What is the condition for Rayleigh Ritz method?

The Rayleigh–Ritz method determines the approximate solution u ¯ x by substituting the constants ai into Eq. (1.22). The method is generally understood to be a method which determines the coefficients ai so as to make the distance between the approximate solution u ¯ x and the exact one u(x) minimum.

Why preferred the Rayleigh Ritz method?

The Rayleigh–Ritz method is often used in mechanical engineering for finding the approximate real resonant frequencies of multi degree of freedom systems, such as spring mass systems or flywheels on a shaft with varying cross section. It is an extension of Rayleigh’s method.

What is the principle used in Rayleigh method for determination of frequencies of multi degrees of freedom systems?

The Rayleigh’s quotient represents a quick method to estimate the natural frequency of a multi-degree-of-freedom vibration system, in which the mass and the stiffness matrices are known. equal to the static displacement from an applied force that has the same relative distribution of the diagonal mass matrix terms.

What are essential boundary conditions?

The essential boundary conditions are the set of. boundary conditions that are sufficient for solving the differential equations completely. The natural. boundary conditions are the boundary conditions involving higher order derivative terms and are not.

What is variational method in FEM?

It is widely used for deriving finite element equations whenever classical variational statement is available for the given problem. A basic knowledge of calculus of variations is required to use variational approach. The Rayleigh-Ritz method is an approximate method based on the variational formulation.

What is trial function?

The exact function is not known; the trial function contains one or more adjustable parameters, which are varied to find a lowest energy configuration. The trial wave-function will always give an expectation value larger than or equal to the ground-energy.