Analytical solution of seismic power-based equation of motion.

This research proposes an innovative power-based equation of motion (PBEM) for the single degree of freedom (SDOF) system considering seismic excitation. The external or input frequency function, solution of time, relation between external and kinetic powers, and equation of strain-power (SP) are obtained by solving the power balance equation (PBE). The external frequency function is related to both the particular and total solutions of the PBEM.

Analytical solution of nano-concrete-epoxy interaction area considering static equilibrium.

This research proposes an analytical solution of the nano-concrete-epoxy interaction area within nano crack region of the reinforced concrete beam by applying Newton's third law in static equilibrium. For deriving the governing equation, the imaginary beam with free ends (no support) is considered within nano crack region. This imaginary beam is acted along the imaginary line of concrete-epoxy interface.