Calculation of Fourier Spectra of Amplitude Function of Incommensurate Superstructure Described by Two Components Parameter of Order (N=4)

In this work, a comparative study is performed to investigate the influence of time-varying normal forces on the friction properties and friction-induced stick-slip vibration by experimental and theoretical methods. In the experiments, constant and harmonic-varying normal forces are applied, respectively. The measured vibration signals under two loading forms are compared in both time and frequency domains. In addition, mathematical tools such as phase space reconstruction and Fourier spectra are used to reveal the science behind the complicated dynamic behaviour. It can be found that the friction system shows steady stick-slip vibration, and the main frequency does not vary with the magnitude of the constant normal force, but the size of limit cycle increases with the magnitude of the constant normal force. In contrast, the friction system harmonic normal force shows complicated behaviour, for example, higher-frequency larger-amplitude vibration occurs as the frequency of the normal force increases. The interesting findings offer a new way for controlling friction-induced stick-slip vibration in engineering applications.

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Ground motion accelerogram analysis including dynamical instrumental correction

Bulletin of the Seismological Society of America ◽

10.1785/bssa05406a2087 ◽

1964 ◽

Vol 54 (6A) ◽

pp. 2087-2098

Author(s):

V. A. Jenschke ◽

J. Penzien

Keyword(s):

Ground Motion ◽

Analytical Method ◽

Strong Motion ◽

Instrumental Error ◽

Underground Nuclear Explosions ◽

Nuclear Explosions ◽

Damping Characteristics ◽

Standard Response ◽

Fourier Spectra

abstract Due to inertial and damping characteristics of strong motion seismographs, recorded ground motion accelerograms may in some cases be sufficiently in error to significantly affect the results obtained when generating standard response or Fourier spectra. Therefore, the objectives of this paper are to present an analytical method of generating standard spectra which will eliminate the above instrumental error and to show the significance of this error by presenting some sample results obtained from accelerograms representing both earthquakes and underground nuclear explosions.

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Vibrations of beams with a breathing crack and large amplitude displacements

Proceedings of the Institution of Mechanical Engineers Part C Journal of Mechanical Engineering Science ◽

10.1177/0954406215589333 ◽

2015 ◽

Vol 230 (1) ◽

pp. 34-54 ◽

Cited By ~ 6

Author(s):

Gonçalo Neves Carneiro ◽

Pedro Ribeiro

Keyword(s):

Time Domain ◽

Equations Of Motion ◽

Shape Functions ◽

Breathing Crack ◽

Dimensional Theory ◽

One Dimensional ◽

Time Histories ◽

Linear Effects ◽

Fourier Spectra ◽

The Time Domain

The vibrations of beams with a breathing crack are investigated taking into account geometrical non-linear effects. The crack is modeled via a function that reduces the stiffness, as proposed by Christides and Barr (One-dimensional theory of cracked Bernoulli–Euler beams. Int J Mech Sci 1984). The bilinear behavior due to the crack closing and opening is considered. The equations of motion are obtained via a p-version finite element method, with shape functions recently proposed, which are adequate for problems with abrupt localised variations. To analyse the dynamics of cracked beams, the equations of motion are solved in the time domain, via Newmark's method, and the ensuing displacements, velocities and accelerations are examined. For that purpose, time histories, projections of trajectories on phase planes, and Fourier spectra are obtained. It is verified that the breathing crack introduce asymmetries in the response, and that velocities and accelerations can be more affected than displacements by the breathing crack.

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