Vibration of a transversely isotropic, simply supported and layered rectangular plate

✍ Scribed by Ernian Pan

• Publisher: Springer Netherlands
• Year: 1992
• Tongue: English
• Weight: 515 KB
• Volume: 27
• Category: Article
• ISSN: 0374-3535
• DOI: 10.1007/bf00041648

✦ Synopsis

The propagator matrix method is used in this paper to study the vibration of a transversely isotropic, simply supported and layered rectangular plate. A new system of vector functions is constructed to deal with general surface loading, and general solutions and layer matrices of exact closed form are obtained in this system. The particular solution for forced vibration, and the characteristic equations for free vibration of various surface conditions are then obtained by simple multiplication of layer matrices. These results are presented in such a way that the dilatational and distortional modes of vibration are separated. As a special case of the layered plate, results for the corresponding homogeneous thick plate are also derived. They are presented in a very simple form, and contain the previous results for the static transversely isotropic and the dynamic isotropic plates.

AMS subject classification (1980): 73C99.

List of symbols

h k = z~ -zk _ 1 = thickness of layer k zk_ 1, zk = coordinates of upper and lower interfaces of layer k x, y, z = Cartesian coordinates a, b, H= length, width and thickness of the layered rectangular plate, respectively e) = harmonic oscillation frequency as in exp( -i~ot) p = mass density ui = displacements a~ = stress components S(x, y; m, n), Sl(x, y; m, n) = scalar functions m, n = integers Pxz(m, n), Pea(m, n), P~z(m, n) = loading coefficients ix, it, i Z = unit vectors L, M, N = vector functions UL(z), U~t(z), UN(Z ) = expansion coefficients of displacement vector u TL(z), TM(z), TN(Z ) = expansion coefficients of traction vector T