Vítězslav Adámek

PROBLEM OF NON-STATIONARY WAVES IN VISCOELASTIC ORTHOTROPIC STRIP SOLVED USING ANALYTICAL METHOD

The transient response of an infinite orthotropic strip subjected to a transverse load is investigated using an analytical method in this work. The material properties of the strip are described by the discrete model of standard linear viscoelastic solid. In this study, the case of special orthotropy is assumed, i.e., the principal material and geometric axes of the strip are coincident. Once the final system of equations describing the plane-stress problem solved is derived, the integral transform method is used to obtain the Laplace transforms of displacement and velocity components. The inversion of the resulted formulae back to time domain is carried out by the help of numerical inverse Laplace transform. In particular, an algorithm based on the FFT and Wynn’s epsilon accelerator was used for this purpose. In the last part of this work, the analytical results obtained for selected orthotropic material are compared to those resulted from numerical simulation performed in the finite element code MSC.Marc. The comparison made showed good agreement between analytical and numerical results and proved their correctness. Finally, the efficiency of both approaches is discussed.

ANALYSIS OF VIBRO-ACOUSTIC PROPAGATION IN A MOBILE SCREW COMPRESSOR FOR THE DETERMINATION OF EMITTED ACOUSTIC POWER RADIATED OUTSIDE ITS HOUSING

The method for a numerical solution of the vibro-acoustic problem in a mobile screw compressor is proposed and in-house 3D finite element (FE) solver is developed. In order to reduce the complexity of the problem, attention is paid to the numerical solution of the acoustic pressure field in the compressor cavity interacting with the linear elastic compressor housing. Propagation of acoustic pressure in the cavity is mathematically described by the Helmholtz equation in the amplitude form and is induced by periodically varying surface velocity of the engine and compressor assembly. In accordance with prescribed boundary conditions, numerical solution of the Helmholtz equation for the distribution of acoustic pressure amplitudes within the cavity is performed using the finite element method on tetrahedral meshes. For the FE discretisation of the elastic compressor housing, a new 6-noded thin flat shell triangular finite element with 21 DOF based on the Kirchhoff plate theory was developed and implemented. The resulting strong coupled system of linear algebraic equations describing the vibro-acoustic problem, i.e., the problem of interaction between the air inside the cavity and the screw compressor housing, is solved numerically by well-known algorithms implemented in MATLAB. By considering two different benchmark test cases, the developed 3D FE solver is successfully verified against the numerical results provided by the professional computational FE system Radioss. Finally, the vibro-acoustic problem is solved in a simplified model of a real mobile screw compressor by prescribing experimentally measured acoustic velocity on the surface of the engine and compressor assembly. The numerical solution is carried out only with the professional computational FE system Radioss as our developed solver is still unable to process large-sized problems without encountering memory limits. Thus, for the assessment of results computed by Radioss, we use results acquired during experimental measurements on a real mobile screw compressor under operating conditions.

Analytical Solution of In-Plane Response of a Thin Viscoelastic Disc Under Impact Load

This paper concerns the analytical solution of the in-plane response of a thin viscoelastic disc to a dynamic load applied to its rim. The exact analytical relations for the Laplace transforms of radial and circumferential displacements are derived in terms of Bessel functions for the case of radial and torsional loads defined by even and odd functions of angular variable, respectively. The numerical evaluation of the analytical solution is then made for the case of an impulse radial load and transient wave phenomena are studied in the disc. With respect to the complexity of presented formulae, the multi-precision implementation of FFT based numerical algorithm for the inverse Laplace transform is used. The obtained analytical results are then compared to the results of numerical simulation performed in the finite element system MSC.Marc. The presented analytical solution can be used as a benchmark solution for the testing of numerical methods.