Approximations for Natural Frequencies of Interconnected Walls and Frames

Several approximate formulae for the determination of natural frequencies of interconnected walls and frames with uniform mass and stiffness throughout their height are compared and the range of their applicability discussed. It is found that none of the approximations give high accuracy for the entire range of the stiffness parameter αH encountered in practice. It is recommended that for the fundamental frequency the flexural beam approximation be used for the lower end of the range (αH < 7) and the large αH asymptotic formula be used elsewhere. This ensures that the error never exceeds 5%. For the higher modes there is a choice between three approximations, the maximum error associated with each being practically identical: 10% in the second mode and 5% in the third.