The free vibration and transient wave in a prestressed Rayleigh-Timoshenko beam subject to arbitrary transverse forces are analyzed by the newly developed method of reverberation-ray matrix (MRRM). The effects of shear deformation and rotational inertia are taken into consideration. With a Fourier transform technique, the general wave solutions with two sets of unknown amplitude coefficients are obtained in the transformed domain for an unbonded prestressed beam under the action of arbitrary external excitations. From the coupling at joints and the compatibility of displacements in each member, the free and forced vibration responses of a beam with various boundary conditions are finally evaluated through certain numerical algorithms. Results are presented for a simply-supported beam subject to either a point fixed load or moving load. Good agreement with the finite element method (FEM) is obtained. The present work is instructive for high-speed railway bridge design and structural health monitoring.
A general formulation of the method of the reverberation-ray matrix (MRRM) based on the state space formalism and plane wave expansion technique is presented for the analysis of guided waves in multilayered piezoelectric structures. Each layer of the structure is made of an arbitrarily anisotropic piezoelectric material. Since the state equation of each layer is derived from the three-dimensional theory of linear piezoelectricity, all wave modes are included in the formulation. Within the framework of the MRRM, the phase relation is properly established by excluding exponentially growing functions, while the scattering relation is also appropriately set up by avoiding matrix inversion operation. Consequently, the present MRRM is unconditionally numerically stable and free from computational limitations to the total number of layers, the thickness of individual layers, and the frequency range. Numerical examples are given to illustrate the good performance of the proposed formulation for the analysis of the dispersion characteristic of waves in layered piezoelectric structures.
GUO YongQiang1, CHEN WeiQiu2,3 & ZHANG YongLiang4 1 Key Laboratory of Mechanics on Disaster and Environment in Western China, Ministry of Education, and School of Civil Engineering and Mechanics, Lanzhou University, Lanzhou 730000, China
