Search

A nonlinear thermoelastic model of a circular plate is presented in the paper. The model, based on the Mindlin plate theory, is extended by taking into account nonlinear geometrical terms. Partial differential equations of plate’s dynamics are derived for a fully coupled thermal and mechanical fields. Then the model is reduced to a set of ordinary differential equations taking into account the first three natural modes and assuming a constant thermal field. The influence of elevated temperature on the resonance curves and the mode involvement due to nonlinear and thermal couplings is presented. The analysis shows that the increased temperature may lead to various bifurcation scenarios. The buckling phenomenon and post-buckling nonlinear regular and chaotic oscillations are studied.

An effect of thermal loading on vibrations of beams is investigated in the paper. A beam is considered as an extended Timoshenko beam model with nonlinear terms resulted from large deflections. Dynamics of the structure is analysed under thermal and mechanical loadings considering transient dynamics due to a heat pulse imposed to the beam. The numerical method for solving coupled thermo-mechanical problem is presented. On this basis the importance of the heat pulse intensity around the first resonance condition is demonstrated. The effect of the heat on the the complex transient dynamics of the beam and its qualitatively different response is shown as well.

Nonlinear vibrations of a circular plate subjected to mechanical and thermal loadings are presented in the paper. A model of the plate is based on the extended Mindlin theory, taking into account nonlinear geometrical terms and acting heat uniformly distributed along the plate span. The dynamics of a coupled thermo-mechanical problem is reduced from a set of partial differential equations to ordinary differential equations. Considering oscillations around the first natural frequency just one mode reduction is proposed. The analysis shows that elevated temperature shifts the resonance curve and new post-buckling oscillations arise. Depending on initial conditions for the post-buckling state various scenarios of bifurcations take place and transient irregular oscillations may occur. The proposed one degree of freedom model shows a good agreement with response of the model based on three or five-modes reduction.

In this work, the large amplitude vibration of a heated Timoshenko composite beam having delamination is studied. The model of delamination considers the contact interaction between sublaminates including normal forces, shear forces, and additional damping due to the interaction of sublaminates. This work is an extension of the previous analysis based on a model of the dynamic behavior of a beam with delamination considering additionally the nonlinearities due to large displacements and temperature changes. Numerical calculations are performed in order to estimate the influence of the delamination, the geometrically nonlinear terms, and elevated temperature on the response of the beam.

Dynamics of a Timoshenko beam under an influence of mechanical and thermal loadings is analysed in this paper. Nonlinear geometrical terms and a nonuniform heat distribution are taken into account in the considered model. The mathematical model is represented by a set of partial differential equations (PDEs) which takes into account thermal and mechanical loadings. The problem is simplified to two PDEs and then reduced to ordinary differential equations (ODEs) by means of the Galerkin method taking into account three modes of a linear Timoshenko beam. Correctness of the analytical model is verified by a finite element method. Then, the nonlinear model is studied numerically by a continuation method or by a direct numerical integration of ODEs. An effect of the temperature distribution on the resonance near the first natural frequency and on stability of the solutions is presented. The increase of mechanical loading results in hardening of the resonance curve. Thermal loading may stabilise the beam dynamics when the temperature is decreased. The elevated temperature may transit dynamics from regular to chaotic oscillations.

Large amplitude vibrations of a Timoshenko beam under an influence of temperature are analysed in this paper. In the considered model the temperature increases instantly and the heat is uniformly distributed along the beams length and cross-section. The mathematical model, represented by partial differential equations takes into account thermal and mechanical loadings. Next, the problem is reduced by means of the Galerkin method, considering the first three natural vibration modes of a simply supported beam in the both ends. The influence of the temperature on amplitudes and localisation of the resonance zones and stability of the solutions is studied numerically and analytically by the multiple time scale method. The bifurcation points, existence of unstable lobes and transition from regular to chaotic oscillations are shown.

Large amplitude vibrations of a Timoshenko beam under an influence of thermal and mechanical loadings are studied in the paper. The structural parameters of the beam are considered enabling internal resonance conditions. Moreover, it is assumed that the beam gets instantly temperature which is distributed along its length and thickness. The mathematical model represented by a set of partial differential equations takes into account coupled mechanical and thermal fields. The problem is transformed to a set of ODEs by the Galerkin method and three modes of a simply supported beam at both ends are studied. The effect of temperature on internal and external resonances is analysed on the basis of the proposed reduced model.Copyright © 2014 by ASME

Vibrations of a nonlinear self-excited system driven by parametric and/or external excitations are studied in the paper. The model is composed of a self-excitation term represented by a nonlinear van der Pol function, periodically varied stiffness which represents parametric excitation and external harmonic force. Interactions between self and parametric or/and external force lead to complex behaviours observed by quasi-periodic or chaotic motions but under specific conditions, near resonance zones the response is harmonic. The transition from quasi-periodicity to periodic oscillations is caused by so called the frequency locking phenomenon which in fact corresponds to the second kind Hopf bifurcation (Neimark-Sacker bifurcation). The periodic resonances can be determined analytically, quasi-periodic oscillations however are investigated mainly numerically. The goal of this paper is to determine quasi-periodic dynamics and Hopf bifurcations analytically by using the multiple time scale method (MSM) in two steps: (1) to determine periodic solutions of the fast flow by the first order MSM and (2) to determine periodic solutions of the slow–flow by the second order MSM. The analytical solutions obtained in both scales allow determining bifurcation points of the system.Copyright © 2014 by ASME

The goal of this paper is to study large amplitude vibrations of a Timoshenko beam under an influence of the elevated temperature. It is assumed that the beam gets the elevated temperature instantly and the temperature is uniformly distributed along the beam’s length and cross-section. The mathematical model represented by a set of partial differential equations is derived taking into account boundary conditions for a simply supported beam in the both ends. Next, the problem is reduced by the Galerkin method by means of free vibration modes. The influence of the temperature on a resonance localisation and nonlinear oscillations is studied numerically and analytically by the multiple time scale method.

Vibrations of a nonlinear self-excited system driven by parametric excitation are presented in the paper. The considered model with one DOF includes a self-excitation term represented by a nonlinear Rayleigh function and also a periodically varied stiffness coefficient which represents parametric excitation. The influence of the external force or/and time delay, treated as a control signal, is demonstrated. Nonlinear parametric resonance is determined numerically and analytically by the multiple time scale method. The influence of time delay on the resonance zones and the frequency locking phenomenon is analysed.Copyright © 2013 by ASME

Dynamics of a composite beam subjected to thermal and mechanical loadings is presented in the paper. The extended Timoshenko beam model takes into account shear and inertia of the cross-section and nonlinear longitudinal displacement caused by mechanical and thermal loadings. It has been shown that thermal and mechanical fields are fully coupled and the heat pulse may change the transient dynamics of the system. For the case of elevated temperature and a steady state problem the model is reduced to nonlinear ordinary differential equations of motion. It has been shown that the elevated ambient temperature may drastically change its response.