Y. X. Hao

Bio: Y. X. Hao is an academic researcher from Beijing Information Science & Technology University. The author has contributed to research in topics: Nonlinear system & Galerkin method. The author has an hindex of 13, co-authored 30 publications receiving 444 citations.

Nonlinear vibrations of FGM truncated conical shell under aerodynamics and in-plane force along meridian near internal resonances

Abstract: This paper focuses on the nonlinear dynamics near internal resonance of a truncated FGM conical shell. The FGM conical shell is subjected to the aerodynamic load and the in-plane excitation along the meridian direction. Material properties depend on the temperature and the constituent phases of the truncated FGM conical shell. The volume fractions are modified in the thickness direction based on a power-law function continuously and smoothly. The first-order piston theory is applied for the supersonic aerodynamic pressure. Based on the first-order shear deformation theory, von-Karman type nonlinear geometric assumptions, Hamilton principle and Galerkin method, the nonlinear equations of motion for the truncated FGM conical shell are derived. The averaged equations of the truncated FGM conical shell are obtained under the situation of 1:1 internal resonance and 1/2 subharmonic resonance by using the method of multiple scales. The frequency-response curves, the force-response curves, the bifurcation diagrams, the phase portraits, the time history diagrams, and the Poincare maps are obtained by using numerical calculations. The influences of the Mach number, the exponent of volume fraction and the in-plane excitation on the nonlinear resonant behaviors of the truncated FGM conical shell are investigated.

Nonlinear Dynamics of Cantilever FGM Cylindrical Shell under 1:2 Internal Resonance Relations

Abstract: An analysis on the nonlinear dynamics of a cantilever functionally graded materials (FGM) cylindrical shell subjected to the transversal and static in-plane pre-applied excitation is presented in a thermal environment. Material properties are assumed to be temperature-dependent. Based on Reddy's first-order shell theory, the nonlinear governing equations of motion for the FGM cylindrical shell are derived using Hamilton's principle. Galerkin's method is utilized to discretize the governing partial equations to a two-degree-of-freedom nonlinear system including the quadratic and cubic nonlinear terms under combined external excitations. It is desirable to choose a suitable mode function to satisfy the first two modes of transverse nonlinear oscillations and the boundary conditions for the cantilever FGM cylindrical shell. The effects of external excitations on the internal resonance relationship and nonlinear dynamic response of FGM cylindrical shell are studied. The resonant case considered here is 1:2 in...

Non-linear vibrations of shells: A literature review from 2003 to 2013

Abstract: The present literature review focuses on geometrically non-linear free and forced vibrations of shells made of traditional and advanced materials. Flat and imperfect plates and membranes are excluded. Closed shells and curved panels made of isotropic, laminated composite, piezoelectric, functionally graded and hyperelastic materials are reviewed and great attention is given to non-linear vibrations of shells subjected to normal and in-plane excitations. Theoretical, numerical and experimental studies dealing with particular dynamical problems involving parametric vibrations, stability, dynamic buckling, non-stationary vibrations and chaotic vibrations are also addressed. Moreover, several original aspects of non-linear vibrations of shells and panels, including (i) fluid–structure interactions, (ii) geometric imperfections, (iii) effect of geometry and boundary conditions, (iv) thermal loads, (v) electrical loads and (vi) reduced-order models and their accuracy including perturbation techniques, proper orthogonal decomposition, non-linear normal modes and meshless methods are reviewed in depth.