Dynamic response of simple systems to periodic forces

Text includes handwritten formulasA study of the response of viscously damped single-degree-of-freedom systems to non-harmonic periodic excitations is presented. The objectives have been (1) to assess the effects of the various factors that affect the response of such systems; and (2) to present information and concepts with which the salient features of the response may be identified readily. The following aspects of the response are examined: (a) the steady-state response, which is the response obtained after the free vibrational component is damped and the resulting motion repeats itself; (b) the absolute maximum response, which is generally obtained prior to the attainment of the steady-state response; (c) the rate of "build-up" of the response; and (d) the effects of possible cessation of the excitation. The factors investigated include the characteristics of the structure and the excitation. Special attention is paid to the behavior of low-frequency systems. For a number of excitations, closed-form expressions are also presented for the steady-state response of undamped systems

Vertex results for the robust analysis of uncertain biochemical systems

We consider the problem of assessing the sensitivity of uncertain biochemical systems in the presence of input perturbations (either constant or periodic) around a stable steady state. In particular, we propose approaches for the robust sensitivity analysis of systems with uncertain parameters assumed to take values in a hyper-rectangle. We highlight vertex results, which allow us to check whether a property is satisfied for all parameter choices in the hyper-rectangle by simply checking whether it is satisfied for all parameter choices at the vertices of the hyper-rectangle. We show that, for a vast class of systems, including (bio)chemical reaction networks with mass-action kinetics, the system Jacobian has a totally multiaffine structure (namely, all minors of the Jacobian matrix are multiaffine functions of the uncertain parameters), which can be exploited to obtain several vertex results. We consider different problems: robust non-singularity; robust stability of the steady-state; robust steady-state sensitivity analysis, in the case of constant perturbations; robust frequency-response sensitivity analysis, in the presence of periodic perturbations; and robust adaptation analysis. The developed theory is then applied to gain insight into some examples of uncertain biochemical systems, including the incoherent feed-forward loop, the coherent feed-forward loop, the Brusselator oscillator and the Goldbeter oscillator

Analysis of crankshaft–crankcase interaction for the prediction of the dynamic structural response and noise radiation of IC engine structures

This thesis presents research work which is concerned with the development of analytical and numerical methods for the dynamic analysis of the crankshaft-crankcase assembly. The effects of interaction of crankshaft and crankcase on the dynamic response of an IC engine block structure are studied. These methods are especially attractive for the simulation of the steady state response of rotating systems with many degrees of freedom which are forced by multiple periodic excitations. A major novelty of the methods is the ability to model the system non-linearities successfully as frequency dependent properties. [Continues.

Non-linear frequency response analysis of the kinetics of electrochemical reactions: a case study – ferrocyanide oxidation kinetics

In general, electrochemical (EC) systems are non-linear, which means they respond nonlinearly to a frequency-dependent periodic input perturbation of high amplitude imposed around a steady-state. In addition, the kinetics of EC reactions are quite complex and different rivalling model presentations can be formulated for certain EC reaction. While standard electrochemical methods (steady-state and electrochemical impedance spectroscopy) showed low sensitivity towards the model discrimination, non-linear frequency response analysis (NLFRA) of EC kinetics can appear advantageous for this purpose. In this work, NLFRA is applied in experimental and theoretical study of ferrocyanide oxidation as a model EC reaction.Belgrade, Serbia, June 6-10, 2010Related to the published paper in the Proceedings of the Second Regional Symposium on Electrochemistry South-East Europe, [http://cer.ihtm.bg.ac.rs/handle/123456789/3539

Non-linear frequency response analysis of the kinetics of electrochemical reactions: a case study – ferrocyanide oxidation kinetics

In general, electrochemical (EC) systems are non-linear, which means they respond nonlinearly to a frequency-dependent periodic input perturbation of high amplitude imposed around a steady-state. In addition, the kinetics of EC reactions are quite complex and different rivalling model presentations can be formulated for certain EC reaction. While standard electrochemical methods (steady-state and electrochemical impedance spectroscopy) showed low sensitivity towards the model discrimination, non-linear frequency response analysis (NLFRA) of EC kinetics can appear advantageous for this purpose. In this work, NLFRA is applied in experimental and theoretical study of ferrocyanide oxidation as a model EC reaction.Belgrade, Serbia, June 6-10, 2010Related to the published paper in the Proceedings of the Second Regional Symposium on Electrochemistry South-East Europe, [http://cer.ihtm.bg.ac.rs/handle/123456789/3539

Frequency Response Based Repetitive Control for Periodic Coefficient Systems Motivated by Cam Followers

Cam follower systems are generally designed to operate at a fixed speed or a range of fixed speeds. However manufacturing defects, wear, or a change of design goals may require altering the camshaft speed to produce a follower trajectory which is not possible using a fixed speed. The follower trajectory may also be optimized for some performance criteria such as minimizing vibration and wear. Like most real world systems, the differential equations governing a cam follower system are nonlinear. A common approach for controlling a nonlinear system is to first linearize the system about a nominal operating point, then apply linear control laws. In many cases, such as the cam follower system, one can create a trajectory and numerically solve the nonlinear system for the inputs required to follow it. Linearizing about this solution creates a linear time varying system whose states are deviations from the desired solution. The speed trajectory in the cam follower system is periodic, which results in a linear system with periodic coefficients. Repetitive control creates control systems that aim to converge to zero tracking error following a periodic command, or aim to completely cancel the effects of a periodic disturbance. Using the inverse of the steady state frequency response as a compensator has been shown to be very effective for linear time invariant systems. That idea is applied here to linear time periodic systems. The periodic state matrices lend themselves well to frequency domain representations, which can be used to construct a matrix form of the steady state frequency response. The first law studied in this work analyzes a moving window implementation which monitors the output errors and previous commands to create an update to the change in the command for the current time step using the inverse of the steady state frequency response matrix. Asymptotic convergence conditions for zero tracking error are derived. When the number of samples in one period is not an integer number, the moving window method is not feasible without interpolation. Therefore a second method based on the projection algorithm from adaptive control is developed and analyzed. In linear constant coefficient systems, one generally needs to incorporate a frequency cutoff filter to robustify to high frequency model error. The additional intricacies of designing a cutoff filter for periodic systems is considered, aiming to handle the fact that for periodic coefficient systems, addressing error components below the intended cutoff can excite harmonics above the cutoff. The control laws developed in this work are applicable to any nonlinear system which may be linearized about a periodic trajectory. Development of these control laws is motivated by improving the performance of a cam follower system. Additional improvements in cam follower behavior can be done through parameter optimization. This includes optimizing a nonlinear follower spring such that it provides just sufficient force to maintain contact while reducing the load on the cam

A frequency domain approach to the analysis and optimization of valve spring dynamics

In this thesis a method is derived and presented, for the efficient analysis of the steady state response of dynamic systems with time variant propenies. The method is especially attractive for the simulation of the steady state response of lightly damped systems with low numbers of degree of freedom which are forced by a periodic excitation. A major feature of the method is that the system non-linearities can be successfully modelled as time variant propenies. An ideal application for this approach is the calculation of the dynamic response of a modal model for progressive valve springs in the frequency domain. The solution method is explained and derived using this example. The differences, drawbacks, and advantages are assessed by comparison with both a linear modal model and a discrete time-domain model; correlation with actual measurement is also shown. The extreme efficiency of the method allows its application in a more general study of the dynamic propenies of valve springs. This analysis is initially discussed and examined using statistical methods. Then the frequency domain solution method is employed to perform an automatic optimization of the spring frequency characteristic for a 16 valve prototype engine application. The spring design obtained from this study has been manufactured and the resulting hardware is discussed. The measured response of this hardware is compared with simulation results for the same configuration, verifying the fmdings from the statistical investigation and the optimization. Finally open issues and further envisaged work in the area of damping mechanisms in valve springs and manufacturing issues are diScussed and an approach for the next steps to take is outlined

A frequency domain approach to the analysis and optimization valve spring dynamics

In this thesis a method is derived and presented, for the efficient analysis of the steady state response of dynamic systems with time variant propenies. The method is especially attractive for the simulation of the steady state response of lightly damped systems with low numbers of degree of freedom which are forced by a periodic excitation. A major feature of the method is that the system non-linearities can be successfully modelled as time variant propenies. An ideal application for this approach is the calculation of the dynamic response of a modal model for progressive valve springs in the frequency domain. The solution method is explained and derived using this example. The differences, drawbacks, and advantages are assessed by comparison with both a linear modal model and a discrete time-domain model; correlation with actual measurement is also shown. The extreme efficiency of the method allows its application in a more general study of the dynamic propenies of valve springs. This analysis is initially discussed and examined using statistical methods. Then the frequency domain solution method is employed to perform an automatic optimization of the spring frequency characteristic for a 16 valve prototype engine application. The spring design obtained from this study has been manufactured and the resulting hardware is discussed. The measured response of this hardware is compared with simulation results for the same configuration, verifying the fmdings from the statistical investigation and the optimization. Finally open issues and further envisaged work in the area of damping mechanisms in valve springs and manufacturing issues are diScussed and an approach for the next steps to take is outlined