As this equation is a set of uncoupled equations, hence, each equation is similar to that of a single degree of freedom system and the solution of this system of equations can be easily obtained. Here is known as principal coordinates.

Summary

In this chapter the following concepts are learned

• Flexibility influence coefficients
• Reciprocity theorem
• Stiffness matrix approach
• Flexibility matrix approach
• Normal mode of vibration
• Eigenvalues and eigenvectors
• Determination of normal modes by adjoint matrix method
• Free vibration using normal modes
• Orthogonality principle of normal modes
• Modal matrix
• Weighted modal matrix
• Reduction of coupled equation of motion to uncoupled equation of motion.