motion based on vibration tests and CFD method

This paper implements the parameter identification of ship roll motion based on vibration tests and the computational fluid dynamics (CFD) method. By applying sinusoidal moment excitations from a shaker, we successfully simulate the quasi-roll motion behavior of the ship model in the air. We conduct two vibration tests, including a constant-amplitude angular displacement test and a constant-amplitude angular velocity test, to identify the restoring moment and the damping moment coefficients of the quasi-roll motion. In addition, we perform the approximate equivalence of the fluid around the ship through the CFD method and the fluid-solid coupling technique. Thus, we obtain the hydrodynamic coefficients, such as the added mass moment of inertia and the equivalent damping, to accomplish the parameter identification of the ship’s real roll motion. Finally, the accuracy of the identified parameters is verified by means of numerical simulations based on the Runge–Kutta method.

An expansion technique for the estimation of unmeasured rotational frequency response functions

Often numerical and measured data are not compatible both in type and number of degrees of freedom (DOFs). While finite element modelling can provide a full data set, the conventional vibration testing is usually limited, allowing only the measurement of part of the receptance matrix, namely the responses at translational DOFs due to applied forces. Therefore, the experimental frequency response function (FRF) matrix usually does not contain any information regarding rotational DOFs, especially those related to pure moment excitations. In this work, the authors propose a process that starts with a set of translational FRFs, conventionally measured, and expand it to estimate the entire receptance matrix. A generalized version of Kidder’s method, together with the principle of reciprocity, is used in the expansion process, which has the advantage of avoiding modal identification. The accuracy of the estimated FRFs is assessed by comparing the results with those of experimental data collected at a simple structure. It is worth mentioning that the use of a T-block is considered to obtain experimental rotational FRFs with the simple purpose of accuracy assessment.

Numerical Noise Transfer Analysis of a Flexible Supported Gearbox Based on Impedance Model and Noise Transfer Function

To investigate the gearbox radiation noise properties under various rotational speeds, a noise prediction method based on impedance model and noise transfer function (NTF) is proposed. One only needs to extract the NTF of the housing once rapid gearbox noise prediction under different working conditions is realized. Taking a flexible supported gearbox as a research object, the external excitation of the housing (the bearing excitation load and isolator excitation load) is calculated through a gear-housing-foundation-coupled impedance model, and the noise transfer function is simulated through the vibroacoustic-coupled boundary element model; then the radiation noise is obtained. Based on this model, the noise transfer analysis of the housing is carried out, different excitation components and NTF components are compared, and the contributions of different excitation components to noise are compared. Results show that the radiation noise of gearbox is mainly excited by the high-speed bearing, while the low-speed bearing and isolator have little influence on noise. At low speed, vertical force, axial force, and moment excitation of bearings all contribute to the radiation noise while at high speed, the gearbox radiation noise is mainly generated by vertical excitation force of bearings.

Estimation and measurement of effective line mobility on a non-deterministic thin plate excited by a piezoelectric patch

This paper derived the expression to estimate the effective line moment mobility of a non-deterministic thin plate under moment excitation by a piezoelectric patch actuator. The piezoelectric patch actuator is assumed to generate purely line moments at each of its edges and regarded as a finite number of point moments acting on an infinite plate, which is achieved by integration method. The theoretical model is validated using MATLAB simulation and compared with experimental measurements on a randomized thin plate. The derived effective line moment mobility managed to closely estimate high-frequency response while cutting significant computational time and resource. Results from this study can be used in many applications ranging from vibration isolation where power transmission between the isolator with an area distribution and its host structure can be determined more accurately, and to design the optimal shunt circuit of a piezoelectric shunt damper for maximum power dissipation in order to reduce vibration of a non-deterministic thin plate.

Frequency response function measurements of rotational degrees of freedom using a non-contact moment excitation based on nanosecond laser ablation

Frequency response functions (FRFs) are generally measured by investigating the input–output relationship of a target structure. An input is applied to the target structure and the output is measured. Typical vibration tests measure inputs as excitation forces using load cells or similar devices and outputs as velocities or accelerations using laser Doppler vibrometers or accelerometers. Each input or output has three translational degrees of freedom (DOF). Consequently, experimental models established based on such tests have three translational DOF. However, numerical models using finite element analysis (FEA) for existing structures have six DOF at each node (three translational and three rotational DOF). Therefore, numerical models using FEA and experimental models have gaps in their DOF, leading to diverse problems. This study realizes a non-contact measurement method for rotational DOF FRFs using an impulse excitation force generated by laser ablation (LA) where the input is a moment and the output is the velocity. A laser beam radiated from an Nd:YAG pulse laser emitter is divided using a half mirror, halving the laser pulse energy. Then, these laser beams are radiated on two points near a target structure's excitation point. The simultaneous occurrence of LA at these two points realizes a moment that acts on the target structure in a non-contact manner. This experiment uses a 5052 aluminum alloy plate where one end is fixed as a test piece. Both the auto FRFs and cross FRFs for the rotational DOF between two arbitrary points on the test piece are measured. The FRFs obtained by our method agree well with those obtained by FEA, demonstrating its efficacy.

Robust adaptive fuzzy sliding mode control of nonlinear uncertain MIMO fluttering FGP plate based on feedback linearization

In this study using an adaptive fuzzy sliding mode control (AFSMC) scheme, the robust stabilization of multi-input–multi-output (MIMO) nonlinear aero-elastic fluttering of the Functionally Graded Piezoelectric (FGP) plate in the presence of mismatched time-varying uncertainties have been investigated. It is assumed that the aerodynamic load is modeled by the first order piston theory and the piezoelectric patches are assumed to be bonded to the top and bottom surfaces of the plate in order to produce the controlling bending moment excitations. Using the airy stress function and applying the Hamilton's principle the governing coupled partial differential equations of motion are derived. Then considering the immovable simply supported edges boundary conditions and employing the aero-elastic multi-mode interactions and applying the Galerkin's method, the nonlinear coupled partial differential equations of motion are reduced to nonlinear ordinary differential equations in time. Then using the full state input-output feedback linearization technique, the nonlinear dynamics of the model is linearized and transformed into the multiple decupled single input-single output uncertain subsystems. In order to overcome the chattering phenomenon arises due to the sliding mode control (SMC) discontinuous inputs, a hybrid adaptive fuzzy sliding mode control technique is utilized to approximate the discontinuous synthetic control inputs. It is showed that considering the physical input limitations, the designed AFSMC control system, effectively suppress the fluttering motions in presence of the bounded external inaccuracies and it prevents the unwanted chattering of the subsystems inputs.

On the optimization, and the intensity dependence, of the excitation rate for the absorption of two-photons due to the direct permanent dipole moment excitation mechanism

A model two-level dipolar molecule, and the rotating wave approximation and perturbation theory, are used to investigate the optimization and the laser intensity dependence of the two-photon excitation rate via the direct permanent dipole mechanism. The rate is proportional to the square of the laser intensity I only for small intensities and times when perturbation theory is applicable. An improvement on perturbation theory is provided by a small time RWA result for the rate which is not proportional to I2; rather it is proportional to the square of an effective intensity Ieff. For each laser intensity the optimum RWA excitation rate as a function of time, for low intensities, is proportional to I, not I2, and for high intensities it is proportional to Ieff. For a given two-photon transition the laser-molecule coupling optimizes for an intensity Imax which, for example, leads to a maximum possible excitation rate as a function of time. The validity of the RWA results of this paper, and the importance of including the effects of virtual excited states, are also discussed briefly.

706 吸着型モーメント印加装置による計測の妥当性検証(機械力学・計測制御VII)

706 吸着型モーメント印加装置による計測の妥当性検証(機械力学・計測制御VII)

Active Structural Acoustic Control of a Softcore Sandwich Panel Using Multiple Piezoelectric Actuators and Reddy's Higher Order Theory

The purpose of the present work is to theoretically investigate the active control of radiated sound power from a simply supported soft-core sandwich panel with a line moment excitation. Since noise transmission in the low frequency region through a soft-core sandwich panel mainly occurs due to flexural and dilatational modes, therefore, the focus of this study is to control these modes and achieve sound attenuation in a large frequency band. Two control methods, volume velocity and weighted sum of spatial gradients (WSSG) are used to drive three piezoelectric actuators (PZTs) attached on the exterior side of the bottom face plate. The governing equation of the sandwich panel with the PZTs is derived using the Hamilton's principle considering Reddy's third order shear deformation theory. Numerical studies indicate that while the line moment is at the mid vertical line, WSSG is able to attenuate the radiated sound power irrespective of core loss factor whereas volume velocity could not. However, both the control metrics are able to attenuate most of the structural modes, when the line moment is off the midline, and therefore, attenuate significant amount of radiated sound power in a broad frequency range. And the maximum increase in sound power is small in WSSG as compared to volume velocity. These results show that WSSG can be used as an effective control metric to mitigate low frequency sound.

Multi-pulse orbits and chaotic dynamics of a symmetric cross-ply composite laminated cantilever rectangular plate

The multi-pulse homoclinic orbits and chaotic dynamics of a symmetric cross-ply composite laminated cantilever rectangular plate under in-plane and moment excitations are investigated with 1:2 internal resonance. Based on the explicit expressions of normal form associated with a double zero and a pair of pure imaginary eigenvalues, the energy-phase method proposed by Haller and Wiggins is employed to analyze the multi-pulse homoclinic bifurcations and chaotic dynamics of the composite laminated cantilever rectangular plate. The analysis of the global dynamics indicates that there exist the Shilnikov-type multi-pulse jumping orbits homoclinic to certain invariant sets for the resonance case which may lead to chaos in the sense of Smale horseshoes for the system. Homoclinic trees that describe the repeated bifurcations of multi-pulse solutions are presented. It can be found a gradual breakup of the homoclinic tree and the reducing of pulse numbers for the jumping homoclinic orbits if the dissipation factor is increased. The chaotic motions of the symmetric cross-ply composite laminated cantilever plate are also found by using the numerical simulation.

A power flow mode approach dedicated to structural interface dynamic characterization

This study is related to structural vibration transmission at low frequencies and aims to propose a new approach to dynamically characterize the interface between different substructures of a complex coupled structure. A power flow mode method based on the imaginary part of the dynamic flexibility matrix is presented, which allows determining eigenvalues and eigenvectors representing qualitative and quantitative information on the power flowing inside the structure, respectively. It is further applied to study the power transmitted at the interface, making it possible to identify the direction associated to the dominant power flow patterns and to quantify their contributions. Specific properties dealing with moment excitation and mid-frequency approximation are also detailed to provide complementary insights into their dynamic meaning and behavior.

Comparative study for non-statistical fluctuation of net- proton, baryon, and charge multiplicities

We investigate the higher moments of net-proton, net-baryon, and net-charge event distributions in Au+Au collisions at from 11.5 to 200 GeV. The non-statistical moments are defined as the differences between the real event moments and mixed event moments. The real events are generated with the parton and hadron cascade model PACIAE, while the mixed events are constructed by combining particles randomly selected from different real events. It is found that the theoretical results of net-proton and net-charge real higher moment excitation functions of Sσ and κσ2 are consistent with the STAR data, and that the properties of higher moment excitation functions are significantly dependent on the window sizes. In addition, the centrality dependence of the net-proton, net-baryon, and net-charge non-statistical higher moments are also studied.

The Effect of Uncertainty in the Excitation on the Vibration Input Power to a Structure

In structural dynamic systems, there is inevitable uncertainty in the input power from a source to a receiver. Apart from the nondeterministic properties of the source and receiver, there is also uncertainty in the excitation. This comes from the uncertainty of the forcing location on the receiver and, for multiple contact points, the relative phases, the force amplitude distribution at those points, and also their spatial separation. This paper investigates quantification of the uncertainty using possibilistic or probabilistic approaches. These provide the maximum and minimum bounds and the statistics of the input power, respectively. Expressions for the bounds, mean, and variance are presented. First the input power from multiple point forces acting on an infinite plate is examined. The problem is then extended to the input power to a finite plate described in terms of its modes. The uncertainty due to the force amplitude is also discussed. Finally, the contribution of moment excitation to the input power, which is often ignored in the calculation, is investigated. For all cases, frequency band-averaged results are presented.

Multi-component power transmission from structure-borne sound sources into lightweight structures

The power transmission between structure-borne sound sources and adjacent structures is generally of complex nature. For an accurate description, the interaction between multiple contact points and several directional components must be taken into account. While calculation methods to predict the transmitted power are generally available, the main problem is the acquisition of extensive source and receiver data. This is especially true with regard to lightweight structures where source and receiver mobilities exhibit matched conditions and when rotational components of motion are involved. Therefore, the description needs to be simplified while at the same time a sufficient accuracy has to be retained. This work investigates the power transmission of a fan unit source that is mounted to a rib-stiffened aluminium plate at several contact points. Full data sets of source and receiver have been measured using a finite difference technique, including translational motion perpendicular to the structure as well as moment excitation around the in-plane axes of the plate. Both a rigid connection as well as a connection using resilient mounts is considered. Contributions of different components of motion are discussed and possible simplifications are deduced.

Nonlinear responses of a symmetric cross-ply composite laminated cantilever rectangular plate under in-plane and moment excitations

The nonlinear dynamic responses of a composite laminated cantilever rectangular plate under the in-plane and moment excitations are studied. The Reddy’s higher-order shear deformation theory and the von Karman type equations for the geometric nonlinearity are used to establish the governing equations of motion. The nonlinear governing partial differential equations of motion for the composite laminated cantilever rectangular plate are derived by using the Hamilton’s principle, which are transformed into a two-degree-of-freedom nonlinear system by using the Galerkin approach. A new kind of expression of the displacement functions is given. The case of 1:2 internal resonance and primary parametric resonance is taken into account. The influence of the in-plane and moment excitations on the nonlinear vibrations of the composite laminated cantilever rectangular plate is discussed by using numerical simulation. The numerical results demonstrate that there exist the bifurcation and chaotic motions of the composite laminated cantilever rectangular plate. The nonlinear frequency–response curves of this system under different excitations are investigated to show the relationships between the excitations and the amplitudes of the first two modes.

Moment excitation and the measurement of moment mobilities

Frequency response functions (FRF), such as mobilities, are widely used in the analysis of vibration and structure-borne sound and it is important that this FRF data can be measured accurately for all important degrees of freedom. In some cases three translational and three rotational components of both excitation and response may be of importance; i.e. three forces and moments, and three velocities and angular velocities. Of these, the measurement of angular velocity due to moment excitation is one of the most challenging. This paper describes a known approach, sometimes referred to as the central difference method, which can be used for this purpose. The central difference method is thought to be one of the most practicable methods for measuring moment mobilities because it avoids the need for a moment exciter; instead finite differences are used to approximate the moment mobility which is a spatial derivative of the more easily measured velocity to force mobility ratio. There does however remain some doubt regarding the accuracy of the central difference method because of the finite difference approximation made and the method's possible susceptibility to random and bias errors. To better understand the finite difference error, an error analysis using a Taylor series expansion and simulated experiments for plate and beam structures are provided. It is then argued that random and bias errors associated with the measurement chain should now, with modern instrumentation, be less of a problem. An experimental validation of the method using two approaches is used to test this hypothesis. It is concluded that the central difference method provides a good balance between measurement effort and data quality making it widely applicable.

446 分離型モーメント印加装置の性能向上に関する研究

In the experimental modal analysis, the treatment device has to be fixed on the target structure in order to obtain the vibration response to the moment excitation. However, if the treatment device is used, the vibration property must be changed because of the additional mass of the device. Hence, it is difficult to obtain the accurate vibration response to the moment excitation. A detach type moment excitation device that an impulse moment can be impacted on the structure without using treatment device was proposed. The proposed device is easy to handle and realizes the accurate measurement without additional weight. But, in this way, excitation force and moment are limited to the small value. In this study, an attachment for the device that bigger moment and force can be impacted on the structure is proposed. First of all, the principle of the proposed device is shown. Then, the experimental results are shown to confirm the validity of the proposed technique.