Home HomeK.Y. Fung, The Hong Kong Polytechnic University (Hong Kong)
Long-time stable time-domain numerical solution of wave propagation in a bounded domain even with one spatial dimension has been a formidable challenge despite the recent advances in algorithmic development and numerical analysis, The key issue is the treatment of end conditions for a finite domain where waves are allowed to rebound from the ends and return indefinitely with cumulative error due to the inconsistencies and mismatches between the inner scheme and the end scheme. The paper delineates the importance of formulation in characteristic variables, as opposed to the analytically equivalent primitive variables, demonstrates the cumulative error, and presents a long-time stable implicit scheme for computation of wave propagation with a distribution of wave sources, forced and unforced boundary conditions, including the recently introduced time-domain impedance boundary for bounded domains, Examples of duct and room acoustics, resonance, active noise cancellation and control will be given.
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TOPR.J. Astley, University of Canterbury (New Zealand)
The application of wave-envelope element numerical scheme to steady and transient unbounded wave problems is described. The formulation is characterised by the use of conjugated weighting functions in the frequency domain. This yields frequency-independent mass, stiffness and damping matrices and leads to a direct formulation inthe time-domain in which a discrete system of ordinary differential equations can be solved to give transient nodal values of acoustical pressure. The transient equations are local in time and can be integrated by standard single or multi-step methods. There are advantages to formulating the proposed elements in spheroidal rather than conventional spherical polar coordinates. Specifically, the size of the conventional finite element mesh which is required in the vicinity of slender or flat radiating objects can be reduced without compromising the completeness of the trial solution in the outer region. A mapped spheroidal formulation is proposed and computed test solutions are presented. An indirect transient solver is also proposed for the solution of the transient discrete equations. This does not require the storage of non-zero or fill terms and reduces by a large factor the matrix storage and overall CPU requirements for large three - dimensional transient problems.
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Tao Li, Victoria University of Technology (Australia)
Jimin He, Victoria University of Technology (Australia)
Structural modification is a technique to modify dynamic characteristics of a structure by changing its mass, stiffness and damping properties (also known as spatial properties). The most important dynamic characteristics of a structure are its natural frequencies since they dictate the vibration resonances. This paper describes a method for structural modification based on solutions for linear simultaneous equations. The method can be used to determine multiple mass or stiffness modifications of an undamped structural system in order to relocate a resonance or resonances. It analyses the relationship between the spatial property changes and the natural frequency and mode shape changes. The method provides a more generalised solution for mass and stiffness modifications than some earlier analytical work reported in the literature. The main advantage of this method is that it does not rely on a complete eigenvalue solution of the original system to provide exact solution. However, some drawbacks also exist that hinders wide application of this method in structural modification. These drawbacks will be discussed. Examples of implementation of this method will be presented in the paper.
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Vladis Kosse, Monash University (Australia)
Joseph Mathew, Monash University (Australia)
Harmonic drives were invented in the mid-60s and are currently used in transmissions where large speed reduction ratios are required. Over the last decade several models of harmonic drives for heavy machinery have been developed with an output torque ut to 3000 kNm. It is of utmost importance, at the design stage, to obtain reliable data regarding the behaviour of harmonic drives during transition processes and to estimate its parameters (natural frequencies, magnification factor, torque variation in different parts of the drive). This enables the minimisation of stresses, reduction in overall dimensions and weight of the transmission, and increase in reliability. Equations of motion for these transmissions can be derived using the energy method or by considering the dynamic equilibrium of each link. For analysis of transition processes it is important to account for damping, which is normally considered viscous. This approach is suitable for the analysis of transition processes in conventional transmissions. Attempts to employ this method for the analysis of harmonic drives yields confusing results due to the presence of the stationary link. To overcome this discrepancy, the hypothesis of a moving wall was introduced, and equations of motion for power transmissions incorporating harmonic drives were developed. As a numerical example, a transmission for a walking excavator incorporating a harmonic drive was considered. Peculiarities of computer modelling of such transmissions are also discussed in this paper.
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Jae Wook Kim, Korea Advanced Institute of Science and Technology (Korea)
Duck Joo Lee, Korea Advanced Institute of Science and Technology (Korea)
Exhaust noise from an electrical power plant is generated owing to high pressure inside the boiler when the gas is suddenly exhausted through a safety valve. To reduce the noise, an expansion chamber with a perforated diffuser is used. Noise generation, propagation and radiation from the exhaust gas system are numerically simulated to investigate the noise generation mechanism and to design the efficient perforated diffuser. The high-order compact schemes which were optimized in the wavenumber domain for high-resolution characteristics are used in this numerical simulation. The OHOC schemes are non-dissipative and much less dispersive than the other low-order standard schemes, and well adapted to computational aeroacoustic (CAA) problems. The OHOC schemes are coupled with the artificial dissipation terms and the fourth-order low dissipation and dispersion Runge-Kutta (LDDRK) time-marching method for solving nonlinear unsteady Euler equations accurately. The characteristics-based boundary conditions are implemented as physical boundary conditions for the OHOC schemes. It is shown that the application of these schemes to simulation of the exhaust gas noise reduction system presents time accurate results with partially oscillating supersonic flows near the perforated diffuser and the reduced acoustic pressure fields through the expansion chamber.
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Wim Desmet, Katholieke Universiteit Leuven (Belgium)
P. Sas, Katholieke Universiteit Leuven (Belgium)
D. Vandepitte, Katholieke Universiteit Leuven (Belgium)
In a coupled vibro-acoustic analysis, the structural finite element model and acoustic finite or boundary element model must be solved simultaneously. This results in a very large, non-symmetrical coupled model, which requires a computationally expensive solving procedure. To reduce the size of a coupled model, a wave based modelling technique has been developed. Instead of dividing the structural and acoustic domain into small elements and solving the dynamic equations within each element using simple approximating shape functions, the entire structural and acoustic domain are described by wave functions, which are exact solutions of the structural and acoustic homogeneous wave equation. To these wave functions, particular solutions of the inhomogeneous wave equations are added, so that the governing dynamic equations are exactly satisfied. The contributions of the wave functions to the coupled vibro-acoustic response are determined by applying the boundary conditions in a weighted residual formulation. In this paper, the method is applied to the two-dimensional cases of an acoustic cavity, of which the whole boundary surface consists of a force excited cylindrical shell structure, as well as a cavity, of which only a part of the boundary surface consists of a force excited cylindrical shell section.
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D.W. Lee, The University of Auckland (New Zealand)
D.C. Hesterman, The University of Auckland (New Zealand)
R.W. Jones, The University of Auckland (New Zealand)
Friction is present in all mechanical systems that incorporate sliding contacts, but is often ignored when developing models to study system behaviour. This is largely because of the difficulties that arise in the numerical simulation of friction models, the equations of motion for which are discontinuous and implicit. The problem is exacerbated when considering oscillatory mechanisms, where multiple velocity zero crossings, and thus friction discontinuities, occur. However the inclusion of friction effects in the models of these systems can be very important when the models are used to quantitatively (rather than qualitatively) represent the system; for example, for the design and testing of system controllers, and for system parameter estimation. This paper begins with a brief summary of the types of friction models currently used and their relative advantages and disadvantages. The difficulties of solving the models using numerical simulation are also discussed. A new method is then introduced, using the example of a simple oscillating mechanism, which has the potential to reduce computing time and to avoid certain other problems encountered with friction simulation.
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Jean-Pierre Coyette, LMS Numerical Technologies (Belgium)
Christophe Lecomte, LMS Numerical Technologies (Belgium)
Karl Meerbergen, LMS Numerical Technologies (Belgium)
Vibro-acoustic testing procedures frequently involve the consideration of a diffuse acoustic excitation (as obtained for instance in a reverberant chamber). Such an excitation can be modeled as a stationary random process. The related spatial correlation functions for pressure and pressure gradients are examined. Handling of such a random acoustic excitation in a coupled (elasto-acoustic) context is studied. An efficient decomposition procedure is proposed in order to recast strongly correlated acoustic excitations into a set of a uncorrelated pseudo-load cases. Numerical applications are presented in order to demonstrate the efficiency of the proposed method.
sv970301.pdf (Scanned) TOPMiodrag Zlokolica, University of Novi Sad (Yugoslavia)
Different kinds of mechanical variators are used as a part of complex machine system. Variators, as transmission system , with a changeable transmission ration, are involved in a lot of complex machines. They are used for changing speed in agricultural machines, industries of cable, carpet and paper industries, mining machines, account machines, etc. Seeing this large use of mechanical variators in industry, the aim of this paper is to describe a dynamical behavior of the general example of the variators of speed as non-holonomic system. In this paper a frontal variator of speed with two discs, half ball and regulator will be analyzed. The non-holonomic connection is in points of physical contact between the discs and half ball. To this system is added mechanical regulator for regulation of variable transmission relation between input and output elements. A damper is added for stabilizing movement. Differential equations of moving will be solved by using Appell's equations and by resolving the numerical method. In this way, we are getting an answer to a dynamical and kinematical behavior of mechanical systems under the give us the answer to a working stability a system being observed. Keywords: dynamic, kinematic, non-holonomic system, variator
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Guangyu Shi, National University of Singapore (Singapore)
K.Y. Lam, National University of Singapore (Singapore)
T.E. Tay, National University of Singapore (Singapore)
The objectives of this paper are two fold, one is to present a simple and accurate third-order composite beam element, and the other is to use this new element for the frequency analysis of composite beams. In the analysis of composite beams and plates, a higher-order shear deformation theory can lead to finite elements having the same number of nodal variables but giving solutions with different accuracy. By studying the interpolation order of the element bending strain, this paper presents a simple but accurate third-order composite beam element, which possesses a linear bending strain as opposed to the constant bending strain in existing higher-order composite beam elements. The variational consistent mass matrices are derived from Hamiltons Principle. The present new element is used to solve some frequency analysis of composite beams. The numerical examples show that the transverse shear strains play a very important role in the dynamic behaviour of composite beams. The numerical examples also illustrate that the present composite beam element is more accurate than the higher-order beam elements which are based on the same higher-order theory and having the same number of nodal variables but using a different bending strain expression.
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Masato Saeki, Niigata Institute of Technology (Japan)
E. Takano, Niigata University (Japan)
The flow of granular materials on vibratory conveyors- was studied analytically. Vibratory conveyors have proved useful for widely differing duties from feeding small and delicate components on automatic assembly lines to the transportation of large quantities of raw materials. There is a considerable descriptive data of vibratory conveyors, but for simplicity of analysis much previous theoretical analysis only predicts the motion of a particIe on a vibrating plate. For optimum operating conditions, the behavior of granular materials during vibration must be known. In the present work the distinct element method proposed by Cundall was adapted for a dynamic analysis of vibratory conveyance of granular materials. Granular materials are first assumed as ellipse models by considering shape anisotropy. Then the contact forces are modeled by mechanical units such as springs, dashpots and fiction sliders. It is shown that the mean velocity of transport of granular materials depends on the frequency and amplitude of the vibratory input as well as various physical parameters. The flow patterns obtained by this method appear realistic.,
sv970140.pdf (Scanned) TOPLivija Cveticanin, Faculty of Technical Sciences, Trg D. Obradovica (Yugoslavia)
An elliptic perturbation method is developed for calculating solutions of strongly nonlinear systems of the form z + c z + c z = ef(z,z,cc), where z is the complex deflection function. The Jacobian elliptic functions are employed instead of the usual circular functions. The suggested procedure can give also a second approximate solution. The method is applied for the equation which describes cyclic motion. The analytically obtained results are compared with numerical ones. They show a good agreement.
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