Browsing by Author "Chandiramani, Naresh K."

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    Dynamic stability of shear deformable viscoelastic composite plates
    Chandiramani, Naresh K. (Virginia Polytechnic Institute and State University, 1987)
    Linear viscoelasticity theory is used to analyze the dynamic stability of composite, viscoelastic flat plates subjected to in-plane, biaxial edge loads. In deriving the associated governing equations, a hereditary constitutive law is assumed. In addition, having in view that composite-type structures exhibit weak rigidity in transverse shear, the associated governing equations account for the transverse shear deformations, as well as the transverse normal stress effect. The integro-differential equations governing the stability are solved for simply-supported boundary conditions by using the Laplace transform technique, thus yielding the characteristic equation of the system. In order to predict the effective time-dependent properties of the orthotropic plate, an elastic behavior is assumed for tile fiber, whereas the matrix is considered as linearly viscoelastic. In order to evaluate the nine independent properties of the orthotropic viscoelastic material in terms of its isotropic constituents, the micromechanical relations developed by Aboudi [24] are considered in conjunction with the correspondence principle for linear viscoelasticity. The stability behavior analyzed here concerns the determination of the critical in-plane normal edge loads yielding asymptotic stability of the plate. The problem is studied as an eigenvalue problem. The general dynamic stability solutions are compared with their quasi-static counterparts. Comparisons of the various solutions obtained in the framework of the Third Order Transverse Shear Deformation Theory (TTSD) are made with its first order counterpart. Several special cases are considered and pertinent numerical results are compared with the very few ones available in the field literature.
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    Nonlinear flutter of composite shear-deformable panels in a high-supersonic flow
    Chandiramani, Naresh K. (Virginia Tech, 1993)
    The nonlinear dynamical behavior of a laterally compressed, flat, composite panel subjected to a high supersonic flow is analyzed. The structural model considers a higher-order shear deformation theory which also includes the effect of the transverse normal stress and satisfies the traction-free condition on both faces of the panel. The possibility of small initial imperfections and in-plane edge restraints are also considered. Aerodynamic loads based on the third-order piston theory are used and the panel flutter equations are derived via Galerkin’s method. Periodic solutions and their bifurcations are obtained by using a predictor-corrector type of numerical integration method, i.e., the Shooting Method, in conjunction with the Arclength Continuation Method for the static solution. For the perfect panel, the amplitudes and frequency of flutter obtained by the Shooting Method are shown to compare well with results from the Method of Multiple Scales when linear aerodynamics is considered and compressive loads are absent. It is seen that the presence of aerodynamic nonlinearities could result in the hard flutter phenomenon, i.e., a violent transition from the undisturbed equilibrium state to that of finite motions which may occur for pre-critical speeds also. Results show that linear aerodynamics correctly predicts the immediate post-flutter behavior of thin panels only. When compressive edge loads or edge restraints are applied, in certain cases multiple periodic solutions are found to coexist with the stable static solution, or multiple buckled states are possible. Thus it is seen that the panel may remain buckled beyond the flutter boundary, or it may flutter within the region where buck-led states exist. Furthermore, the presence of edge restraints normal to the flow tends to stabilize the panel by decreasing the flutter amplitudes and the possibility of hard flutter. Nonperiodic motions (i.e., quasiperiodic and chaotic) of the buckled panel are found to exist, and their associated Lyapunov exponents are calculated. The effects of transverse shear flexibility, aerodynamic nonlinearities, initial imperfections, and in-plane edge restraints on the stability boundaries are also studied. It is observed that the classical plate theory over-predicts the instability loads, and only the shear deformation theory correctly models the panel which is flexible in transverse shear. When aerodynamic nonlinearities are considered, multiple flutter speeds may exist.