Chaotic and bifurcation dynamics of a simply-supported thermo-elastic circular plate with variable thickness in large deflection

Bifurcations and chaos in a periodic time-varying temperature-excited bimetallic shallow shell of revolution

“…The problem related to numerical realization is the lack of a relatively simple estimate of the errors and, in many cases, the lack of a mathematical background for the proper choice of basis functions. As proved by Yeh [9], the present method with one mode function is sufficiently accurate, and the Chebyshev polynomial showed some advantages such as high convergence rate and stability in Cheung and Zhou's analysis of plates [40,41]. So one can expect that the present treatment gives a sufficient simulation of the properties of the original shallow shell.…”

“…Shu et al [7] employed a double-mode approach to predict the chaotic motion of a large deflection plate by using the method of Melnikov [8]. Yeh et al [9] characterized the conditions that can possibly lead to chaotic motion and bifurcation behavior for a simply supported large deflection thermo-elastic circular plate with variable thickness by utilizing the criteria of fractal dimensions, maximum Lyapunov exponents, and bifurcation diagrams. Zhang [10] analyzed the global bifurcation and chaotic dynamics of a parametrically excited rectangular thin plate and found the chaotic motion from numerical simulation.…”

Chaotic synchronization of vibrations of a coupled mechanical system consisting of a plate and beams

“…In the field of mechanical continuous systems like beams/plates/shells there exists already a vast number of paper devoted to investigation of their bifurcational and chaotic behaviour. For instance, axially accelerating beams have been analysed in [1][2][3][4] using analytical approaches, whereas squared plates parametrically excited have been studied in [5][6][7] with respect to local and global bifurcations, the existence of heteroclinic and Shilnikov-type homoclinic orbits, Smale horseshoes and chaotic dynamics. Recently, in three companion papers chaotic dynamics of flexible plate and cylinder like panels of infinite length, rectangular spherical and cylindrical shells, closed cylindrical shells, axially symmetric plates, as well as spherical and conical shells have been studied (see [8][9][10]).…”

A lower bound on snap-through instability of curved beams under thermomechanical loads

“…In many studies [22,23], thermal strain due to applied temperature is included without modeling thermoelastic coupling: temperature changes are thus treated as a simple mechanical expansion or contraction of the material. This can be useful in tracing static solution paths, and may also give information about the temperature-sensitivity of a particular structure, but the absence of thermoelastic coupling can impact the accuracy of dynamic simulations, especially as amplitudes of vibration become large.…”