Rayleigh-Ritz Method

The Rayleigh-Ritz method is a mathematical technique used to approximate the natural frequencies and modes of complex systems, such as structures or vibrations. It involves choosing a set of simple, approximate functions that satisfy the system’s basic conditions. By evaluating an energy-like quantity called the Rayleigh quotient using these functions, the method finds the best approximation of the system’s behavior. Essentially, it transforms a complicated problem into a simpler one, helping engineers and scientists predict how structures or materials will respond to forces without solving extremely difficult equations exactly.