In-plane vibrations of a transversely isotropic arch

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Virginia Polytechnic Institute and State University


A model for the dynamic response of a laminated composite arch is developed from classical shell theory. The problem is reduced from a shell to an arch by making an assumption that the variation of the field of variables in the direction of the width of the arch is small compared to those in other directions. Standard separation of variables is used to change from a system of partial differential equations to that of ordinary differential equations. Several methods of solution are explored, namely the Laplace transformation, the method of particular solutions, and the eigensolution. The eigensolution is chosen as the the most efficient in terms of computer time and is the easiest to modify. The free vibration of the arch is explored and the natural frequencies of the system are determined. The response of the arch to general forcing functions is also considered, by the use of the Fourier transformation technique. Damping through material viscoelasticity and use of the model in evaluation of experimental data are also discussed.