{[ promptMessage ]}

Bookmark it

{[ promptMessage ]}

201-Lect 9 - 5 EIGENVALUE PROBLEMS 5.1 The engenvalue and...

Info icon This preview shows pages 1–3. Sign up to view the full content.

View Full Document Right Arrow Icon
MECH201 Engineering Analysis (2009) p. 21 5 EIGENVALUE PROBLEMS 5.1 The engenvalue and eigenvectors Section 27.2.1 Eigenvalue or characteristic value problems are used in a wide variety of engineering contexts involving vibrations, elasticity, and oscillating systems. Let us consider a set of non-homogenous linear algebraic equations of the form [ ] { } { } A x b = where [A] is a square matrix of n rows and columns, {x} and {b} are column vector of n elements. If the determinant of [A] is not zero, [ ] 0 A |, then it is possible to construct the inverse of [A], that is [ ] 1 A - , and a set of unique solution existed and is given by: { } [ ] { } 1 x A b - = On the other hand, the inverse for [A] does not exist if [ ] 0 A = . The result is that there will be no unique solution for {x} For example, [ ] 3 4 1 6 10 2 9 7 3 A - = - the determinant of [A] is zero. The solution for [ ] { } { } 0 A x = is { } 0 3 x α α = - where α is any values. This means that there is not unique solution for the above system of equations. Eigenvalue problems associated with engineering are of the form [ ] { } { } A x x λ = Where λ is an unknown parameter called the eigenvalue or characteristic value. Let [I] be a unit matrix of the same size as [A]. The above equation can be rewritten as [ ] [ ] { } 0 A I x λ - = The determinant [ ] [ ] A I λ - must be zero to determine λ , giving a solution {x} as an eigenvector .
Image of page 1

Info icon This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document Right Arrow Icon
MECH201 Engineering Analysis (2009) p. 22 5.2 A Mass-Spring System
Image of page 2
Image of page 3
This is the end of the preview. Sign up to access the rest of the document.

{[ snackBarMessage ]}

What students are saying

  • Left Quote Icon

    As a current student on this bumpy collegiate pathway, I stumbled upon Course Hero, where I can find study resources for nearly all my courses, get online help from tutors 24/7, and even share my old projects, papers, and lecture notes with other students.

    Student Picture

    Kiran Temple University Fox School of Business ‘17, Course Hero Intern

  • Left Quote Icon

    I cannot even describe how much Course Hero helped me this summer. It’s truly become something I can always rely on and help me. In the end, I was not only able to survive summer classes, but I was able to thrive thanks to Course Hero.

    Student Picture

    Dana University of Pennsylvania ‘17, Course Hero Intern

  • Left Quote Icon

    The ability to access any university’s resources through Course Hero proved invaluable in my case. I was behind on Tulane coursework and actually used UCLA’s materials to help me move forward and get everything together on time.

    Student Picture

    Jill Tulane University ‘16, Course Hero Intern