Abstract
Three new Fourier p-elements of rectangular, skew and trapezoidal shapes are given analytically for plane viscoelastic vibration problems. The natural frequencies of the plane viscoelastic structures with complex Young’s modulus are computed by a complex eigenvalue solver. With the additional Fourier degrees of freedom, the accuracy of the computed natural frequencies is greatly increased. Since trigonometric functions are used as enriching functions instead of polynomials in the proposal elements, the ill-conditioning problems associated with polynomials of higher degree in the traditional p-version finite element method are avoided. The two mapped plane coordinates in the Jacobian are uncoupled for trapezoidal elements whose element matrices can then be integrated analytically. A triangle can easily be divided into three trapezoids. Therefore, any plane viscoelastic problem with polygonal shape can be analyzed by a combination of rectangular and trapezoidal elements. Numerical examples show that the convergence of the present elements is very fast with respect to the number of trigonometric terms. The natural frequencies of several polygonal viscoelastic plates subject to in-plane vibration are presented.
Published Version
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.
