Abstract
Actual structures have continuously distributed properties, say distributed elasticity and mass, which are continuous systems with infinite DOFs. In the present chapter, the fundamental procedure of analyzing the dynamic properties and dynamic responses of continuous systems is illustrated by using a bending straight beam (Bernoulli–Euler beam). The differential equation of motion of a straight beam is derived, and the dynamic properties (natural frequencies and modes) are investigated. Using Betti’s law and the concept of principal vibration, the orthogonality of mode shapes is demonstrated. Based on the modal expansion of displacements and the mode superposition method, the differential equation of motion is transformed into independent differential equations, which are easily solved by Duhamel integral method. Finally, the responses of free and forced vibrations are evaluated using the mode superposition method.
Sign-in/Register to access full text options 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callDisclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.
