A. Żak

Elastic beam finite element with a transverse elasto-plastic crack

Abstract A cracked beam finite element has been formulated in this paper. The model of the element is based on elasto–plastic fracture mechanics and the finite element method. Crack tip plasticity, at the cracked cross-section, is included in the model of local flexibility. The inertia and stiffness matrices take into account the effect of flexural bending deformation due to the crack presence. The elaborated model can be applied to static, dynamic and stability analysis of cracked beam-like structures.

Dynamics and buckling of a multilayer composite plate with embedded SMA wires

Abstract In this paper stress–strain relationships for a single composite lamina with embedded shape memory materials (SMA) fibres are presented. The paper illustrates influence of the SMA fibres upon changes in natural frequencies and thermal buckling of a composite multilayer plate with the SMA components. Governing equations based on the finite element method are also described in the work. The plate is modelled by plate finite elements. The elements have eight nodes with five degrees of freedom at each node (i.e. three axial displacements and two independent rotations). For both axial displacements and independent rotations biquadratic shape functions are used.

Vibration of a Laminated Composite Plate with Closing Delamination

Vibration of a laminated composite plate with a single and closing delamination is analysed in the present paper by using the finite element method. The delamination of layers is modelled by using additional boundary conditions in the delamination front. Contact forces between delaminated layers are also considered in the model by applying a node-to-node contact model. The influence of the delamination length and position on changes in natural frequencies and modes of vibrations of the plate are investigated in the paper. In the present study the plate is excited to vibrate by a harmonic force or by a force impulse and the resulting time series are analysed using FFT. Results of numerical calculations are verified and compared against experimental data obtained for laminated composite plates with delaminations.

Damage detection strategies based on propagation of guided elastic waves

This paper demonstrates the effectiveness of certain structural health monitoring (SHM) strategies based on propagation of guided elastic waves within thin-walled shell structures. This is realized based on results of numerical and experimental investigations obtained by the use of the spectral finite element method (SFEM) together with laser scanning vibrometry (LSV) and subsequent application of two different integral-based indices for damage quantification, these being the integral mean value (IMV) and the root mean square (RMS). Numerical tests by SFEM were carried out for a square plate with through-hole damage, a cracked fuselage section with two stiffeners and a cracked wing section skin, all made out of aluminium. Experimental measurements by LSV included tests on a square aluminium plate, composite plate and a composite stabilizer of a PZL W-3A helicopter, all with simulated damage. During numerical and experimental investigations damage sensitivity of both IMV and RMS indices was tested by considering various displacement components, signal timescales or weighting factors. A certain practical method for quick construction of RMS damage maps based on experimental measurements by LSV was also presented.

Analytical modeling and vibration analysis of partially cracked rectangular plates with different boundary conditions and loading

This study proposes an analytical model for vibrations in a cracked rectangular plate as one of the results from a program of research on vibration based damage detection in aircraft panel structures. This particular work considers an isotropic plate, typically made of aluminum, and containing a crack in the form of a continuous line with its center located at the center of the plate and parallel to one edge of the plate. The plate is subjected to a point load on its surface for three different possible boundary conditions, and one examined in detail. Galerkins method is applied to reformulate the governing equation of the cracked plate into time dependent modal coordinates. Nonlinearity is introduced by appropriate formulations introduced by applying Bergers method. An approximate solution technique-the method of multiple scales-is applied to solve the nonlinear equation of the cracked plate. The results are presented in terms of natural frequency versus crack length and plate thickness, and the nonlinear amplitude response of the plate is calculated for one set of boundary conditions and three different load locations, over a practical range of external excitation frequencies.

Finite element model of plate with elasto-plastic through crack

Abstract A rectangular plate finite element with a through crack has been developed in this paper. The model of the element is based on elasto-plastic fracture mechanics and the finite element method. The considered crack is non-propagating and open. Crack tip plasticity, at the cracked cross-section, is included in the model of local flexibility. The stiffness matrix takes into account the effect of flexural bending deformation due to the crack presence, whereas the inertia matrix remains unchanged. The elaborated model can be applied to static, dynamic and stability analysis of cracked plate-like structures.

Dynamics and Control of a Rotor Using an Integrated SMA/Composite Active Bearing Actuator

It has been shown that judicious integration of SMA wires or stri ps within composite components of certain geometries can lead to substantially enhanced dynamic effects within the component. These effects relate to natural frequency placements, m ode shapes, and forced response characteristics, in particular. One application area of conside rable interest involves the installation of bespoke technology exploiting this controllability within rotor syst ems, and this is the subject of this paper. It is shown that for a laboratory rotor system suppo rted n two bearings, one of which is an active component comprising a cylindrical sleeve with speciall y configured and integrated SMA strips, the critical speeds can be usefully shifted about their nomi nal values. The paper shows how such an active bearing installation can be designed and discusses the many trade-offs required to optimise the performance in a useful way. It is shown that the princ i al compromises relate to stress in the composite host, physical size and shape of this component, quantit y and distribution of SMA, and the local operating dynamics. It is also shown that glassepoxy is superior to graphite-epoxy in terms of dynamic controllability for the composite cylindrical s leeve host component when used as an active support for one of the bearings, and that this useful perf ormance can be accentuated by means of careful design.

Natural frequencies of a multilayer composite plate with shape memory alloy wires

Abstract The results presented in this study are obtained for a shape memory alloy (SMA) fibre-reinforced multilayer composite plate made of graphite-epoxy composite. The influence of SMA fibres upon natural frequencies of the plate is investigated. The constitutive relations for a composite plate with embedded SMA fibres are developed. Finite element governing equations and solution procedures for the SMA fibre-reinforced composite plate are also presented. The results of numerical calculations show that the SMA fibres can greatly influence in the natural frequencies of the plate.

Influence of Electric, Magnetic, and Electromagnetic Fields on the Circadian System: Current Stage of Knowledge

One of the side effects of each electrical device work is the electromagnetic field generated near its workplace. All organisms, including humans, are exposed daily to the influence of different types of this field, characterized by various physical parameters. Therefore, it is important to accurately determine the effects of an electromagnetic field on the physiological and pathological processes occurring in cells, tissues, and organs. Numerous epidemiological and experimental data suggest that the extremely low frequency magnetic field generated by electrical transmission lines and electrically powered devices and the high frequencies electromagnetic radiation emitted by electronic devices have a potentially negative impact on the circadian system. On the other hand, several studies have found no influence of these fields on chronobiological parameters. According to the current state of knowledge, some previously proposed hypotheses, including one concerning the key role of melatonin secretion disruption in pathogenesis of electromagnetic field induced diseases, need to be revised. This paper reviews the data on the effect of electric, magnetic, and electromagnetic fields on melatonin and cortisol rhythms—two major markers of the circadian system as well as on sleep. It also provides the basic information about the nature, classification, parameters, and sources of these fields.

Application of RMS for damage detection by guided elastic waves

This paper presents certain results of an experimental study related with a damage detection in structural elements based on deviations in guided elastic wave propagation patterns. In order to excite guided elastic waves within specimens tested piezoelectric transducers have been applied. As excitation signals 5 sine cycles modulated by Hanning window have been used. Propagation of guided elastic waves has been monitored by a scanning Doppler laser vibrometer. The time signals recorded during measurement have been utilised to calculate the values of RMS. It has turned out that the values of RMS differed significantly in damaged areas from the values calculated for the healthy ones. In this way it has become possible to pinpoint precisely the locations of damage over the entire measured surface. All experimental investigations have been carried out for thin aluminium or composite plates. Damage has been simulated by a small additional mass attached on the plate surface or by a narrow notch cut. It has been shown that proposed method allows one to localise damage of various shapes and sizes within structural elements over the whole area under investigation.