By N. Shanmugam, C. Wang
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Additional resources for Analysis and Design of Plated Structs. [V. 2 - Dynamics]
92 The stiffness and mass matrices for each element ( )e may be assembled into the global counterpart matrices K and M using equilibrium and compatibility in the usual way. When the energy function Π remains stationary with respect to the vector of structural or global deformations Q, dΠ/dQ = 0, so that in Eq. 93 The nontrivial solution of Eq. 94 where (K + KR – ω M) is known as the dynamic stiffness matrix of the tapered member. 94 is a standard eigenvalue problem, that can be solved using standard packages to determine the natural frequencies ω.
S. (2001), Exact solutions for free vibration of shear-type structures with arbitrary distribution of mass or stiffness. Journal of Acoustical Society of America, 110(4), 1958–1966. , Xiang, Y. and Kitipornchai, S. (1995a), Benchmark solutions for regular polygonal Mindlin plates. Journal of the Acoustical Society of America, 95, 2801– 2871. , Xiang, Y. and Kitipornchai, S. (1995b), Research on thick plate vibration: a literature survey. Journal of Sound and Vibration, 180, 163–176. , Xiang, Y.
A few years later, Okamura and Fukasawa (1998) developed a semianalytical finite strip to analyse the free and forced vibration behaviour of thin-walled members. In the context of the analysis of members acted on by periodic applied loads, these authors carried out a preliminary study concerning the influence of (nonperiodic) compressive normal stresses on the local-plate vibration of I-section and square hollow section members − they drew some important conclusions about the vibration mode configurations and the relation between the member natural frequencies and bifurcation stresses/loads.