this paper presents the high order frequency-amplitude relationship for nonlinear transversely vibrating beams with odd and even nonlinearities using homotopy perturbation method with an auxiliary term (hpmat). the governing equations of vibrating buckled beam, beam carrying an intermediate lumped mass and quintic nonlinear beam are investigated to exhibit the reliability and ability of the pro...

This paper presents a fixed-end two-mass system (TMS) with end constraints that permits uncoupled solutions for different masses. The coupled nonlinear models for the present fixed-end TMS were solved using the continuous piecewise linearization method (CPLM) and detailed investigation on the effect of mass-ratio on the TMS response was conducted. The investigations showed that increased mass-r...

In this contribution we study the statistical properties of a number of closed-loop identiication methods and parameterizations. A focus will be on asymptotic variance expressions for these methods. By studying the asymptotic variance for the parameter vector estimates we show that indirect methods fail to give better accuracy than the direct method. Some new results for bias distribution in cl...

The famous Hirzebruch signature theorem asserts that the signature of a closed oriented manifold is equal to the integral of the so called L-genus. An immediate corollary of this is the homotopy invariance of < L(M); [M ] >. The L-genus is a characteristic class of tangent bundles, so the above remark is a non-trivial fact. The problem of higher signatures is a generalization of the above consi...

In this paper, some of the formal arguments given by Jones and Kline [J. Math. Phys., v. 37, 1958, pp. 1-28] are made rigorous. In particular, the reduction procedure of a multiple oscillatory integral to a one-dimensional Fourier transform is justified, and a Taylor-type theorem with remainder is proved for the Dirac 8-function. The analyticity condition of Jones and Kline is now replaced by i...

The origin of symbolic manipulation derives from the sheer magnitude of the work involved in the building of perturbation theories, which made inevitable that scientific community became interested in the possibility of constructing those theories with the help of computers. Perturbation theories for differential equations containing a small parameter are quite old. The small perturbation theor...