This paper presents a nonlinear dynamic analysis of a flexible portal frame subjected to support excitation, which is provided by an electro-dynamical shaker. The main goal of this study is to investigate the dynamic interactions between a flexible portal frame and a nonlinear electrical support excitation. The numerical analysis shows a complex behavior of the system, which can be observed by phase spaces, Poincar&#xe9; sections and bifurcation diagrams.

Aline Souza de Paula

Jos&#xe9; Manoel Balthazar

Jorge Luis Palacios Felix

Some Comments on the Nonlinear Dynamics of a Portal Frame under Base Excitation

The nonlinear response of a three degree of freedom autoparametric system with a double pendulum, including the magnetorheological (MR) damper when the excitation comes from a DC motor which works with limited power supply, has been examined. The non-ideal source of power adds one degree of freedom which makes the system have four degrees of freedom. The influence of damping force in MR damper on the phenomenon of energy transfer has been studied numerically. Near the internal and external resonance region, except periodic vibration also chaotic vibration has been observed. Results show that MR damper can be used to change the dynamic behavior of the autoparametric system.

Danuta Sado

Nonlinear Dynamics of a Non-ideal Autoparametric System with MR Damper

The paper presents vibration analysis of a simply supported beam with a fractional order viscoelastic material model. The Bernoulli-Euler beam model is considered. The beam is excited by the supports movement. The Riemann &#x2013; Liouville fractional derivative of order 0 &#x3b1; &#x26;les; 1 is applied. In the first stage, the steady-state vibrations of the beam are analyzed and therefore the Riemann &#x2013; Liouville fractional derivative with lower terminal at &#x2212;&#x221e; is assumed. This assumption simplifies solution of the fractional differential equations and enables us to directly obtain amplitude-frequency characteristics of the examined system. The characteristics are obtained for various values of fractional derivative of order &#x3b1; and values of the Voigt material model parameters. The studies show that the selection of appropriate damping coefficients and fractional derivative order of damping model enables us to fit more accurately dynamic characteristic of the beam in comparison with using integer order derivative damping model.

Jan Freundlich

Vibrations of a Simply Supported Beam with a Fractional Viscoelastic Material Model &#x2013; Supports Movement Excitation

In this paper an inextensible cantilever beam subject to a concentrated axial load and a lateral harmonic excitation is investigated. Special attention is given to the effect of the axial load on the frequency-amplitude relation, bifurcations and instabilities of the beam. To this aim, the nonlinear integro-differential equations describing the flexural-flexural-torsional coupling of the beam are used, together with the Galerkin method, to obtain a set of discretized equations of motion, which are in turn solved by using the Runge-Kutta method. Both inertial and geometric nonlinearities are considered in the present analysis. Due to symmetries of the beam cross section, the beam exhibits a 1:1 internal resonance which has an important role on the nonlinear oscillations and bifurcation scenario. The results show that the axial load influences the stiffness of the beam changing its nonlinear behavior from hardening to softening. A detailed parametric analysis using several tools of nonlinear dynamics unveils the complex dynamic behavior of the beam in the parametric and external resonance regions. Bifurcations leading to multiple coexisting solutions are observed.

Eulher C. Carvalho

Paulo B. Gon&#xe7;alves

Giuseppe Rega

Zen&#xf3;n J.G.N. Del Prado

Influence of Axial Loads on the Nonplanar Vibrations of Cantilever Beams

This contribution investigates the influence of parametric excitation on the dynamic stability of a microelectromechanical system. In systems with just a single degree of freedom, parametric excitation causes the oscillator to exhibit unstable behavior within certain intervals of the parametric excitation frequency. In multi-degree of freedom systems on the other hand, unstable behavior is caused within a wider range of intervals of the parametric excitation frequency. Moreover, such systems show frequency intervals of enhanced stability, an effect known as anti-resonance phenomenon. Both types of phenomena, the parametric resonance and anti-resonance, are modeled and studied for a microelectromechanical system with two degrees of freedom and some novel results are discussed.

Johannes Welte

Till Jochen Kniffka

Horst Ecker

Parametric Excitation in a Two Degree of Freedom MEMS System

Paulo Batista Gon&#xe7;alves

Andr&#xe9; Fenili

Nonlinear Vibrations in Elastic Structures: Dynamics and Control

In this paper the author investigates the angular position and vibration control of a nonlinear rigid-flexible two link robotic manipulator considering fast angular maneuvers. The nonlinear control technique named State-Dependent Riccati Equation (SDRE) is used here to achieve these aims. In a more realistic approach, it is considered that some states can be measured and some states cannot be measured. The states not measured are estimated in order to be used for the SDRE control. These states are all the angular velocities and the velocity of deformation of the flexible link. A SDRE-based estimator is used here. Not only different initial conditions between the system to be controlled (here named &#x22;real&#x22; system) and the estimator but also a different mathematical model is considered as the estimation model in order to verify the limitations of the proposed state estimation and control techniques. The mathematical model that emulates the real system to be controlled considers two modes expansion and the estimation model considers only one mode expansion. The results for the different approaches are compared and discussed.

The Rigid-Flexible Robotic Manipulator: Nonlinear Control and State Estimation Considering a Different Mathematical Model for Estimation

An application of the nonlinear saturation control (NSC) algorithm for a self-excited strongly nonlinear beam structure driven by an external force is presented in the paper. The mathematical model accounts for an Euler-Bernoulli beam with nonlinear curvature, reduced to first mode oscillations. It is assumed that the beam vibrates in the presence of a harmonic excitation close to the first natural frequency of the beam, and additionally the beam is self-excited by fluid flow, which is modelled by a nonlinear Rayleigh term for self-excitation. The self- and externally excited vibrations have been reduced by the application of an active, saturation-based controller. The approximate analytical solutions for a full structure have been found by the multiple time scales method, up to the first-order approximation. The analytical solutions have been compared with numerical results obtained from direct integration of the ordinary differential equations of motion. Finally, the influence of a negative damping term and the controller's parameters for effective vibrations suppression are presented.

J. Warminski

M. P. Cartmell

A. Mitura

M. Bochenski

Active Vibration Control of a Nonlinear Beam with Self- and External Excitations

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Shock and Vibration publishes papers on all aspects of shock and vibration, especially in relation to civil, mechanical and aerospace engineering applications, as well as transport, materials and geoscience.&nbsp;

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Chief Editor&nbsp;Dr Tai Thai&nbsp;is based at the University of Melbourne and his current research focuses on high strength materials for sustainable construction of buildings, bridges and other infrastructure.

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Shock and Vibration | Hindawi

Shock and Vibration

This Issue is now open for submissions.
Papers are published upon acceptance, regardless of the Special Issue publication date.

Shock and Vibration

Nonlinear Vibrations in Elastic Structures: Dynamics and Control

Nonlinear Vibrations in Elastic Structures: Dynamics and Control

Articles

Some Comments on the Nonlinear Dynamics of a Portal Frame under Base Excitation

Nonlinear Dynamics of a Non-ideal Autoparametric System with MR Damper

Vibrations of a Simply Supported Beam with a Fractional Viscoelastic Material Model – Supports Movement Excitation

Influence of Axial Loads on the Nonplanar Vibrations of Cantilever Beams

Parametric Excitation in a Two Degree of Freedom MEMS System

Nonlinear Vibrations in Elastic Structures: Dynamics and Control

The Rigid-Flexible Robotic Manipulator: Nonlinear Control and State Estimation Considering a Different Mathematical Model for Estimation

Active Vibration Control of a Nonlinear Beam with Self- and External Excitations