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Vibrations of a Plate with Periodically Changing Parameters

Vestnik St. Petersburg University, Mathematics, 2021
In this paper, the equation of vibrations of a plate with periodically changing parameters (material properties and thickness) are derived, and the eigenfrequencies are determined. Solution of the problem is obtained with the approximate theory (Bubnov-Galerkin method). The approximate results are presented by analytical formulas. Asymptotic averaging (
Naumova, N. V.   +2 more
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Free Vibration of a Disordered Periodic Beam

Journal of Applied Mechanics, 1974
Using a first-order perturbation procedure the statistical properties of the natural frequencies and their associated normal modes of a disordered N-span beam are investigated. Two types of disorder are considered: the random deviation of span length from an ideal design value and the random fluctuation of the bending stiffness along the beam.
Lin, Y. K., Yang, J. N.
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Active Isolation of Periodic Machinery Vibrations

Journal of Sound and Vibration, 1993
Abstract Passive systems for the isolation of machinery vibrations can be supplemented by active techniques. It is shown that using secondary force inputs in parallel with a passive isolation stage has considerable potential advantages, both in the improvement of isolator performance and in the stability of the mounted machine.
Jenkins, M. D.   +3 more
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Vibration of Rotationally Periodic Structures

Journal of Sound and Vibration, 1994
Abstract The purpose of this paper is to determine eigensolutions of a rotationally periodic structure P of period N in terms of those of the i th substructure S(i) of P. Let y(i) be the generalized displacement vector and f(i) be the generalized force vector at interface I(i) , where substructures S(i) and S(i - 1) are connected.
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Bouncing ball on a vibrating periodic surface

Chaos: An Interdisciplinary Journal of Nonlinear Science, 2018
We present an investigation of a partially elastic ball bouncing on a vertically vibrated sinusoidal surface. Following the work of McBennett and Harris [Chaos 26, 093105 (2016)], we begin by demonstrating that simple periodic vertical bouncing at a local minimum of the surface becomes unstable when the local curvature exceeds a critical value.
Avishai Halev, Daniel M. Harris
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Periodic vibration of plates with large displacements

19th AIAA Applied Aerodynamics Conference, 2001
An algorithm based on the shooting and Newton methods was used to solve the finite element (FE) equations of motion of isotropic plates. To validate it and to demonstrate that this algorithm has advantages when compared with other methods, results were compared with published ones.
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On Periodic Solutions of a Beam Vibration Equation

Differential Equations, 2018
zbMATH Open Web Interface contents unavailable due to conflicting licenses.
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Periodic Control of Vibrations in Helicopters

IFAC Proceedings Volumes, 2000
Abstract The problem of rejecting periodic disturbances in helicopters is here addressed by means of a periodic LMI technique. The computational advantage offered by this technique allows to face the important case of helicopter operating at variable velocity.
Francesco A. Cuzzola, Sergio Bittanti
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Vibration of Prestressed Periodic Lattice Structures

AIAA Journal, 1981
Equations are developed for vibration of general lattice structures that have repetitive geometry. The method of solution is an extension of a previous paper for buckling of similar structures. The theory is based on representing each member of the structure with the exact dynamic stiffness matrix and taking advantage of the repetitive geometry to ...
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On Vibration Absorbers for Periodic Excitation

Dynamic Systems and Control: Volume 1 — Vibration Control; Dynamic Systems; Robotics; Sliding Mode Control; Robust and Nonlinear Control; Automated Modeling; Control of Manufacturing Processes; Precision Control, 1995
Abstract The dynamic vibration absorber is a commonly-used device for reducing the vibrations of a primary system subjected to harmonic excitation. In this paper, the absorber concept is generalized from harmonic to periodic excitation functions.
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