1,720,996 research outputs found
Calculating the forced response of two-dimensional homogeneous media using the wave and finite element method
No full textThe forced response of two-dimensional, infinite, homogenous media subjected to time harmonic loading is treated. The approach starts with the wave and the finite element (WFE) method where a small segment of a homogeneous medium is modelled using commercial or in-house finite element (FE) packages. The approach is equally applicable to periodic structures with a periodic cell being modelled. This relatively small model is then used, along with periodicity conditions, to formulate an eigenvalue problem whose solution yields the wave characteristics of the whole medium. The eigenvalue problem involves the excitation frequency and the wavenumbers (or propagation constants) in the two directions. The wave characteristics of the medium are then used to obtain the response of the medium to a convected harmonic pressure (CHP). Since the Fourier transform of a general two-dimensional excitation is a linear combination of CHPs, the response to a general excitation is a linear combination of the responses to CHPs. Thus, the response of a two-dimensional medium to a general excitation can be obtained by evaluating an inverse Fourier transform. This is a double integral, one of which is evaluated analytically using contour integration and the residue theorem. The other integral can be evaluated numerically. Hence, the approach presented herein enables the response of an infinite two-dimensional or periodic medium to an arbitrary load to be computed via (a) modelling a small segment of the medium using standard FE methods and post-processing its model to obtain the wave characteristics, (b) formulating the Fourier transform of the response to a general loading, and (c) computing the inverse of the Fourier transform semi-analytically via contour integration and the residue theorem, followed by a numerical integration to find the response at any point in the medium. Numerical examples are presented to illustrate the approac
Waves in a three-dimensional model of the cochlea
No full textThe conventional travelling wave theory of the cochlea assumes that only a single “slow” wave, which determines the overall response in the cochlea, can propagate. Various different mechanisms, such as longitudinal coupling in the fluid or the basilar membrane, BM, may give rise to other types of wave. In this paper the wave finite element method is used to predict all possible waves in a three-dimensional model of the passive cochlea using an orthotropic plate model for the BM, in terms of wave mode shape and wavenumber as a function of position along the cochlea. Mode conversion in waves can then be explored by decomposing results from a full finite element model. It is found that only one wave, the slow wave, is dominant basal to the characteristic place and then a higher order fluid mode starts to make a significant contribution to the overall response when system damping is small
Uncertainty in structural dynamics
No full textThe effects of uncertainty are of growing concern in the design of engineering structures. The fact that the properties of the structure are uncertain implies that there is consequent uncertainty in the dynamic response. Similarly, there is inevitable manufacturing variability: mass-produced items are never identical. Indeed the properties of an individual system will change with time due to environmental conditions, loads, wear, etc.Uncertainty and variability raise issues concerning safety, reliability, quality of performance, worst-case behaviour and so on, and in turn these issues lead to demands for modelling methods which specifically include uncertainties in the properties of the structure. In the past, factors of safety might be introduced. However, the desire for greater efficiency, improved performance and reduced costs has led to a demand for improved computational methods, especially for high-cost structures. The goal is to apply such methods at the design stage to produce structures which are safe, reliable and have acceptable noise and vibration performance under all environmental and operating conditions which they are expected to encounter, and to produce designs which are robust with respect to manufacturing variability
Vibration modelling of helical springs with non-uniform ends
No full textHelicalsprings constitute an integral part of many mechanical systems. Usually, a helicalspring is modelled as a massless, frequency independent stiffness element. For a typical suspension spring, these assumptions are only valid in the quasi-static case or at low frequencies. At higher frequencies, the influence of the internal resonances of the spring grows and thus a detailed model is required. In some cases, such as when the spring is uniform, analytical models can be developed. However, in typical springs, only the central turns are uniform; the ends are often not (for example, having a varying helix angle or cross-section). Thus, obtaining analytical models in this case can be very difficult if at all possible. In this paper, the modelling of such non-uniformsprings are considered. The uniform (central) part of helicalsprings is modelled using the wave and finite element (WFE) method since a helicalspring can be regarded as a curved waveguide. The WFE model is obtained by post-processing the finite element (FE) model of a single straight or curved beam element using periodic structure theory. This yields the wave characteristics which can be used to find the dynamic stiffness matrix of the central turns of the spring. As for the non-uniformends, they are modelled using the standard finite element (FE) method. The dynamic stiffness matrices of the ends and the central turns can be assembled as in standard FE yielding a FE/WFE model whose size is much smaller than a full FE model of the spring. This can be used to predict the stiffness of the spring and the force transmissibility. Numerical examples are presente
Slow motor neuron stimulation of locust skeletal muscle: model and measurement
No full textThe isometric force response of the locust hind leg extensor tibia muscle to stimulation of a slow extensor tibia motor neuron is experimentally investigated, and a mathematical model describing the response presented. The measured force response was modelled by considering the ability of an existing model, developed to describe the response to the stimulation of a fast extensor tibia motor neuron and to also model the response to slow motor neuron stimulation. It is found that despite large differences in the force response to slow and fast motor neuron stimulation, which could be accounted for by the differing physiology of the fibres they innervate, the model is able to describe the response to both fast and slow motor neuron stimulation. Thus, the presented model provides a potentially generally applicable, robust, simple model to describe the isometric force response of a range of muscles.<br/
Response statistics of stochastic built-up structures
No full textCollections of essentially identical manufactured built-up structures display natural variations in their response. These variations arise from many sources including variability in the manufacturing process, variations in the response measurement process and environmental variations. Current techniques for response prediction focus on estimating the response of an ’ideal’ or nominal realisation of the structure. Further understanding is required into the statistics of the response of collections of mass produced structures. An appreciation of the distribution of response enables a cost effective design process with improved knowledge of worst-case behaviour and failure modes. Relevant measures include mean and variance, together with their statistical distributions. This paper considers response statistics in various situations. First, an idealised situation is considered and possible methods of analysis discussed. Then some existing measured response data from industrial products is examined. The availability of such data is extremely limited. Various statistical distributions are fitted to the data and compared using chi-squared tests
The evolution of mechanical engineering curricula: mechatronics
No full textThis paper discusses one area in the ongoing evolution of Mechanical Engineering curricula, Mechatronics. Mechatronic devices are widespread – CD players, cars, autowashers, robots, disc drives, photocopiers etc. – mechanical devices which involve a microprocessor, electronics and control. The evolution of the classical Mechanical Engineering degree into a separate degree in Mechatronics is fully in keeping with the desire for a hightech, knowledge-based economy. The philosophy and the rise of Mechatronics-related teaching is briefly reviewed and the possible diversity of courses indicated. Two case studies are presented. The first describes the experiences of two of the authors in developing a Mechatronics undergraduate degree programme when they were at the University of Auckland, the motivation behind the decision and the structure of the course. The second case study is a proposal for a multi-media based course in mechatronics which could be utilised for a European-wide degree
Application of a dielectric electro-active polymer actuator for active vibration isolation
No full textThis paper describes the use of a tubular dielectric electro-active polymer (DEAP) actuator for active vibration isolation. The DEAP tubular push actuator developed by Danfoss PolyPower A/S has been used. First, the characteristics of the actuator are examined. It is seen that the actuator is inherently non-linear, involving an approximately quadratic relationship between excitation and extension. Next, it is seen that internal resonances in the actuator limit the bandwidth over which it can be used for active control (to 75 Hz or so). The potential for active vibration isolation is then explored. The dynamic performance is limited by the potential bandwidth, the inherent nonlinearity, the maximum force that can be generated and the maximum range of movement. Performance for tonal disturbances is investigated experimentally within an adaptive feedforward control scheme. Attenuation of 67dB of the excitation frequency is achieved but compensation is required to avoid increase in the higher harmonics introduced by the actuator nonlinearity. In an alternative approach adaptive control is applied not only at the harmonic of the disturbance but also at twice that frequency, to suppress the harmonic distortion introduced by the nonlinearity. In this case the first harmonic is reduced by 52dB and the second harmonic by 3dB. Isolation in response to a bandlimited random input is then demonstrated, with attenuation of 19dB being achieved over a frequency range from 2-8 H
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