INTEGRATION OF BEAM FUNCTIONS

The beam functions satisfying d4φ/dξ4=β4φ with the associated boundry conditions are convenient admissible comparison functions for the approximated solutions of complex structural problems by the well known Rayleigh-Ritz method. Reliable integration formulae for products of various beam functions φ and ψ with an arbitrary funtion θ are essential. Felgar's recurrence formula for ∫θφψ dξ is found to be in error and is corrected here. The condition when the characteristic values of φ and ψ are identical is also considered. A simple subroutine is given to evaluate ∫θ(ξ) (dnφ/dξn)(dmφ/dξm)dξ for all possible sets of boundary conditions. Applications to the free vibration of nonuniform beams and plate systems are demonstrated.