Home HomeMorten Skaarup Jensen, Odegaard & Danneskiold-Samsoe (Denmark)
The key strength of the finite element (FE) method in acoustics is it's ability to predict the solutions to a very wide range of problems with high accuracy. Unfortunately, increased accuracy usually implies increased computation costs, so means for evaluating accuracy of such calculations are therefore essential for practical use of the method. This paper presents an accuracy criterion that is well suited for time domain calculations - using traditional convergence theory and some tabulated values, one can easily obtain an a'priori estimate of the element and time step sizes that will be required to fulfil this criterion. The criterion has the advantage of being based on the dispersion error, which is the main error in time domain FE-calculations. In addition, it has the advantage of being flexible regarding element type and will presumably also be able to incorporate singularies. By contrast, the commercial standard - the six elements per wavelength rule of thumb - is not as theoretically well founded and works only for linear elements when singularities can be neglected. The two methods are compared in an example that doesn't contain singularities.
sv970533.pdf (Scanned)
TOP
Jean-Pierre Coyette, LMS Numerical Technologies (Belgium)
Luc Cremers, LMS Numerical Technologies (Belgium)
Sound radiation from plate structures usually relies on either direct or indirect boundary element (BE) formulations. BE formulations offer some specific advantages (exact treatment of the Sommerfeld radiation condition, boundary surface mesh). On the other side, finite element (FE) formulations can be extended in such a way that exterior acoustic problems can be treated and offer attractive features (reduced CPU times, uniqueness of the solution). A refined infinite element formulation has been used for this purpose. This formulation enables the use of variable order interpolation functions and the selection of different coordinate systems (spherical and oblate spheroidal coordinates in the present case). A practical comparison of these two approaches is presented for sound radiation from an elastic plate mechanically excited. Both field values and integrated quantities (like the radiated power) are involved in this comparison.
sv970302.pdf (Scanned) TOP
Toru Otsuru, Oita University (Japan)
Tomoyuki Uchida, Oita University (Japan)
In the analysis of architectural acoustics, the transient response in the three dimensional room with absorbent walls is essentially important. Then, several approaches are presented here to treat the dissipation and to obtain the transient response efficiently. Although the finite element method requires more memory in a computer compared to that of the boundary element method, the finite element method has stronger points in some cases. However, some physical assumptions and some mathematical considerations help to reduce the required memory, which makes a way to such an analysis as is on an auditorium. So, the choice of the combination of them is essential, especially in the analysis on a huge system. To make the point clearer, several computations are carried out. With the results, the characteristics of them are discussed.
sv970182.pdf (Scanned) TOP
Kari Saine, Wartsila NSD Corporation (Finland)
Olli Nuutila, Tampere University of Technology (Finland)
Hannu Tienhaara, Wartsila NSD Corporation (Finland)
A way to use finite element method (FEM) to create an FE-model of an entire aggregate, total mass 100-700 ton, is presented in this paper. The aggregate consists of a medium speed diesel engine and an alternator, which have been mounted to a concrete block. The whole system can be mounted flexibly or rigidly to the ground.Usually international standards do not take into account elastic natural frequencies of the concrete block when defining the dimensions. That is why these structures are in many cases over dimensioned. The rapid development of the digital computers have however brought new possibilities to calculate big and complex structures beforehand. In this context the exact dimension is very important because a combustion engine has many excitation frequencies and most of them are not allowed to be near a natural frequency.The methodology of realistic modelling of a big aggregate using finite element method is described in this paper. The natural frequencies of the structure can be calculated with the achieved model. Also the static and dynamic stresses and responses for given excitations are computed. On the basis of the results the concrete block can be optimized by which noticeable cost savings can be achieved.The results of calculations and the realistic FE-model were verified by measurements on complete aggregate in the field. The measurements were carried out by using servo-hydraulic shaker, by which the natural frequencies and mode shapes of the concrete block could be found. Also the operational deflection shapes and responses were measured. The calculated values correspond to the measured ones very well.
sv970165.pdf (Scanned) TOPPeter M. Juhl, Technical University of Denmark (Denmark)
Although boundary element methods have been used for three decades for the numerical solution of acoustic problems, the issue of convergence is not well known among acoustic engineers. In this paper the concept of convergence is introduced in an intuitive and empirical style. The convergence of an axisymmetric boundary element formulation is studied using linear, quadratic or superparametric elements. It is demonstrated that the rate of convergence of these formulations is reduced for calculations involving bodies with edges (geometric singularities). Two methods for improving the rate of convergence for these cases are suggested and examined.
sv970098.pdf (Scanned) TOPJaehwan Kim, Inha University (Korea)
This paper deals with a hybrid finite element modeling of wave scattering problems in infinite domains. Scattering of waves involving complex geometries in conjunction with infinite domains is modeled by introducing a mathematical boundary. On the mathematical boundary, the finite element representation is matched with analytical solution in the infinite domain in terms of fields and their derivatives. Drilling degrees of freedom at each nodes of the finite element model are introduced to take into account the transverse component of the elastodynamic field more precisely. To verify the roles of drilling degrees freedom and the slope constraint, normal incidences of P and SV waves are considered. For the P-wave incidence, the use of slope constraint suppresses artificial reflection at the mathematical boundary and for the SV-wave case, the use of drilling degrees freedom reduces numerical error at irregular frequencies.
sv970474.pdf (Scanned) TOP
Osman Tokhi, The University of Sheffield
Z. Mohamed, University of Technology Malaysia (Malaysia)
A.K.M. Azad, The University of Sheffield
This paper presents an investigation into the performance evaluation of finite difference and finite element methods in the real-time simulation of flexible robot manipulator systems. A constrained planar single-link flexible manipulator is considered. Finite-dimensional simulation environments characterising the dynamic behaviour of the manipulator are developed using finite difference and finite element methods. The simulation algorithms thus developed are implemented on general-purpose digital processors. Experimental results verifying the performance of the algorithms in characterising dynamic behaviour of the system and comparative performance evaluation of the algorithms on the basis of accuracy and computational efficiency are presented and discussed.
sv970358.pdf (Scanned) TOP
Ivan Prebil, University of Ljubljana (Slovenia)
Robert Kunc, University of Ljubljana (Slovenia)
Matjaz Torkar, Institute of Metals and Technology (Slovenia)
The paper deals with the problem of the actual carrying capacity of a rolling contact in large axial bearings with surface hardened raceway. The carrying capacity of such bearings is usually given with the maximal permissible force on the rolling element with the highest load. The established criteria of maximal permissible plastic deformation of the raceway, and the maximal allowed subsurface stress on the hardened layer boundary give widely varying values for the carrying capacity of the rolling contact. In order to determine the actual carrying capacity of the rolling contact in axial bearings with low speed of rotation, considering base material properties, hardness and thickness of the hardened layer, and the geometry of the contact, we have measured the models of bearing raceways made of 42CrMo4 and C45 materials. The loads were static and low cycle dynamic. We have determined the cyclic curves (force - deformation), limit of fast increase in (elastic and plastic) deformation gradient, and the size of the contact surface. Simultaneously with the experiment, we have checked the sub surface stresses using a FEM model, considering the material nonlinearities. On the basis of the measurement results and the FEM model we would like to set up a simplified mathematical relation that gives the permissible contact force considering the base and hardened material properties, and the geometric model of the rolling contact.
sv970335.pdf (Scanned) TOP
G. Verbeek, Eindhoven University of Technology (The Netherlands)
N.C.P.J. Geerts, Eindhoven University of Technology (The Netherlands)
Jan W. Verheij, TNO Institute for Applied Physics TU-Delft (The Netherlands)
The analysis of linear dynamic (acoustic) systems with deterministic loading, boundary conditions, and material parameters can nowadays be performed by routine FEM/BEM calculations. Even for very large systems this approach is feasible by application of commonly used CMS reduction techniques. However the FEM analysis still is limited for a specific problem to a frequency band with a sufficiently low upper excitation frequency. This low frequency restriction is present because of the maximal number of degrees of freedom, despite of the ever increasing computer power. Complex envelope displacement analysis (CEDA, introducted by Carcaterra and Sestieri) seems to be a promising approach in the mid or high frequency range to eliminate this upper frequency limit. This can be done because CED analysis solves for a smooth or low frequency transformed displacement variable from an accordingly transformed partial differential equation. A drawback for future applications in the original CED analysis is the fact that it is limited to undamped deterministic vibrations. This paper addresses the specific problems that have been solved for application of the CED analysis to both damped high frequency vibrations in two point boundary value problems as well as the implementation for damped FEM calculations.
sv970305.pdf (Scanned) TOP
Seney Sirichai, Curtin University of Technology (Australia)
Ian Howard, Curtin University of Technology (Australia)
Laurie Morgan, Curtin University of Technology (Australia)
Kian Teh, Curtin University of Technology (Australia)
This paper presents a finite element analysis of two spur gears in mesh. The model predicts the torsional mesh stiffness of the two gears in mesh when one of the gears is restrained from rotating, with the other gear having a torque input load. The mesh stiffness of two gears in mesh varies with the meshing position as the teeth rotate within the mesh cycle and the resulting torsional stiffness decreases and increases dramatically as the meshing of the teeth change from the double pair in contact to the single pair of teeth in contact and vice-versa. The accuracy of finite element modelling of contact problems depends on the choice of the penalty parameter for the contact element. For modelling of gear teeth in mesh, the penalty parameter also varies as the gear teeth rotate through the cyclic mesh. This paper presents a simple strategy of how to determine an appropriate value of the penalty parameter as the gears rotate through the mesh cycle. The resulting torsional stiffness is predicted as a function of the position of the mesh point in the mesh cycle. The results which are presented show evidence of a change in the torsional stiffness during the double pair of teeth in contact.
sv970264.pdf (Scanned) TOP
Chong Wang, Australian Defence Force Academy (Australia)
Joseph C.S. Lai, Australian Defence Force Academy (Australia)
The acoustic radiation from circular cylindrical shells is of fundamental and applied interest. In previous studies of the subject, cylindrical shells are categorised into thin, and thick shells in terms of the ratio of the ring frequency fr to the critical frequency fc , i.e. fr/fc<1 for thin shells, and fr/fc>1 for thick shells. For thin shells, it has been found analytically that the radiation efficiency of cylindrical shells has a peak at the ring frequency, and above the ring frequency, the shells would behave like flat plates. For thick shells, however, the behaviour is not fully understood because it is difficult to carry out an analytical analysis especially for finite length cylindrical shells. In this paper, the radiation efficiency of a thick circular cylindrical shell with finite length has been examined by calculations using the boundary element method for three different boundary conditions, and by conducting experiments using point excitation with the boundary conditions being free at both ends. Both the numerical and experimental results indicate that the radiation efficiency attains a value of unity at frequencies well below the critical frequency. Analysis has been made to explain the behaviour of thick shells.
sv970235.pdf (Scanned) TOP
Enrico Gargano, Instituto di Tecnologie Industriali e Automazione (Italy)
Alessandro Bartolini, ITIA - CNR (Italy)
The study of acoustic fields is becoming very important for industrial design: in fact it allows to predict the emitted noise levels of a source and to correlate them to the vibrations that are the origin of acoustic phenomena. In such way we have the possibility to make structural changes during the design of a product to decrease the noise level. In our paper we have considered as noise source an air compressor and we have utilized the boundary element method (BEM) to study the acoustic field behaviour produced in nearby field; let us suppose as condition that the normal component of particle velocity of fluid equals the normal component of vibrational velocity of structure surface. After a preliminary survey of correlation between noise and structural vibration autospectra we have choosen meaningful frequencies utilized for the experimental check of sound pressure levels detected on a reference plane 0.5 meter far from the superior surface of the air compressor.
sv970059.pdf (Scanned) TOP
Mabrouk Ben Tahar, Universite de Technologie de Compiegne (France)
Eugenie Goy, Universite de Technologie de Compiegne (France)
One of the most important question arises when studying the vibro-acoustic phenomenon in the presence of non uniform mean flow is the justification of the boundary conditions at the structure-fluid interface. Primarily, we are presenting the linear acoustic equations in a mixed representation for a heterogeneous moving medium and associated boundary conditions. In the mixed representation, the equations verified by Lagrangian perturbations are written in Eulerian variables in association with mean flow of the medium concerned. The choice of this approach allows us to represent - in the sense of distribution theory - the acoustic field equations provided that one uses normal acoustic displacement continuity, and to deduce boundary conditions at the interface between two moving media. Secondly, we are proposing a new formulation for the elasto- acoustic coupling problem using the previous results. In this approach the acoustic domain is divided in two sub-domains : 1- where the flow of fluid coupling fluid- is non uniform and discretised by finite elements, 2-bounding the first domain and where the flow is supposed to be zero- is discretised by boundary elements. The coupling of these two domains is obtained by applying the condition of continuity of acoustic displacement. The association of functional structure, discretised by finite element, gives us the final vibro-acoustic system to solve.
sv970005.pdf (Scanned) TOP