Introduction to Finite Element Vibration Analysis

Abstract

This is an introduction to the mathematical basis of finite element analysis as applied to vibrating systems. Finite element analysis is a technique that is very important in modeling the response of structures to dynamic loads. Although this book assumes no previous knowledge of finite element methods, those who do have knowledge will still find the book to be useful. It can be utilised by aeronautical, civil, mechanical, and structural engineers as well as naval architects. This second edition includes information on the many developments that have taken place over the last twenty years. Existing chapters have been expanded where necessary, and three new chapters have been included that discuss the vibration of shells and multi-layered elements and provide an introduction to the hierarchical finite element method.

Thickness-shear vibration analysis of circular quartz crystal plates by a differential quadrature hierarchical finite element method

“…The Serendipity shape functions at other corners and edges are of similar form as Eqs. (24) and (25). The subscripts k ¼ 1; 2; .…”

“…This work corrected some mistakes therein, made a few improvements and applied the DQHFEM to TS vibration of crystal plates. The DQHFEM incorporated the advantages of high accuracy and compact formulas of the DQFEM [18,19] into the hierarchical finite element method (HFEM) [25,26]. The numerical stability problem of high-order or very high-order hierarchical basis is overcome by using the recursion formula.…”

Modelling piezoelectric excitation in waveguides using the semi-analytical finite element method

“…In this work an 8-node quadrilateral biquadratic element was used for which the shape functions may be found in any standard textbook on the finite element method, e.g. [37].…”

Static and free vibration analyses of stiffened folded plates using a cell-based smoothed discrete shear gap method (CS-FEM-DSG3)

“…in which e is the eccentricity between the mid-plane of plate and the centroid of beam; A is the cross area of beam; I s is the second moment of stiffener cross-sectional area about the axis which goes through the centroid of the stiffener and is parallel with the s-axis; and J is the St Venant's torsion constant [57] and approximated by J ≈ 0.025A 4 /I r where I r is the second moment of stiffener cross-sectional area about an axis going through the centroid of stiffener and being parallel with the r-axis.…”