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1

Design of damping systems with required frequency spectrum

Dymarek A., Dzitowski T.

Journal of Achievements in Materials and Manufacturing Engineering

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2011

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Vol. 49, nr 2

269--274

EN

Purpose: The presented work extends the task of synthesis with new methods, with particular focus on the method of active and passive synthesis of vibrating damping mechanical systems. This paper is concerned with the formulation and formalisation of the problem of active and passive synthesis of mechanical damping systems. Design/methodology/approach: The work proposes a combination of the synthesis method of vibrating systems with the method of determining the active force as the method for active synthesis of mechanical damping systems and the values of two-terminal damping in case passive synthesis of mechanical damping systems. Findings: The performed active and passive synthesis of restrained systems has demonstrated an ambiguity of synthesis of damping systems. The resulting structures and set system parameters are not the only ones that can be obtained in the case of the assumed frequencies. Research limitations/implications: The scope of discussion is the synthesis of discrete damping systems. Practical implications: The advantage of the proposed method of determining the active force in the system is the ease of its programming. The proposed method can be included in the method of proportional control with force feedback from the state. Originality/value: The document is also an attempt at identifying new opportunities and a direction of research in the design of machine components with a desired frequency spectrum.

2

On solutions of an extended Dugué problem

Wolińska-Welcz A.

Prace Instytutu Podstaw Informatyki Polskiej Akademii Nauk

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2007

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Nr 1004

1-8

EN

The paper presents an improved concise form of the solution of the Dugué problem concerning the characteristic functions fi1 and fi2 such that p

PL

W pracy przedstawiona jest nowa zwięzła postać rozwiązania zadania Dugue znajdowania funkcji charakterystycznych fi1 i fi2 takich, że pfi(t) + (1 - p) 2. Rozwiązania problemu Dugue są uwzględnione w badaniach dotyczących kopuł i mieszanin rozkładów prawdopodobieństwa.

3

The functional equation and strictly substable random vectors

Borowiecka-Olszewska M.

Probability and Mathematical Statistics

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2005

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Vol. 25, Fasc. 2

267--278

EN

A random vector X is β-substable, β ∈ (0, 2), if there exist a symmetric β-stable random vector Y and a random variable Θ ≥ 0 independent of Y such that X [symbol] YΘ1/β. In this paper we investigate strictly β-substable random vectors which are generated from a strictly β-stable random vector Y. We study some of their properties. We obtain the theorem that every strictly β-stable random vector X with Θ ∼ Sα/β (σ, 1, 0) is also strictly α-stable, α < β (for the case of random variable X see, e.g., [1], [6]). The opposite theorem is also satisfied, but we obtain something more. We obtain some functional equation and we show that if astrictly β-substable random vector X is α-stable, then it has to be strictly α-stable and the mixing random variable Θ has to have a distribution Sα/β (σ, 1, 0). This is the main result of the paper.

4

Remarks about the Dugué problem

Krakowiak W.

Probability and Mathematical Statistics

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2003

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Vol. 23, Fasc. 1

93--104

EN

The paper presents some new results of the Dugué problem of finding the characteristic functions φ1 and φ2 such that (1 − c) φ1 + cφ2 = φ1 φ2, 0 < c < 1.