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This paper presents a new receptance-based method for the robust assignment of natural frequencies. This method aims to address the deviation of the actually achieved natural frequencies for target natural frequencies when assigning natural frequencies, which usually arises due to uncertainties in passive structural modifications (i.e. mass and stiffness modifications). The mathematical expression is derived for the sensitivity of the target natural frequency to the uncertainties in modification parameters, which are subsequently employed to characterize the potential deviations of the target natural frequencies in the total differential form. The obtained deviation expression is integrated into the optimization calculation of the natural frequency assignment as an extra penalty term to boost the acquisition of highly robust modification parameters. The proposed robust assignment method, as a non-probabilistic technique, can be employed without any knowledge of the probabilistic distribution of uncertainty in modification parameters. Moreover, it uses only the measured frequency response functions (FRFs), preserving the advantage of the receptance method not needing a numerical model. Two numerical examples and a comparison with a typical eigenstructure assignment method (reported in the literature) demonstrate that the proposed method can provide highly robust modification parameter solutions. The application of the proposed method to the natural frequency assignment of a laboratory water-filled pipeline system gives experimental evidence of its effectiveness. [ABSTRACT FROM AUTHOR]

In structural receptances, the zeros (antiresonances) define those frequencies at which vibrations disappear. In this paper, the zero sound pressure frequency is defined as the frequency at which the sound pressure is zero at certain locations. A method for the assignment of zero sound pressure frequencies using measured sound pressure receptances and structural receptances is proposed through two forms of structural modifications: rank-one modification and higher-rank modification. In rank-one modification, the sound pressure receptances of the modified structure are obtained by using the structural receptances with the Sherman-Morrison formula. In higher-rank modification, the modifications are determined by an analysis of the null space of a matrix consisting of structural receptances and sound pressure receptances. This method requires only a few structural receptances and sound pressure receptances, and no structural models or acoustic models are needed. Numerical examples involving a baffled plate vibrating in air and a fluid-loaded finite cylindrical shell are used to demonstrate the methods. Numerical results show that the zero sound pressure frequencies can be assigned to specific frequencies by structural modification. [ABSTRACT FROM AUTHOR]

Featured Application: The proposed control strategy can be used to impose the closed-loop system dynamics behaviour in flexible mechatronic systems in the presence of time delay, such as robots where delay is introduced by sensors, actuators or communication networks, or systems with inherent delay such as milling and cutting machines. The use of receptances remarkably simplifies the controller design. This paper proposes a method for active vibration control to a two-link flexible robot arm in the presence of time delay, by means of robust pole placement. The issue is of practical and theoretical interest as time delay in vibration control can cause instability if not properly taken into account in the controller design. The controller design is performed through the receptance method to exactly assign a pair of pole and to achieve a given stability margin for ensuring robustness to uncertainty. The desired stability margin is achieved by solving an optimization problem based on the Nyquist stability criterion. The method is applied on a laboratory testbed that mimic a typical flexible robotic system employed for pick-and-place applications. The linearization assumption about an equilibrium configuration leads to the identification of the local receptances, holding for infinitesimal displacements about it, and hence applying the proposed control design technique. Nonlinear terms, due to the finite displacements, uncertainty, disturbances, and the coarse encoder quantization, are effectively handled by embedding the robustness requirement into the design. The experimental results, and the consistence with the numerical expectations, demonstrate the method effectiveness and ease of application. [ABSTRACT FROM AUTHOR]

[Objectives]The fluid-conveying pipes may vibrate under external excitation. In order to reduce the vibration of the fluid-conveying pipes and study the vibration-reduction characteristics of the Dynamic Vibration Absorber(DVA),[Methods]the receptance matrix of the multi-degree-of-freedom (DOF)system of the additional spring-mass system was derived based on the passive modification method in the receptance method,and the zero assignment of the target DOF in the multi-DOF system was performed to suppress the corresponding vibration under the target DOF. On this basis,a DVA was designed and applied to the fluid-conveying pipes for experiments to verify its vibration-reduction effect.[Results]The results show that the designed DVA can well absorb the vibration at the target frequency, and the vibration reduction is better for a larger tuned mass when the target frequency is the same.[Conclusions]Such DVA is convenient to install and has a wide application range,which can provide a certain reference for pipe vibration reduction research.

This paper proposes a novel method for pole placement in linear vibrating systems through state feedback and rank-one control. Rather than assigning all the poles to the desired locations of the complex plane, the proposed method exactly assigns just the dominant poles, while the remaining ones are free to assume arbitrary positions within a pre-specified region in the complex plane. Therefore, the method can be referred to as "regional pole placement". A two-stage approach is proposed to accomplish both the tasks. In the first stage, the subset of dominant poles is assigned to exact locations by exploiting the receptance method, formulated for either symmetric or asymmetric systems. Then, in the second stage, a first-order model formulated with a reduced state, together with the theory of Linear Matrix Inequalities, are exploited to cluster the subset of the unassigned poles into some stable regions of the complex plane while keeping unchanged the poles assigned in the first stage. The additional degrees of freedom in the choice of the gains, i.e., the non-uniqueness of the solution, is exploited through a semidefinite programming problem to reduce the control gains. The method is validated by means of four meaningful and challenging test-cases, also borrowed from the literature. The results are also compared with those of classic partial pole placement, to show the benefits and the effectiveness of the proposed approach. [ABSTRACT FROM AUTHOR]

This paper proposes a method for active vibration control to a two-link flexible robot arm in the presence of time delay, by means of robust pole placement. The issue is of practical and theoretical interest as time delay in vibration control can cause instability if not properly taken into account in the controller design. The controller design is performed through the receptance method to exactly assign a pair of pole and to achieve a given stability margin for ensuring robustness to uncertainty. The desired stability margin is achieved by solving an optimization problem based on the Nyquist stability criterion. The method is applied on a laboratory testbed that mimic a typical flexible robotic system employed for pick-and-place applications. The linearization assumption about an equilibrium configuration leads to the identification of the local receptances, holding for infinitesimal displacements about it, and hence applying the proposed control design technique. Nonlinear terms, due to the finite displacements, uncertainty, disturbances, and the coarse encoder quantization, are effectively handled by embedding the robustness requirement into the design. The experimental results, and the consistence with the numerical expectations, demonstrate the method effectiveness and ease of application.

A closed-form analytical solution is developed for the first time that fully addresses the problem of choosing feedback gains that minimize the control effort required for partial pole placement in multi-input, multi-output systems. The norm of the feedback gain matrix is shown to take the form of an inverse Rayleigh quotient, such that the optimal closed-loop system eigenvectors are given as a function of the dominant (highest) eigenvectors of the matrix in the quotient. The feedback gains that deliver the required pole placement with minimum effort may then be determined using standard procedures. The original formulation by the receptance method proposed an arbitrary choice of the closed loop eigenvectors that assigned the poles exactly but was generally wasteful of control effort that might otherwise be conserved or put to good use in satisfying additional control objectives. The analytical solution is validated against a set of numerical examples. [ABSTRACT FROM AUTHOR]

• A method for uncertainty minimisation using active control is proposed. • The method does not require knowledge of the system since receptances are used. • Pole spreads, due to parameter variability, are minimised by global optimisation. • Uncertainty is quantified globally by variances taken via polynomial chaos expansion. • Uncertainty is modelled as modifications to a randomly measured nominal system. The problem of pole placement in dynamic systems with uncertainties is addressed using a global optimisation approach. Variability between nominally identical systems, which arises from manufacturing tolerances, wear and environmental variability, is considered. In the proposed method, receptances are measured from one of the open-loop, nominal systems chosen at random. In this case, in addition to the variability about the parameter means, the parameter means are also random. The receptance method is then used to place the poles of the measured system such that their spread, due to parameter uncertainty, is minimised. The measure used to assess the spread is the variance, determined efficiently by a polynomial chaos expansion. Among the advantages of the method are: (i) there is no requirement to model the system since experimental receptances are used, (ii) it is not necessary to measure the mean system, and (iii) uncertainty in poles is quantified across its full range by using variances. Numerical and experimental examples are provided to illustrate the working of the proposed method. [ABSTRACT FROM AUTHOR]

Input–output partial feedback linearisation is experimentally implemented on a non-smooth nonlinear system without the necessity of a conventional system matrix model for the first time. The experimental rig consists of three lumped masses connected and supported by springs with low damping. The input and output are at the first degree of freedom with a non-smooth clearance-type nonlinearity at the third degree of freedom. Feedback linearisation has the effect of separating the system into two parts: one linear and controllable and the other nonlinear and uncontrollable. When control is applied to the former, the latter must be shown to be stable if the complete system is to be stable with the desired dynamic behaviour. [ABSTRACT FROM AUTHOR]

This paper proposes a novel method for pole placement in linear vibrating systems through state feedback and rank-one control. Rather than assigning all the poles to the desired locations of the complex plane, the proposed method exactly assigns just the dominant poles, while the remaining ones are free to assume arbitrary positions within a pre-specified region in the complex plane. Therefore, the method can be referred to as “regional pole placement”. A two-stage approach is proposed to accomplish both the tasks. In the first stage, the subset of dominant poles is assigned to exact locations by exploiting the receptance method, formulated for either symmetric or asymmetric systems. Then, in the second stage, a first-order model formulated with a reduced state, together with the theory of Linear Matrix Inequalities, are exploited to cluster the subset of the unassigned poles into some stable regions of the complex plane while keeping unchanged the poles assigned in the first stage. The additional degrees of freedom in the choice of the gains, i.e., the non-uniqueness of the solution, is exploited through a semidefinite programming problem to reduce the control gains. The method is validated by means of four meaningful and challenging test-cases, also borrowed from the literature. The results are also compared with those of classic partial pole placement, to show the benefits and the effectiveness of the proposed approach.

Uncertainty caused by a parameter measurement error or a model error causes difficulties for the implementation of the control method. Experts can divide the uncertain system into a definite part and an uncertain part and solve each part using various methods. Two uncertainty problems of the control system arise: problem A for the definite part—how does one find out the optimal number and position of actuators when the actuating force of an actuator is smaller than the control force? Problem B for the uncertain part—how does one evaluate the effect of uncertainty on the eigenvalues of a closed-loop control system? This paper utilizes an interval to express the uncertain parameters and converts the control system into a definite part and an uncertain part using interval theory. The interval state matrix is constructed by physical parameters of the system for the definite part of the control system. For Problem A, the paper finds out the singular value element sensitivity of the modal control matrix and reorders the optimal location of the actuators. Then, the paper calculates the state feedback gain matrix for a single actuator using the receptance method of pole assignment and optimizes the number and position of the actuators using the recursive design method. For Problem B, which concerns the robustness of closed-loop systems, the paper obtains the effects of uncertain parameters on the real and imaginary parts of the eigenvalues of a closed-loop system using the matrix perturbation theory and interval expansion theory. Finally, a numerical example illustrates the recursive design method to optimize the number and location of actuators and it also shows that the change rate of eigenvalues increases with the increase in uncertainty.

A combined experimental-numerical approach for the pole assignment of fluid-loaded structures using the receptance method is proposed in this paper. The in-air measurements of structural receptances and numerically simulated fluid loading computed using acoustic boundary element analysis are combined to obtain the receptances of the fluid-loaded structures. It does not require evaluating the fluid-loaded model which usually contains errors, and it does not require receptance measurements of the fluid-loaded structure which are usually difficult and time-consuming. A partial pole assignment can also be achieved with the combined approach. The accuracy and efficiency of the proposed combined approach are demonstrated on a water-loaded plate. Numerical results indicate that the chosen poles of the water-loaded plate can be assigned to the predetermined values with the proposed approach, and the in-air mode shapes may represent the water-loaded mode shapes in the combined approach for suppression of spillover. [ABSTRACT FROM AUTHOR]

Abstract In this paper, a new set of six-variable linear partial differential equations of motion of fluid-conveying pipes with general boundary conditions are derived using the Hamilton principle and these equations are solved by the receptance method. The frequencies of the straight pipes conveying fluid with or without elastic supports are determined and the results are compared with experimental ones. Then a fluid-conveying, semi-circular pipe and complex piping system with different kinds of boundary conditions are studied. These pipes are divided into some straight pipe units and are assembled using the receptance method. The numerical results show that the receptance method is efficient for pipes with arbitrary geometrical layouts and support types, and once the dynamic receptance of the elastic support of a piping system is obtained via experiment, its dynamic stability at different fluid velocities can be analysed by the receptance method. Highlights • The receptance method can easily deal with the dynamic response of real complex piping systems at various fluid velocities. • The presented method has the advantage of simulating arbitrary supports to pipe systems. • For the same pipe element, the cut-off frequency based on the receptance method is higher than that based on theFEM. [ABSTRACT FROM AUTHOR]

In this paper, a nonlinear time-varying dynamic model of a drivetrain composed of a spiral bevel gear pair, shafts and bearings is developed. Gear shafts are modeled by utilizing Timoshenko beam finite elements, and the mesh model of a spiral bevel gear pair is used to couple them. The dynamic model includes the flexibilities of shaft bearings as well. Gear backlash and time variation of mesh stiffness are incorporated into the dynamic model. Clearance nonlinearity of bearings is assumed to be negligible, which is valid for preloaded rolling element bearings. Furthermore, stiffness fluctuations of bearings are disregarded. Multi-term harmonic balance method (HBM) is applied on the system of nonlinear differential equations in order to obtain a system of nonlinear algebraic equations. Utilizing receptance method, system of nonlinear algebraic equations is grouped in nonlinear and linear sets of algebraic equations where the nonlinear set can be solved alone decreasing the number of equations to be solved significantly. This reduces the computational effort drastically which makes it possible to use finite element models for gear shafts. In the calculation of Fourier coefficients, continuous-time Fourier transform as opposed to the gear dynamics studies that utilize discrete Fourier Transform is used. Thus, convergence problems that arise when the number of nonlinear DOFs is large are avoided. Moreover, analytical integration is employed for the calculation of Fourier coefficients rather than numerical integration in order to further reduce the computational time required. Nonlinear algebraic equations obtained are solved by utilizing Newton’s method with arc-length continuation. Direct numerical integration is employed to verify the solutions obtained by HBM. Several case studies are carried out, and the influence of backlash amount, fluctuation of gear mesh stiffness and variation of bearing stiffness are investigated. In addition to these, the response of the coupled gear system model is compared with that of gear torsional model in order to study the influence of the coupling on dynamics of the system. [ABSTRACT FROM AUTHOR]

Sound transmission through a fluid-loaded finite perforated panel set in an infinite unperforated rigid baffle is considered. Using a fully coupled formulation in the 2-D wavenumber domain, the transmitted pressure due to an incident plane wave is obtained. The change in the panel resonances caused by the perforations is accounted for. The formulation also takes into account the self- and inter-modal coupling coefficients arising due to the fluid-loading effect. The derivation is almost entirely analytical with numerical computations done at the very end. Transmission loss (TL) curves are plotted for various cases and the physics is discussed. Along the way an uncoupled calculation is also done for the sake of comparison. The results are mainly for a light medium like air. For a light medium, in general, the perforate impedance is lower than the panel impedance. Thus, most of the transmission happens through the perforations. The panel velocity contribution is insignificant and hence the uncoupled calculation is adequate. In general, the absolute perforate impedance increases with increasing frequency. So does the TL. At low frequencies, because the resistive component of the hole impedance increases, the absolute perforate impedance rises. Thus, the TL curves rise at the lower frequencies. This effect is prominent for sub-millimeter hole radii, i.e., for micro-perforations. An important issue with the TL values for perforated panels is that they sometimes acquire negative values at low frequencies. This apparent anomaly is resolved by showing that at low frequencies there is an additional power component that flows from the baffle region onto the panel. Upon inclusion of this additional term, the TL values remain positive at all frequencies. [ABSTRACT FROM AUTHOR]

New output feedback-linearisation theory is presented for the treatment of nonlinear vibration problems by a receptance-based approach. An important aspect is a new formulation for investigating the stability of the zero dynamics. The overall methodology possesses the usual benefits of the receptance method, namely that the system matrices (with associated assumptions and approximations) do not have to be known. In addition, it has the distinction of not requiring the form and parameter values of the nonlinearity when the input and output degrees of freedom are away from the nonlinearity itself. This represents a valuable advance over the conventional time-domain feedback linearisation approach. [ABSTRACT FROM AUTHOR]

The pole-zero assignment problem for high-order systems with time delay is addressed. The approach described here uses measured receptances absolutely without requirements for the system matrices. Our solution is easy to achieve and need not solve the Sylvester equation or turn high-order systems into the first-order form. The method is supplemented by a series of illustrative numerical examples. [ABSTRACT FROM AUTHOR]

An explicit solution to the partial eigenvalue assignment problem of high order control system is presented by the method of receptance. Conventional methods, e.g. finite elements, are known to contain inaccuracies and assumptions that may hinder the calculations. An alternative approach was given by Ram and Mottershead [1] in the form of receptances, typically available from a modal test. This paper generalizes the earlier work on partial assignment that is applicable to multi-input delayed system without use of the Sherman–Morrison formula. The results of our numerical experiments support the validity of our proposed method. [ABSTRACT FROM AUTHOR]

Classical pole-placement theory requires that every degree of freedom shall be accessible to sensing but in physical systems there are often obstructions that make sensing at certain degrees of freedom impractical. In the classical formulation of the pole placement problem the input vector which determines the actuator gains is given and the pole placement problem is linear. If the input vector is not known and it is desired to find the gains of actuators and the gains of the measured state subject to some constraints then the problem becomes nonlinear since the unknown parameters multiply each other. It is shown that this nonlinear active vibration control problem is rendered linear by the application of a new double input control methodology implemented in conjunction with a receptance-based scheme where full pole placement is achieved while some chosen degrees of freedom are free from both actuation and sensing. A lower bound on the maximum number of degrees of freedom inaccessible to both actuation and sensing is established. A numerical example is provided to demonstrate the working of the method using the new double-input approach. [ABSTRACT FROM AUTHOR]

This study investigates the receptance method for the partial pole assignment of time-delay nonlinear systems using multi-input control from measurement output feedback (i.e., acceleration, velocity and displacement). The receptance method has a remarkable advantage compared to other methods in that there is no need to know the mass, damping and stiffness matrices of the system, which are typically obtained from the finite element method. We achieve partial assignment of the desired poles with no spillover using the assigned and unchanged poles and the corresponding eigenvectors of the closed-loop system. We used different types of generalised inverse matrices to obtain the realisable control gains. The modal constraints for the assigned eigenvectors are thus obtained. Because certain components of the measurement output were found to be unmeasurable, a numbering system is proposed for determining zero elements in the control gains. Then, realisable control gains are obtained after zero-column substitutions are made in the corresponding matrix with the numbering system. Our theoretical results show that having multi-input control from the measurement output feedback is effective for a partial pole assignment with time delay in structures. This theory is demonstrated by several numerical examples of a three-degree-of-freedom damped mass-spring system. [ABSTRACT FROM AUTHOR]

This paper proposed a feasible design of an adjustable PZT beam vibration energy harvester. The adjustability of the harvester was achieved via varying the beam׳s support stiffness, off-line for design or on-line for control, which could be accomplished through, for instance, such as magnetic supports. The theoretical approach employed a structure combination technique for the frequency equation, sensitivity matrix and PZT beam voltage output equation. The harvester’s resonance frequencies and voltage outputs at various excitation frequencies were numerically calculated and experimentally verified to be accurate. Adjusting three-support stiffness to precisely tune the harvester׳s first resonance was demonstrated, theoretically. The adjustable frequency range could be up to ±30% and this was significant from a comparison with the existing literature. Simulations of sudden ambient frequency changes of 5%, 10% and 15% were illustrated and an efficient computing algorithm showed that no more than five steps of support adjustment was enough to regain the resonance state and deliver another maximum voltage output. The harvester׳s output voltages through the whole frequency band were calculated as well and it appeared the designed harvester would sustain a high level of voltage output. [ABSTRACT FROM AUTHOR]

A model of the vibration behaviour of a discontinuous slab track installed on a viaduct is presented. It is represented by a three-layer Euler–Bernoulli beam model subjected to a harmonic load. Analytical equations are derived using the receptance method, and they are used to determine the vibration properties of the system. Comparisons are made between the vibration behaviour under various parameter conditions of the Chinese CRTS I slab track and a typical floating slab track installed on a viaduct. Attention is focused on the mobility, vibration isolation and track decay rates. The results show that, as expected, the floating slab track generates significantly lower viaduct vibrations than the CRTS I slab track. A slab track fitted with a relatively stiff rail pad and soft bearing layer is recommended for consideration during the engineering design phase; appropriate choices can lead to the optimization of the vibration isolation performance of a railway track on a viaduct, thus avoiding the creation of excessive rail vibrations. It is also shown that the average response of the viaduct gives a more representative assessment of the vibration isolation effect than if the average force transmitted to the viaduct is used. Moreover, in terms of insertion loss, these results are relatively insensitive to the choice of viaduct parameters. [ABSTRACT FROM AUTHOR]

Recent years, we receive the full benefit of vehicle by the rapid progress of motorization with the development of economy. By contrast, environmental problem occurs from vehicle noise. The noise in Engine and Intake-Exhaust system which is typical source of noise until now has been improved because noise regulation advanced. This situation makes the tire contribution rate to vehicle interior noise increasing relatively. And the reduction of tire noise is the serious problem that we have to work on. It is important to reconstruct the input into the body from road to spindle and suspension for accurate prediction. One of the problems is how to express the tire vibration characteristics in operational condition, which are complex. It is difficult to construct a tire model that expresses the vibration characteristics on the contact and rolling condition because of the rolling effect, contact patch restriction, the property of rubber. In this study, we set a goal of performing vibration analysis on the contact and rolling condition and clear up the vibration characteristic analytically. First, Introducing tire vibration model based on the cylindrical shell theory and applying the receptance method for tire model. Additionally, we derived the mode shape function and the frequency equation on the contact and rolling condition. Secondly, we calculated natural frequency and mode shape on the contact and rolling condition. After that, we clarified the tire vibration characteristics analytically in the difference condition such as rolling speed. From this study, it was found that natural frequency on the contact and rolling condition depends on adapting mode numbers. Additionally, mode shape on the contact is determined by the components of forward wave and backward wave of the non-contact and rolling condition.

• A receptance-based interval multiobjective optimization method is proposed to realize the antiresonant frequency assignment of vibrating systems with uncertainty. • The interval confidence level of the interval optimization algorithm is redefined to suit inverse structural modification. • This study enhances the chance of success in finding the right structure modification in practice. • Vibration experiments are performed to validate the proposed method. This study addresses the antiresonant frequency assignment problem of vibrating systems with uncertainty, which is solved using an interval multi-objective optimization method. The study accounts for several uncertain factors, including in the structural parameters and test data, and defines them as interval variables. The bounds of interval variation of the receptance (frequency response function or FRF) are determined from a small number of numerical or experimental results; thus, it is unnecessary to collect a large amount of data to construct the sample space. The antiresonant frequency assignment problem of uncertain systems is formulated as an interval multi-objective optimization. Optimal solutions (the structural modifications that assign the desired antiresonant frequency frequencies) are determined through the MI-NSGA-II algorithm proposed in this work. It employs the basic framework of the interval multi-objective genetic algorithm INSGA-II and redefines the interval confidence level to evaluate the merits and demerits between individual feasible solutions and improve the stability of INSGA-II. The obtained modifications not only accurately achieve the goal of antiresonant frequency assignment but also stably maximize the robustness of the antiresonant frequency frequencies after modifications. From the perspective of enhancing the applicability of the receptance method, the proposed method can overcome the problems of unsuccessful antiresonant frequency assignment due to measurement inaccuracies and the uncertainty of physical parameters to a certain extent. Numerical and experimental examples have been provided to demonstrate the effectiveness of the proposed method. [ABSTRACT FROM AUTHOR]

The problem of robust pole placement in active structural vibration control by the method of receptance is considered in this paper. Expressions are derived for the eigenvalue sensitivities to parametric perturbations, which are subsequently minimised to improve performance robustness of the control of a dynamical system. The described approach has application to a vibrating system where variations are present due to manufacturing and material tolerances, damages and environment variabilities. The closed-loop eigenvalue sensitivities are expressed as a linear function of the velocity and displacement feedback gains, allowing their minimisation with carefully calculated feedback gains. The proposed algorithm involves curve fitting perturbed frequency response functions, FRFs, using the rational fraction polynomial method and implementation of a polynomial fit to the individual estimated rational fraction coefficients. This allows the eigenvalue sensitivity to be obtained entirely from structural FRFs, which is consistent with the receptance method. This avoids the need to evaluate the M,C,K matrices which are typically obtained through finite element modelling, that produces modelling uncertainty. It is also demonstrated that the sensitivity minimisation technique can work in conjunction with the pole placement and partial pole placement technique using the receptance method. To illustrate the working of the proposed algorithm, the controller is first implemented numerically and then experimentally. • Robust active vibration control by eigenvalue sensitivity minimisation. • Theoretical and experimental development of robust pole placement. • Robust pole placement by the receptance method. • Eigenvalue sensitivity is derived from the receptance matrix. • The proposed method can be applied directly from measured vibration data. [ABSTRACT FROM AUTHOR]

• The receptance method is extended to multi-input zero assignment. • The method handles the simultaneous pole-zero assignment. • The design of the controllers is achieved through the measured rec. • Two different solution methods are proposed. • The method handles either state or state-derivative control. The famous receptance method for the active vibration control has been mainly applied for pole placement. In this paper, it is exploited to solve the multi-input antiresonance assignment and then it is extended to handle the simultaneous pole-zero assignment. The design of the controllers is achieved through the measured receptances. The chief advantage is that system model is not needed, and the controller gains are synthetized through the data collected through experimental measurements. Two different approaches are proposed to compute the gains: a single-step method and a multi-step method. Both the techniques are developed for either state or state-derivative control. Two techniques to handle the non-uniqueness of the solution are proposed as well: the first one allows including specification on the eigenvectors, and hence on the spatial response of the system when excited at the antiresonance frequency; the second one places approximately all the poles through an optimization-based formulation. The proposed methods are validated through some numerical examples taken from common benchmarks in this field of research. [ABSTRACT FROM AUTHOR]

Abstract: The purpose of the present investigation is to obtain the mean power flow radiated by a double-deck circular tunnel and compares it to the one radiated by a simple circular tunnel. To achieve this, a harmonic line load is applied on the interior floor of the first one and at the bottom of the second one. For the double-deck tunnel, a new analytical model based on the receptance method is developed. The proposed model describes the dynamics of the interior floor using the thin plate theory and considers the Pipe in Pipe (PiP) model to describe the tunnel and soil coupled system. Plain strain conditions are assumed for both systems and conservative coupling is considered between them. Numerical results show significant differences between the power flow radiated by both tunnels, with the one radiated by the double-deck tunnel reaching much higher values. The effect of modifying the flexural rigidity of the interior floor is also presented. [Copyright &y& Elsevier]

• Partial eigenstructure assignment is made via state feedback. • Only part of the receptance matrix is required (thus modelling errors are avoided). • Three numerical examples of mass-spring systems demonstrate its effectiveness. • Robustness of the method is analysed and found to be good. The partial eigenvalue assignment problem has drawn much attention for decades because of its usefulness and fascinating appeal in vibration control. It is also a mathematically challenging problem, particularly when the mathematical description is cast in the second-order formulation framework. Previous methods require either the system matrices, such as mass, damping or stiffness matrix, or the eigenvectors of the original system. Those data, especially the system matrices which are usually obtained from a finite element model, are not easy to obtain or very accurate. To overcome this drawback, a new partial eigenvalue assignment method by multi-input active control is proposed in this paper. Only part of the receptance matrix of the original system is required in this method. In addition, this method can simultaneously assign eigenvalues and the associated eigenvectors, including assigning nodes at desired locations. Three numerical examples are used to validate the proposed method and demonstrate the role of the control efforts. The robustness of the proposed method is analysed through a Monte-Carlo simulation. Numerical results show that this method is robust for the four-DoF damped system where there are 5% variations of the needed receptance matrix elements. This paper reports the first attempt to make partial eigenstructure assignment in the second-order eigenvalue framework using only the receptances. [ABSTRACT FROM AUTHOR]

• A vibration controller is presented for eigenvalue assignment with minimum control energy using the squared H 2 -norm. • The proposed method is based on measured receptances without the need to know or the evaluate the system matrices. • Design flexibility is achieved using regional eigenvalue assignment. • Advantages over the standard H 2 -control are demonstrated. This paper proposes a method of H 2 -optimal vibration control using regional eigenvalue assignment based only on measured receptances, typically from a modal test. The sum of the squared weighted H 2 -norm of closed-loop receptance matrix and the transfer matrix from the external input to the control input is minimized by exploiting the flexibility from assigning the closed-loop eigenvalues to prescribed stable regions with single- or multiple-input control. It is found that regional eigenvalue assignment and the optimization of a free parameter matrix (in the multiple-input case) provide extra flexibility for improving the closed-loop performance over and above the selection of weighting matrices, as in standard H 2 control. Therefore, the internal stability, satisfactory response, and minimum control energy are readily guaranteed by the proposed method, whereas the standard approach is dependent upon the arbitrarily chosen weighting matrices. The method inherits the advantages of both optimal control and eigenvalue assignment by the receptance method. The working of the method and its advantages over the standard H 2 control are demonstrated numerically. [ABSTRACT FROM AUTHOR]

This article describes the practical application of a vibration control technique, developed by the authors and known as the receptance method, to the AgustaWestland W30 helicopter airframe in the vibration test house at Yeovil. The experimental work was carried out over a total of 5 days in two visits to the Yeovil site during February and March 2011. In the experiments, existing electro-hydraulic actuators were used; they were built into the airframe structure and originally designed for vibration suppression by the methodology known as active control of structural response developed at the AgustaWestland Helicopters site in Yeovil. Accelerometers were placed at a large number of points around the airframe and an initial open-loop modal test was carried out. In a subsequent test, at higher actuator input voltage, considerable non-linearity was discovered, to the extent that the ordering of certain modes had changed. The vibration modes were, in general, heavily damped. Control was implemented using measured frequency response functions obtained at the higher input level. After acquiring the necessary measurements, simulations were carried out and the controller was implemented using MATLAB/Simulink and dSPACE. The closed-loop poles were mostly assigned with small real parts so that the system would be lightly damped and sharp peaks would be clearly apparent in the measured closed-loop frequency response functions. Locations of the open- and closed-loop poles in the complex s-plane were obtained to verify that the required assignment of poles had taken place. [ABSTRACT FROM AUTHOR]

Abstract: The problem of robust pole placement in structural vibration using receptance data is considered. Expressions are derived for the sensitivities of the eigenvalues to perturbations in the measurements and for robustness to measurement errors these sensitivity terms should be made as small as possible. A sequential multi-input state-feedback approach is described and by this procedure it is shown that a different eigenvalue may be assigned at each step without changing those eigenvalues assigned at previous steps. The columns of the force distribution matrix are chosen to excite easily the eigenvalue considered at the current step of the procedure. The sequential approach has the advantage of a characteristic equation that is linear in the control gains and is shown to be inherently more robust to measurement noise than the single-input method. The effects of sequential multi-input state feedback when combined with minimisation of eigenvalue sensitivity norms are investigated. [Copyright &y& Elsevier]

A new receptance method is proposed for partial quadratic pole assignment problem (PQPAP) of asymmetric systems with multi-input. We use receptance matrices of symmetric parts of open-loop systems to express the solution of PQPAP. Then we derive the sensitivities of changed eigenvalues of close-loop system and give the measure of robustness. On these grounds, an algorithm for solving the robust and minimum norm PQPAP is put forward. Our method utilizes receptance matrices of symmetric parts of asymmetric systems and it is applicable to the systems with multi-input. Finally, numerical results are given to show the efficiency of our method. • Receptance method is proposed for partial quadratic pole assignment problem (PQPAP) of asymmetric system with multi-input. • Our method only uses receptance matrix of symmetric part of asymmetric system. • The close-loop eigenvalue sensitivities are derived and used to measure robustness. • Robust PQPAP is solved by transforming it into an optimization problem. [ABSTRACT FROM AUTHOR]

A stacked multi-disk with read/write head assembly was investigated. The interference of head assembly on the spinning disks was modeled by stationary springs intervening between disks. The receptance method was then applied to join the spinning disks and the stationary springs. A general, recursive equation for natural frequency of a disk-head system was derived. Numerical examples followed for the cases of 3 to 6 stacked disks. The results showed that even for weak spring coupling, the changes of mode shapes were very significant and the changes of natural frequencies were slight. The effects of spring stiffness, location, and disk spinning speed were examined as well. The spinning speed was seen to pull the frequency loci to pass through the crossings of a single disk’s frequency curves and there existed a curve-veering phenomenon. [ABSTRACT FROM AUTHOR]

In this paper, a simplified model is studied to predict analytically the vibration from the helical gear system due to an axial excitation of helical gears. The simplified model describes gear, shaft, bearing, and housing. In order to obtain the axial force of helical gears, the mesh stiffness is calculated in the load deflection relation. The axial force is obtained from the solution of the equation of motion, using the mesh stiffness. It is used as a longitudinal excitation of the shaft, which in turn drives the gear housing through the bearing. In this study, the shaft is modeled as a rod, while the bearing is modeled as a parallel spring and damper only supporting longitudinal forces. The gear housing is modeled as a clamped circular plate with viscous damping. For the modeling of this system, transfer matrices for the rod and bearing are used, using a spectral method with four pole parameters. The model is validated by finite element analysis. Using the model, parameter studies are carried out. As a result, the linearized dynamic shaft force due to the gear excitation in the frequency domain was proposed. Out-of-plan displacement from the forced vibrating circular plate and the renewed mode normalization constant of the circular plate were also proposed. In order to control the axial vibration of the helical gear system, the plate was more important than the shaft and the bearing. Finally, the effect of the dominant design parameters for the gear system can be investigated by this model. [ABSTRACT FROM AUTHOR]

• A receptance method for partial quadratic eigenvalue assignment problem (PQEAP) is proposed by formulating the PQEAP as an optimization problem. • The proposed method only needs the receptance matrices and the undesired eigenpairs of open-loop system. The system matrices and the unchanged eigenpairs of open-loop system are not required. • The norms of feedback matrices and the condition number of close-loop system are simultaneously minimized. • The real form of the proposed method is developed. • The gradient of the objective function is derived. This paper considers the partial quadratic eigenvalue assignment problem (PQEAP) in active vibration control using state feedback. A receptance method is proposed for PQEAP such that the norms of feedback matrices and the condition number of close-loop system are simultaneously minimized. The real form of the proposed method is developed. The proposed method only uses receptance matrices and the unwanted eigenpairs of open-loop system. The system matrices and the unchanged eigenpairs of open-loop system are not required. The efficiency of the proposed method is illustrated by some numerical examples. [ABSTRACT FROM AUTHOR]

This study proposes the parametric active aeroelastic control of a folding wing, which is a promising concept of morphing wings, by integrating the parameterized aeroservoelastic model and the receptance-based control strategy. It starts with establishing the parameterized aeroservoelastic model of the folding wing with respect to its folding angle and air speed. The transfer functions between the embedded sensors and the actuators of the folding wing are then efficiently obtained using the parameterized aeroservoelastic model. Finally, control gains for varying folding angle and air speed of the wing are synthesized using the receptance method. The results of numerical analyses show that smooth evolutions of the control gains can be obtained over a wide range of folding angles and air speeds, although the dynamic behavior of the folding wing is sensitive to these parameters. In addition, the active aeroelastic control can effectively suppress aeroelastic vibrations and expand flutter boundaries of the folding wing. The benefit of the parametric active aeroelastic control for the folding wing, i.e., smoothly switching among the control laws without exciting undesirable vibrations is highlighted. [ABSTRACT FROM AUTHOR]

• Uncertainty in the Receptance Method due to parameter errors in fitted rational transfer functions is considered. • Random pole spreads are quantified by analytical sensitivity formulae, which are derived. • A global optimization approach is used to minimise a robustness metric, which is defined by the sensitivities. • The method is applied numerically to single- and multiple-input systems. The robustness of receptance-based active control techniques to uncertain parameters in fitted transfer function matrices is considered. Variability in assigned closed-loop poles, which arises from uncertain open-loop poles, zeros, and scaling parameters, is quantified by means of analytical sensitivity formulae, which are derived in this research. The sensitivity formulae are shown to be computationally efficient, even for a large number of random parameters, and require only measured receptances, thereby preserving the model-free superiority of receptance-based techniques. An evolution-based global optimisation procedure is used to perform eigenstructure assignment so that the robustness, as defined by a metric, is maximised. The robustness metric is designed to scale the relative importance of each closed-loop pole and their respective real and imaginary parts. The proposed technique is tested numerically on a multi-degree-of-freedom system. It is shown that, in both single- and multiple-input systems, it is possible to increase the robustness by optimally selecting a set of closed-loop poles. However, it is determined that the closed-loop eigenvectors of the system play a significant role in the propagation of uncertainty and hence, since multiple-input systems may independently assign both closed-loop poles and eigenvectors, multiple-input systems are able to reduce the uncertainty propagation to a greater extent. [ABSTRACT FROM AUTHOR]