Modeling, Dimension Reduction, and Nonlinear Vibrations of Thermomechanically Coupled Laminated Plates

Abstract

A unified formulation of thermomechanical, geometrically nonlinear, laminated plates that integrates mechanical and thermal aspects is presented. It allows for constructing and comparing a variety of continuous models of different mechanical richness and with full thermoelastic coupling embedded, as well as for deriving minimal reduced order models suitable to provide useful information on fundamental thermomechanical phenomena occurring in the system nonlinear and complex dynamics. Comparative numerical investigations of free and forced vibrations can be carried out through both models of three, fully coupled, ordinary differential equations and simplified, partially coupled, models of two, or even one, ODEs, with the aim to unveil the actual importance of accounting for the various terms to reliably describe the most important thermomechanical effects on the system response.

Intelligent computing for Duffing-Harmonic oscillator equation via the bio-evolutionary optimization algorithm

“…As evident, the adjustable parameters c i used in equations (2) and 3, for which E c1 , E c2 and E a c ð Þ come closer to zero, the value of E also approaches 0, which then produces approximate solution,Ŷ t ð Þ that are highly compatible with the exact solution.…”

“…Problems of nonlinear vibration in conservative systems, bearing a wide history, have been interpreted to a great extent, in order to study various parametric behaviors of nonlinear vibrations of several mechanical objects. [1][2][3] In this regard, several methods have been established to analyze these problems, analytically as well as numerically. [4][5][6] Particularly, among many well-known oscillatory equations, the Duffing equation is found to be the most widely studied equation for its eminent applications in different fields of science, engineering, and biology.…”

Level‐wise strain recovery and error estimation for natural element hierarchical plate models

“…for every admissible test displacement field v(x) ∈ V(Ω). Here, V(Ω) is an admissible function space defined by {v(x) ∈ [H 1 (Ω)] 3 : v = 0 on Ω D } . 24 And, two functionals a(u, v) and (v) are defined by…”

“…The reduction of problem domain not only decreases the problem size, but it allows one to obtain the analytical solutions. Classical beam, arch, plate, and shell theories are the representatives which were born according to the dimension reduction, 2,3 and those have been effectively used to analyze the behavior of thin elastic structures during several decades. However, these classical models inevitably suffer from the inaccuracy in the analysis of structures with moderate thickness, and furthermore those are insufficient to deal with the complex boundary and the junction with other structural members.…”

“…The limitation of classical lower-order theories could be overcome by employing the concept of hierarchical modeling which was introduced in the early of 1990s. [3][4][5][6] In the hierarchical modeling, several dimensionally reduced models with different model levels, called hierarchical models, are to be combined within a given problem domain (i.e., on the mid-surface of structure). Therefore, one can effectively increase the numerical analysis accuracy and successfully deal with the complex boundary and the junction by appropriately selecting and combining the hierarchical models.…”