Interpreting the input admittance of violins and guitars

The most widespread vibration measurement on musical instrument bodies is of the point mobility at the bridge. Analysis of such measurements is presented, with a view to assessing what range of information could feasibly be extracted from the corpus of data. Analysis approaches include (1) pole-residue extraction; (2) damping trend analysis based on time decay information; (3) statistical estimates based on SEA power-balance and variance theory. Comparative results are shown for some key quantities. Damping trends with frequency are shown to have unexpectedly different forms for violins and for guitars. Linear averaging to estimate the "direct field" component gives a simple and clear visualisation of any local resonance behaviour near the bridge, such as the "bridge hill", and reveals some violins that show a double hill, while viols show only weak hills, and guitars none at all. © S. Hirzel Verlag · EAA.

Identification of damping: Part 4, error analysis

In previous papers (S. Adhikari and J. Woodhouse 2001 Journal of Sound and Vibration 243, 43-61; 63-88; S. Adhikari and J. Woodhouse 2002 Journal of Sound and Vibration 251, 477-490) methods were proposed to obtain the coefficient matrix for a viscous damping model or a non-viscous damping model with an exponential relaxation function, from measured complex natural frequencies and modes. In all these works, it has been assumed that exact complex natural frequencies and complex modes are known. In reality, this will not be the case. The purpose of this paper is to analyze the sensitivity of the identified damping matrices to measurement errors. By using numerical and analytical studies it is shown that the proposed methods can indeed be expected to give useful results from moderately noisy data provided a correct damping model is selected for fitting. Indications are also given of what level of noise in the measured modal properties is needed to mask the true physical behaviour.

Investigation of damping effects on statistical energy analysis of coupled structures

The effects of damping on energy sharing in coupled systems are investigated. The approach taken is to compute the forced response patterns of various idealised systems, and from these to calculate the parameters of Statistical Energy Analysis model for the systems using the matrix inversion approach [1]. It is shown that when SEA models are fitted by this procedure, the values of the coupling loss factors are significantly dependent on damping except when it is sufficiently high. For very lightly damped coupled systems, varying the damping causes the values of the coupling loss factor to vary in direct proportion to the internal loss factor. In the limit of zero damping, the coupling loss factors tend to zero. This is a view which contrasts strongly with 'classical' SEA, in which coupling loss factors are determined by the nature of the coupling between subsystems, independent of subsystem damping. One implication of the strong damping dependency is that equipartition of modal energy under low damping does not in general occur. This is contrary to the classical SEA prediction that equipartition of modal energy always occurs if the damping can be reduced to a sufficiently small value. It is demonstrated that the use of this classical assumption can lead to gross overestimates of subsystem energy ratios, especially in multi-subsystem structures. © 1996 Academic Press Limited.

Towards identification of a general model of damping

Characterization of damping forces in a vibrating structure has long been an active area of research in structural dynamics. In spite of a large amount of research, understanding of damping mechanisms is not well developed. A major reason for this is that unlike inertia and stiffness forces it is not in general clear what are the state variables that govern the damping forces. The most common approach is to use `viscous damping' where the instantaneous generalized velocities are the only relevant state variables. However, viscous damping by no means the only damping model within the scope of linear analysis. Any model which makes the energy dissipation functional non-negative is a possible candidate for a valid damping model. This paper is devoted to develop methodologies for identification of such general damping models responsible for energy dissipation in a vibrating structure. The method uses experimentally identified complex modes and complex natural frequencies and does not a-priori assume any fixed damping model (eg., viscous damping) but seeks to determine parameters of a general damping model described by the so called `relaxation function'. The proposed method and several related issues are discussed by considering a numerical example of a linear array of damped spring-mass oscillators.

Analysis and performance assessment of 6-pulse inverter-fed 3-phase and 6-phase induction machines

The paper describes a model for a 6-phase induction motor driven by an inverter operating in a 6-pulse (square wave) mode. The model is implemented and performance, in terms of torque, current, efficiency and pulsating torque, compared to the performance of a 3-phase motor (both sine and 6-pulse supplied). The models are verified experimentally, in particular the efficiency performance, and it is illustrated that the improvement in inverter efficiency when in 6-pulse operating mode may improve the performance of the overall system. © 2005 IEEE.

Implementation of a PI phase angle controller for finite element analysis of the BDFM

Time-stepping finite element analysis of the BDFM for a specific load condition is shown to be a challenging problem because the excitation required cannot be predetermined and the BDFM is not open loops stable for all operating conditions. A simulation approach using feedback control to set the torque and stabilise the BDFM is presented together with implementation details. The performance of the simulation approach is demonstrated with an example and computed results are compared with measurements.

Sensitivity analysis of a time-delayed thermo-acoustic system via an adjoint-based approach

We apply adjoint-based sensitivity analysis to a time-delayed thermo-acoustic system: a Rijke tube containing a hot wire. We calculate how the growth rate and frequency of small oscillations about a base state are affected either by a generic passive control element in the system (the structural sensitivity analysis) or by a generic change to its base state (the base-state sensitivity analysis). We illustrate the structural sensitivity by calculating the effect of a second hot wire with a small heat-release parameter. In a single calculation, this shows how the second hot wire changes the growth rate and frequency of the small oscillations, as a function of its position in the tube. We then examine the components of the structural sensitivity in order to determine the passive control mechanism that has the strongest influence on the growth rate. We find that a force applied to the acoustic momentum equation in the opposite direction to the instantaneous velocity is the most stabilizing feedback mechanism. We also find that its effect is maximized when it is placed at the downstream end of the tube. This feedback mechanism could be supplied, for example, by an adiabatic mesh. We illustrate the base-state sensitivity by calculating the effects of small variations in the damping factor, the heat-release time-delay coefficient, the heat-release parameter, and the hot-wire location. The successful application of sensitivity analysis to thermo-acoustics opens up new possibilities for the passive control of thermo-acoustic oscillations by providing gradient information that can be combined with constrained optimization algorithms in order to reduce linear growth rates. © Cambridge University Press 2013.

Natural frequency and damping ratio of a vertically vibrated surface foundation

It is possible and common to obtain equivalent natural frequency and damping for a soil-foundation system from results of experimental or numerical analysis assuming the system has a single degree of freedom. Three approaches to extract natural frequency and damping were applied to the vertically vibrated soil-foundation system. The sensitivity of the computed natural frequency and damping to the soil properties was evaluated through parametric studies. About 10-20% of discrepancy in values of natural frequency was observed due to different approaches. The results help to assess the reliability of equivalent soil properties determined from the reported natural frequency of the system. Finally the results obtained using theoretical predictions with linear soil properties measured in situ were compared to those calculated from experimental data. The prediction and experimental results showed good agreements if the embedment of the foundation is neglected with stepped sine test but considered with impulse test. © 2010 Elsevier Ltd.

Shock amplification, curve veering and the role of damping

The circumstances are investigated under which high peak acceleration can occur in the internal parts of a system when subjected to impulsive driving on the outside. Previous work using a coupled beam model has highlighted the importance of veering pairs of modes. Such a veering pair can be approximated by a lumped system with two degrees of freedom. The worst case of acceleration amplification is shown to occur when the two oscillators are tuned to the same frequency, and for this case closed-form expressions are derived to show the parameter dependence of the acceleration ratio on the mass ratio and coupling strength. Sensitivity analysis of the eigenvalues and eigenvectors indicates that mass ratio is the most sensitive parameter for altering the veering behaviour in an undamped system. Non-proportional damping is also shown to have a strong influence on the veering behaviour. The study gives design guidelines to allow permissible acceleration levels to be achieved by the choice of the effective mass and damping of the indirectly driven subsystem relative to the directly driven subsystem. © 2013 Elsevier Ltd.