Theory of Response Spectrum Analysis EES （反应谱理论分析ee）.pdf

Theory of Response Spectrum Analysis Rebecca L. Johnson Department of Earth and Environmental Science, New Mexico Tech 1. Introduction The basis of engineering seismology is the need to quantify how a given structure will respond to complex ground motions. The structure’s response is determined by its mass and stiffness distributions. For example, stiff buildings will experience low accelerations relative to the ground. Tall buildings tend to accelerate away from ground motions, resulting in low absolute accelerations, where absolute acceleration is the sum of the building’s movement relative to the ground and the ground acceleration. Inhomogeneity within the building may cause twisting (de Silva 2005). Italian engineers began tackling the issue of earthquake response in structural design after the 1908 Reggio Calabria earthquake, which, in conjunction with a tsunami, claimed nearly 100,000 lives. They used a static approach and Danusso, in 1909, suggested that buildings ought to “follow docile the shaking action, not opposing it stiffly.” He used acoustic theory to represent building response as the superposition of n pendulums. His work, however, was not widespread (Trifunac and Todorovska, 2008). The response spectrum method (RSM) was introduced in 1932 in the doctoral dissertation of Maurice Anthony Biot at Caltech. It is an approach to finding earthquake response of structures using waves or vibrational mode shapes. The mathematical principles of oscillations in n-degree-of-freedom systems were taken largely from the theories of acoustics developed by Rayleigh. Biot stated “…[a] building…has a certain number of so called