TY - JOUR
ID - 537808
TI - Coupled Bending-Longitudinal Vibration of Three Layer Sandwich Beam using Exact Dynamic Stiffness Matrix
JO - Journal of Solid Mechanics
JA - JSM
LA - en
SN - 2008-3505
AU - Zare, A.
AU - Rafezy, B
AU - Howson, W.P
AD - School of Engineering, Yasouj University, Yasouj, Iran
AD - Sahand University of Technology, Tabriz, Iran
AD - Independent Consultant, Gwanwyn, Craig Penlline, CF71 7RT, UK
Y1 - 2017
PY - 2017
VL - 9
IS - 4
SP - 730
EP - 750
KW - Sandwich beam
KW - Exact dynamic stiffness matrix
KW - Coupled motion
KW - Transcendental eigenvalue problem
KW - Wittrick-Williams algorithm
DO -
N2 - A Newtonian (vectorial) approach is used to develop the governing differential equations of motion for a three layer sandwich beam in which the uniform distribution of mass and stiffness is dealt with exactly. The model allows for each layer of material to be of unequal thickness and the effects of coupled bending and longitudinal motion are accounted for. This results in an eighth order ordinary differential equation whose closed form solution is developed into an exact dynamic member stiffness matrix (exact finite element) for the beam. Such beams can then be assembled to model a variety of structures in the usual manner. However, such a formulation necessitates the solution of a transcendental eigenvalue problem. This is accomplished using the Wittrick-Williams algorithm, whose implementation is discussed in detail. The algorithm enables any desired natural frequency to be converged upon to any required accuracy with the certain knowledge that none have been missed. The accuracy of the method is then confirmed by comparison with five sets of published results together with a further example that indicates its range of application. A number of further issues are considered that arise from the difference between sandwich beams and uniform single material beams, including the accuracy of the characteristic equation, co-ordinate transformations, modal coupling and the application of boundary conditions.
UR - http://jsm.iau-arak.ac.ir/article_537808.html
L1 - http://jsm.iau-arak.ac.ir/article_537808_129dcaa4478507b5a24d97aea6647aa2.pdf
ER -