Titlebook: Vibration Mechanics; Linear Discrete Syst M. Pedro,P. Pahud Book 1991 Kluwer Academic Publishers 1991 Natur.Service.Vibration.fatigue.frict

铁塔等

Periodic Steady State,Harmonic analysis allows one to calculate the steady state of a dissipative oscillator excited by any periodic external force f(t). We mean, by the steady state, that state which maintains itself after the disappearance of transitory terras. . Let us recall that f(t) of period . (figure 5.1), can be decomposed into the Fourier series.

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AVOW

Electrical Analogues,As we said in the introduction, it is sometimes advantageous to search for the electrical system equivalent to a mechanical system.

cumber

Systems with Two Degrees of Freedom,A mechanical system possesses two degrees of freedom, when its configuration can be describe by means of two functions of time x.(t) and x.(t), which are called generalized coordinates in the sense of Lagrangian mechanics. These can represent lengths (m), angles (radians), volumes (m.), etc.

为敌

The Concept of the Generalized Oscillator,A linear mechanical system consisting of any finite number of degrees of freedom, n, and whose behaviour is governed by the following second order differential equation . is called a discrete . linear . — or more simply a generalized oscillator.

MORT

Free State of the Conservative Generalized Oscillator,As we have done for the elementary oscillator, we are going to assume at first that the generalized oscillator is not subject to any external force and that there is no damping ..With these conditions, the solution of the differential system is the conservative free state.

DRAFT

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Example of Visualization of Complex Natural Modes,A natural mode remains a relatively abstract idea because of the nature and the dimension of the space considered. In effect, the n initial generalized coordinates x. in general have different physical dimensions (lengths, angles, etc.), so it is illusory to hope to find a physical interpretation of the space of which they constitute a basis.

AFFIX

Harmonic Steady State, is the subject of chapter 6. We will first consider a very important special case, that of the ., caused by a pure harmonic external force, after the disappearance of the transitory terms. It will then be possible to tackle, by means of the Fourier series, the . due to any form of periodic force (chapter 5).

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