Abstract
Contributions of the second and higher modes to the overturning moment at the base of any classical linear system whose fundamental mode is given by a straight line are shown to vanish identically. A necessary and sufficient condition for a nonuniform shear beam to exhibit a linear first mode is obtained. In particular, it is shown that a shear beam with uniform cross section and mass density will have a linear fundamental mode shape if and only if the shearing stiffness is distributed parabolically. For such a beam, the higher mode shapes are given by odd degree Legendre polynomials.
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.
