Dynamic analysis of RC beams externally bonded with FRP plates using state space method

The state space method is used to investigate the in-plane linear dynamic behavior of reinforced concrete (RC) beams externally bonded with fiber-reinforced polymer (FRP) plates. The state space formulae are properly set up by selecting the appropriate generalized displacements and their conjugated forces as state variables. By adopting the numerically stable method to solve the homogeneous state equations with respect to the mode function vectors, the frequencies and corresponding modal shapes for the free vibration of the FRP-strengthened RC beams under generalized boundary conditions are subsequently obtained. The orthogonality of the vibration modes is established based on the concept of symplectic inner product. By utilizing the modal superposition method, the analytical solutions of the inhomogeneous governing equations for forced vibration and the dynamic responses of the FRP-strengthened RC beams subjected to a uniformly distributed step load, concentrated triangular impulse load at the mid-span, moving concentrated load, and vertical seismic load are obtained. Finally, several numerical examples are presented to validate the results against those obtained by the general-purpose finite element software ABAQUS. Good agreement between the results is observed. Moreover, para-metric studies are conducted to investigate the effects of the cross-sectional geometric and material properties of the FRP plate and adhesive layer on the peak interfacial shear stress at the plate end when the strengthened beam is subjected to a uniformly distributed step load or a moving concentrated load.