Temat: simple fractions - Prolib Integro

Skocz do pozycji: 1.

Tytuł:: Estimates of \(L_p\) norms for sums of positive functions
Autorzy:: Kayumov, Ilgiz
Tematy:: Simple partial fractions
\(L_p\) estimates.; Pokaż więcej
Wydawca:: Uniwersytet Marii Curie-Skłodowskiej. Wydawnictwo Uniwersytetu Marii Curie-Skłodowskiej
Powiązania:: https://bibliotekanauki.pl/articles/747077.pdf Link otwiera się w nowym oknie
Opis:: We present new inequalities of \(L_p\) norms for sums of positive functions. These inequalities are useful for investigation of convergence of simple partial fractions in \(L_p(\mathbb{R})\).
Dostawca treści:: Biblioteka Nauki

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Skocz do pozycji: 2.

Tytuł:: The use of synthesis methods in position optimisation and selection of tuned mass damper (TMD) parameters for systems with many degrees of freedom
Autorzy:: Dymarek, Andrzej
Dzitowski, Tomasz
Tematy:: structural control system
vibration
simple fractions
synthesis
rational functions
dynamic characteristics; Pokaż więcej
Wydawca:: Polska Akademia Nauk. Czytelnia Czasopism PAN
Powiązania:: https://bibliotekanauki.pl/articles/1409049.pdf Link otwiera się w nowym oknie
Opis:: The paper formulates and formalises a method for selecting parameters of the tuned mass damper (TMD) for primary systems with many degrees of freedom. The method presented uses the properties of positive rational functions, in particular their decomposition, into simple fractions and continued fractions, which is used in the mixed method of synthesis of vibrating mechanical systems. In order to formulate a method of tuning a TMD, the paper discusses the basic properties of positive rational functions. The main assumptions of the mixed synthesis method is presented, based on which the general method of determining TMD parameters in the case of systems with many degrees of freedom was formulated. It has been shown that a tuned mass damper suppresses the desired resonance zone regardless of where the excitation force is applied. The advantages of the formulated method include the fact of reducing several forms of the object’s free vibration by attaching an additional system with the number of degrees of freedom corresponding to the number of resonant frequencies reduced. In addition, the tuned mass damper determined in the case of excitation force applied at a single point can be attached to any element of the inertial primary system without affecting the reduction conditions in this way. It results directly from the methodology formalised in the paper. As part of the paper, numerical calculations were performed regarding the tuning of the TMD to the first form of free vibration of a system with 3 degrees of freedom. The parameters determined were subjected to analysis and verification of the correctness of the calculations carried out. For the considered case of a system with 3 degrees of freedom together with a TMD, time responses of displacement, from each floor, were generated to excitation induced by a harmonic force equal to the first form of vibration of the basic system. In addition, in the case of the parameters obtained, the response of the inertial element system to which the TMD was attached to random white noise excitation was determined.
Dostawca treści:: Biblioteka Nauki

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