Free vibration of fully coupled thermoelastic multilayered composites with imperfect interfaces

Abstract

A fully coupled thermoelastic framework is formulated to cope with the free vibration response of anisotropic multilayered plates in three dimensions. The laminated structure consists of homogeneous laminae of arbitrary thickness and width under simply supported edge conditions in thermal environment. The general and exact field expressions of the temperature, heat flux, displacement and stress components are expressed in terms of double Fourier series expansions in any rectangular plate, which lead to the extended Stroh formalism with thermomechanical coupling effects in a concise and compact matrix form. Different imperfect interface conditions are introduced to characterize specific structural and thermal contact properties at the bounding interfaces, and further to determine the finite complex valued coefficients in the suitable series relations. The complete time-harmonic solutions in the laminated composites in the presence of perfect/imperfect interfaces are recursively obtained by means of the modified dual variable and position technique with explicit layer-to-layer transfer matrices. Results are obtained for different layups, length-to-thickness ratios and interfacial boundary conditions for two application examples, namely the graphite/epoxy cross-ply composites and the thermal barrier coatings on superalloys, without suffering from numerical exponential instability. These investigations reveal that the natural frequencies and first and higher vibration mode shapes of the multilayered structures can be considerably affected by increasing the environmental temperature and the severity of the interfacial imperfections. Since the through-thickness stress distribution in 2, 5, and 10 layered composites appears to be strongly correlated to the layups, such modal stress analysis could be exploited to locate the fatigue hotspots operated in dynamic structures and to guide the structural design of aircraft and spacecraft composite laminates subjected to residual vibrations.

Singularity-free theory and adaptive finite element computations of arbitrarily-shaped dislocation loop dynamics in 3D heterogeneous material structures

“…The recent dual variable and position technique (Pan, 2019, Vattré and Pan, 2019, Liu et al, 2018) is adopted in the present dislocation theory, in lieu of the conventional transfer matrix method for laminated systems (Pan, 1989, Thomson, 1950, Haskell, 1953, Singh, 1970 that might arise numerical instability issues, such as spurious oscillations for large amplitudes of frequencies or half-wave numbers (Pan, 2019, Vattré and Pan, 2021, Vattré et al, 2021. Substituting z by z λ−1 into the linear system in eq.…”

“…In such problems where the multivariate integrand is oscillatory close to the dislocation cores, the numerical evaluation can be difficult for large amplitudes of frequencies or half-wave numbers, where a prohibitive number of points is needed in standard quadratures based on high order Gauss-Legendre integration rules (Hamming, 1973, Laghrouche andBettess, 2000). Nevertheless, for spreading dislocation cores, the prescribed displacement field becomes infinitely differentiable over D, without oscillatory regimes, as illustrated for interfacial dislocations (Vattré and Pan, 2019) and heterogeneously distributed loads at the external surfaces (Vattré and Pan, 2021). With an excellent cubature convergence, the singularity-free property of the present displacement boundary conditions lead tractable the Gauss-Legendre quadrature rules enriched by the Green integral formula for the present theory of arbitrarily-shaped and curved dislocation loops.…”

Study on dynamic characteristics of composite plates under non-uniform gradient temperature along the thickness

“…Valizadeh et al (2013) studied the static and dynamic characteristics of functionally graded material (FGM) plates with thermal distribution obtained by solving a steady-state heat transfer equation. Vattre et al (2021) presented a fully coupled thermo-elastic framework to study free vibration characteristics of anisotropic multilayered plates with imperfect interfaces considering the heat conduction effect. Gupta and Sharma (2016) studied the free transverse vibration of non-homogeneous trapezoidal plates of linear thickness variation in the x direction, considering the effect of the thermal gradient.…”