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This study deals with the influence of manufacturing-induced geometric variability on the identification of material properties of composite sandwich panels. The objective of this article is twofold. First, this work aims to demonstrate the marked influence of geometric uncertainties on a foam core sandwich panel whose skin material properties need to be identified. Several identification cases are studied based on experimentally obtained natural frequencies and mode shapes. The second objective is to propose a numerical method for the identification process in the case where uncertainties can be treated as a random field (e.g., thickness distribution). The identification method is built around a classification-based technique referred to as “fidelity maps”, which has the ability to simultaneously treat several responses to match without any assumption on their correlation. The approach uses a proper orthogonal decomposition for the extraction and the selection of the features of the random field considered as important for the identification. The identification method is demonstrated on a foam core sandwich panel whose thickness distribution is modeled as a random field.

Large-amplitude (geometrically nonlinear) forced vibrations of completely free sandwich rectangular plates are investigated experimentally. Harmonic excitation is applied by using an electro-dynamic exciter and the plate vibration is measured by using laser Doppler vibrometers. A scanning laser Doppler vibrometer is used for experimental modal analysis since it provides non-contact vibration measurements with very high spatial resolution. The large-amplitude vibration experiments are carried out by using a single point laser Doppler vibrometer and a stepped-sine testing procedure. The nonlinear frequency response curves are obtained by increasing and decreasing the excitation frequency in very small steps at specific force amplitudes controlled in a closed-loop. The experimental results are compared to numerical simulations obtained by reduced-order models and show very good agreement. The nonlinear damping is experimentally obtained as a function of the vibration amplitude.

Nonlinear forced vibrations of moderately thick functionally graded (FG) rectangular plates are investigated by considering higher-order shear deformation theories that take into account the thickness deformation effect. The geometrically nonlinear strain–displacement relationships are derived retaining full nonlinear terms in the in-plane and transverse displacements and the three-dimensional constitutive equations are used by removing the assumption of zero transverse normal strain. Both simply supported movable and immovable boundary conditions are considered at the plate edges. The equations of motion are obtained by using multi-modal energy approach. A code based on pseudo arc-length continuation and collocation scheme is utilized for numerical continuation and bifurcation analysis. Results show that higher-order thickness deformation theories yield a significant accuracy improvement for nonlinear vibrations of highly pressurized functionally graded plates.

Nonlinear forced vibrations of water-filled, laminated circular cylindrical shells are studied by using the Amabili–Reddy nonlinear higher-order shear deformation theory and energy approach in the Lagrangian description. The fluid is modeled by potential flow. It is assumed that the shell is subjected to a steady harmonic concentrated force acting in the radial direction. Pseudo arc-length continuation and collocation technique is used to carry out bifurcation analysis and to obtain nonlinear frequency–amplitude responses. Direct time integration of the equations of motion has also been performed by using Gear’s backward differentiation formula (BDF) to obtain time histories, phase space diagrams and Poincare maps. The effect of internal fluid and lamination angle on the frequency–amplitude response in the neighborhood of the resonance frequency, traveling wave solution and internal resonances of simply supported shells are investigated. It is shown that water-filled composite shells may exhibit complex nonlinear dynamics including a rare and intricate 1:1:1:1 internal resonance.

Nonlinear vibrations of completely free laminated and sandwich rectangular plates are investigated for the first time. The equations of motion are obtained via multi-modal energy approach based on Lagrange equations and by using classical and higher-order shear deformation theories with von Karman type nonlinearities. The numerical analysis is carried out in two steps. First, the plate displacements and rotations are expanded in terms of Chebyshev polynomials and a linear analysis is performed to obtain the natural frequencies and modes of vibration. Then, the energy functional is discretized by using the natural modes of vibration and a system of nonlinear ordinary differential equations with quadratic and cubic nonlinear terms is obtained. A code based on pseudo arc-length continuation and collocation scheme is used for bifurcation analysis and the near resonance nonlinear vibrations are studied. The frequency-response curves, time histories and phase space diagrams are presented.

Geometrically nonlinear forced vibrations of thick, deep laminated circular cylindrical panels are studied via multi-modal energy approach based on Lagrange equations. It is assumed that the panel is subjected to a steady harmonic concentrated force acting in the radial direction. Simply supported movable boundary conditions are considered and the energy functional is reduced to a system of nonlinear ordinary differential equations with cubic and quadratic nonlinear terms using admissible eigenfunctions. A code based on pseudo arc-length continuation and collocation method is used to carry out a bifurcation analysis and obtain numerical solutions. Several internal resonances are detected. Direct time integration of the equations of motion has also been performed to obtain the bifurcation diagrams and Poincare maps. It is shown that the panel exhibits complex nonlinear dynamics including quasi-periodic, intermittency and chaos in the vicinity of internal resonances. Moreover, it is illustrated that the choice of Amabili–Reddy higher-order shear deformation theory could be recommended for studying deep and thick panels.

Geometrically nonlinear vibrations of functionally graded (FG) doubly curved shells subjected to thermal variations and harmonic excitation are investigated via multi-modal energy approach. Two different nonlinear higher-order shear deformation theories are considered and it is assumed that the shell is simply supported with movable edges. Using Lagrange equations of motion, the energy functional is reduced to a system of infinite nonlinear ordinary differential equations with quadratic and cubic nonlinearities which is truncated based on solution convergence. A pseudo-arclength continuation and collocation scheme is employed to obtain numerical solutions for shells subjected to static and harmonic loads. The effects of FGM power law index, thickness ratio and temperature variations on the frequency–amplitude nonlinear response are fully discussed and it is revealed that, for relatively thick and deep shells, the Amabili–Reddy theory which retains all the nonlinear terms in the in-plane displacements gives different and more accurate results.

Stress analysis of moderately thick laminated cylindrical panels with different loading and boundary conditions is presented. Boundary conditions include clamped, simply supported and free while uniform and sinusoidal distributed loadings are considered. Assuming effects of shear deformation and initial curvature, governing equations of the problem are derived. The governing partial differential equations (PDEs) in terms of three displacement components, two rotations and ten stress resultants include a system of 15 first order PDEs. Application of the extended Kantorovich method (EKM) to the governing equations yields to a double set of algebric-differential equations in terms of x and θ. The resulted systems are then solved iteratively with very fast convergence. It is demonstrated that the method converges rapidly independent of initial guess functions. Comparisons of the EKM predictions with other analytical and FEM analyses are in close agreement. More results for panels with particular boundary conditions are presented for future studies.