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Effect of a rotational spring support on the stability of a column with internal damping

100%

Przybylski J.

tom Vol. 21

315--318

This work concerns the problem of stability of a geometrically non-linear damped column loaded by a partially follower force. One end of the column is supported by a rotational spring of stiffness, which can be changed as a function of the external load. The loss of stability of such system is of flutter or divergence type what depends on the values of spring rigidity and follower parameter. The limit of stability has been established on the basis of kinetic criterion. For a nonconservative system an adjoint problem has been formulated. Lyapunow stability criterion has been complemented by Suguyama consideration concerning the time of achieving of demanded displacement by a chosen point on the vibrating column.

Modelowanie wpływu tłumienia wewnętrznego na charakterystyki dynamiczne ceramicznych przetworników PZT

100%

Płaczek M.

tom T. 15, nr 46

88--93

Paper presents a process of single piezoelectric transducer plate modelling including influence of structural damping on its characteristics. Constitutive equations of piezoelectric material and equation of motion of the plate’s longitudinal vibration were used to obtain a matrix of characteristics. Both characteristics that describe relations between mechanical parameters (forces and displacements) and between mechanical and electrical parameters (electric voltage and current) were considered [8,11,12]. Geometrical and material parameters of the considered plate were assumed and its rheological properties were being taken into consideration in order to draw the plate’s dynamic flexibility. A Kelvin-Voigt model of material was used in the system’s mathematical model [5,10]. Obtained results were juxtaposed with dynamic flexibility of a PZT plate modelled without structural damping.

W pracy zaproponowano proces modelowania pojedynczej płytki przetwornika piezoelektrycznego typu PZT z podkreśleniem wpływu tłumienia wewnętrznego na charakterystyki dynamiczne przetwornika. Stosując równania konstytutywne tworzyw piezoelektrycznych oraz równanie ruchu drgającej wzdłużnie płytki piezoelektrycznej o ciągłym rozkładzie masy, otrzymano macierz charakterystyk badanego układu. Poprzez szukane charakterystyki rozumie się zarówno zależności zachodzące pomiędzy parametrami mechanicznymi (siłami i przemieszczeniami), jak i pomiędzy wielkościami mechanicznymi oraz elektrycznymi (napięcie i natężenie przepływu prądu elektrycznego) [8,11,12]. Przyjmując parametry geometryczne oraz tworzywowe, a także uwzględniając własności reologiczne badanego przetwornika, wyznaczono przebieg jego podatności dynamicznej. Modelując badany układ, zastosowano model reologiczny Kelvina-Voigta [5,10]. Otrzymany przebieg podatności dynamicznej porównano z charakterystyką przetwornika opisanego modelem matematycznym, w którym pominięto tłumienie wewnętrzne tworzywa.

Effect of cyclic loading on the internal damping of magnesium alloy AZ31

84%

Uhricik M. , Dresslerova Z. , Palcek P.

2017

tom Vol. 15

7--10

The article focuses on the analysis of the internal damping changes depending on the amplitude of the magnesium alloy AZ31. Internal damping reflects the ability of the material irreversibly dissipating mechanical energy oscillations. It means that the material of high internal damping ability is able to significantly reduce the vibration amplitude. Internal damping is, generally, dependent on many factors (temperature, material purity, grain size, mechanical and thermal processing, etc.) and its value is determined by interactions between various mechanisms dissipation of mechanical energy. Ultrasonic resonance method was used in experimental measurements, which is based on continuous excitation of oscillations of the specimen, and the entire apparatus vibrates at a frequency which is near to the resonance. Starting resonance frequency for all measurements was about f = 20470 Hz.

Development of identification procedure for the internal and external damping in a cracked rotor system undergoing forward and backward whirls

67%

Roy D. K. , Tiwari R.

tom Vol. LXVI, nr 2

229--255

In the present work, a procedure for the estimation of internal damping in a cracked rotor system is described. The internal (or rotating) damping is one of the important rotor system parameters and it contributes to the instability of the system above its critical speed. A rotor with a crack during fatigue loading has rubbing action between the two crack faces, which contributes to the internal damping. Hence, internal damping estimation also can be an indicator of the presence of a crack. A cracked rotor system with an offset disc, which incorporates the rotary and translatory of inertia and gyroscopic effect of the disc is considered. The transverse crack is modeled based on the switching crack assumption, which gives multiple harmonics excitation to the rotor system. Moreover, due to the crack asymmetry, the multiple harmonic excitations leads to the forward and backward whirls in the rotor orbit. Based on equations of motions derived in the frequency domain (full spectrum), an estimation procedure is evolved to identify the internal and external damping, the additive crack stiffness and unbalance in the rotor system. Numerically, the identification procedure is tested using noisy responses and bias errors in system parameters.