J. Dupal

Analytical periodic solution and stability assessment of 1 DOF parametric systems with time varying stiffness

The presented paper deals with an approach to analytical periodic solution and to stability assessment of one-degree-of-freedom linear vibrating systems. It is supposed that these systems are excited by the time periodic force and contain time periodic stiffness. The periodic Greens function determined as a response to a Dirac chain of unit impulses repeating with period of excitation is used to transform the equation of motion into the Fredholm integral equation with degenerated kernel. If the Dirac chain is expressed as a Fourier series and a limited number of terms is taken into account, the solution of the integral equation can also be obtained in a series form. It has been found that the real eigenvalues of the system matrix determine the critical values of the fluctuation stiffness parameter. The values of this real parameter correspond to the borders of (in)stability in the plane given by the variation of the angle frequency and of the fluctuation stiffness parameter. Moreover, very interesting property of the system matrix was observed. The positive sign of the real valued determinant of the system matrix means the existence of periodic solution (system is stable). In the opposite case, the periodic solution does not exist (system is unstable). The verification of obtained results was performed on two case studies. The Floquet method was used to validate the stability assessment. Presented analytical periodic solution was compared with steady state obtained by the Runge-Kutta continuation. A very good agreement was achieved in both cases.

Analytical Solution of the Drive Vibration With Time Varying Parameters

The paper deals with an approach to the analytical solution of the periodical vibration of mechanical systems with n DOF esspecially drives containing periodically varying parameters (e.g. stiffnesses). The model is described by means of the Fredholm’s matrix integral equation with degenerated kernel and a periodical Green’s function is used for the solution. The application can be shown e.g. on the Cardan’s mechanism and gear transmission having the time varying tooth stiffnesses. The result correctness is validated by means of Runge-Kutta integration method.Copyright

Lesson learnt from mathematical modeling of primary circuit of VVER 440/213 reactors

For the analysis of flow induced vibrations of a VVER 440/213 unit, a generalised model has been developed which consists of the reactor as a lumped mass model with 77 degrees of freedom. Linking of the loops to the reactor pressure vessel is modelled using translational and rotational stiffnesses. Main results obtained: eigenfrequencies and mode shapes of the whole system and dynamic response of the whole system generated by the main circulating pump pressure pulsations.

Optimization of mechanical systems parameters in transient vibration

Abstract This paper presents the response spectrum method (RSM) and gradient projection method (GPM) for design variable optimization of mechanical systems in transient vibration. The basis for optimization of mass, damping, stiffness and geometrical parameters is a linear damping mathematical model in a matrix form. Optimization algorithms are based on minimization of objective functions in a feasible domain by nonlinear programming methods.

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.

Dependency of the Quality of the Active Vibration Damping on the Sensor and Actuator Location – Simulation and Experiment

The paper deals with the vibration suppressing of cantilever beam. The state feedback control law is used, where the controller and observer are designed by pole assignment method. First two natural frequencies are considered for design of the control law. The analysis of the location of actuator and sensor are investigated. Experimental results obtained from the closed loop system with incomplete pole assignment are compared with uncontrolled system.