Systematic lumped parameter models for foundations based on polynomial fraction approximation. - Wu, Wen-Hwa (Earthquake engineering & structural dynamics.)
Based on the approximation by polynomial fraction, a series of systematic lumped parameter models are developed in this paper for efficiently representing the dynamic behaviour of unbounded soil. Concise formulation is first employed to represent the dynamic flexibility function of foundation with a ratio of two polynomials. By defining an appropriate quadratic error function, the optimal coefficients of the polynomials can be directly solved from a system of linear equations. Through performing partial fraction expansion on this polynomial fraction and designing two basic discrete element models corresponding to the partial fractions, systematic lumped parameter models can be conveniently established by connecting these basic units in series. Since the systematic lumped parameter models are configured without introducing any mass, the foundation input motion can be directly applied to these models for their applications to the analysis of seismic excitation. The effectiveness of these new models is strictly validated by successfully simulating a semi infinite bar on an elastic foundation. Subsequently, these models are applied for representing the dynamic stiffness functions for different types of foundation. Comparison of the new models with the other existing lumped parameter models is also made to illustrate their advantages in requiring fewer parameters and featuring a more systematic expansion.