An Asymptotic Study of the Linear Vibrations of a Stretched Beam with Concentrated Masses and Discrete Elastic Supports

In this paper we investigate a class of combined discrete-continuous mechanical systems consisting of a continuous elastic structure and a finite number of concentrated masses, elastic supports, and linear oscillators of arbitrary dimension. After the motion equations for such combined systems are derived, they are formulated as an abstract evolution equation on an appropriately defined Hilbert space. Our main objective is to ascertain conditions under which the combined systems have classical normal modes. Using the sesquilinear form approach, we show that unless some matching conditions are satisfied, the combined systems cannot have normal modes even if Kelvin-Voigt damping is considered.

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DYNAMIC BEHAVIOR OF AXIALLY MOVING SYSTEMS WITH ELASTIC SUPPORTS

10.26678/abcm.cobem2019.cob2019-0309 ◽

2019 ◽

Author(s):

Gabriella Nehemy ◽

Paulo Gonçalves ◽

EDSON CAPELLO SOUSA

Keyword(s):

Dynamic Behavior ◽

Elastic Supports ◽

Axially Moving

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Influence of Time Delay on Controlling the Non-Linear Oscillations of a Rotating Blade

Symmetry ◽

10.3390/sym13010085 ◽

2021 ◽

Vol 13 (1) ◽

pp. 85

Author(s):

Yasser Salah Hamed ◽

Ali Kandil

Keyword(s):

Time Delay ◽

Natural Frequency ◽

Multiple Scales ◽

Control Process ◽

Control Force ◽

Specific Level ◽

Loop Control ◽

Positive Displacement ◽

Non Linear ◽

Linear Vibrations

Time delay is an obstacle in the way of actively controlling non-linear vibrations. In this paper, a rotating blade’s non-linear oscillations are reduced via a time-delayed non-linear saturation controller (NSC). This controller is excited by a positive displacement signal measured from the sensors on the blade, and its output is the suitable control force applied onto the actuators on the blade driving it to the desired minimum vibratory level. Based on the saturation phenomenon, the blade vibrations can be saturated at a specific level while the rest of the energy is transferred to the controller. This can be done by adjusting the controller natural frequency to be one half of the blade natural frequency. The whole behavior is governed by a system of first-order differential equations gained by the method of multiple scales. Different responses are included to show the influences of time delay on the closed-loop control process. Also, a good agreement can be noticed between the analytical curves and the numerically simulated ones.

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Critical Temperatures for Vibrations and Buckling of Magneto-Electro-Elastic Nonlocal Strain Gradient Plates

Nanomaterials ◽

10.3390/nano11010087 ◽

2021 ◽

Vol 11 (1) ◽

pp. 87

Author(s):

Giovanni Tocci Monaco ◽

Nicholas Fantuzzi ◽

Francesco Fabbrocino ◽

Raimondo Luciano

Keyword(s):

Strain Gradient ◽

Thermal Environment ◽

Scale Effects ◽

Nonlocal Theory ◽

Elastic Plates ◽

Critical Temperatures ◽

Buckling Behavior ◽

Linear Vibrations ◽

Nonlocal Strain Gradient ◽

Plate Kinematics

An analytical method is presented in this work for the linear vibrations and buckling of nano-plates in a hygro-thermal environment. Nonlinear von Kármán terms are included in the plate kinematics in order to consider the instability phenomena. Strain gradient nonlocal theory is considered for its simplicity and applicability with respect to other nonlocal formulations which require more parameters in their analysis. Present nano-plates have a coupled magneto-electro-elastic constitutive equation in a hygro-thermal environment. Nano-scale effects on the vibrations and buckling behavior of magneto-electro-elastic plates is presented and hygro-thermal load outcomes are considered as well. In addition, critical temperatures for vibrations and buckling problems are analyzed and given for several nano-plate configurations.

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