The pseudospectral abscissa is defined as the maximum real part of the characteristic roots in the pseudospectrum and, therefore, it is for instance important from a robust stability point of view.
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Lai H-Y, Hsu J-C, Chen C-K (2008) An innovative eigenvalue problem solver for free vibration of Euler–Bernoulli beam by using the Adomian decomposition method.The pseudospectrum of a linear time-invariant system is the set in the complex plane consisting of all the roots of the characteristic equation when the system matrices are subjected to all possible perturbations with a given upper bound.
Liu Y, Gurram CS (2009) The use of He’s variational iteration method for obtaining the free vibration of an Euler-Bernoulli beam. J Sound Vib 48(4):565–568īanerjee JR (2012) Free vibration of beams carrying spring-mass systems-a dynamic stiffness approach. Maurizi MJ, Rossi RE, Reyes JA (1976) Vibration frequencies for a uniform beam with one end spring hinged and subjected to a translational restraint at the other end. J Sound Vib 302:442–456ĭarabi MA, Kazemirad S, Ghayesh MH (2012) Free vibrations of beam–mass–spring systems: analytical analysis with numerical confirmation. Lin H-Y, Tsai Y-C (2007) Free vibration analysis of a uniform multi-span beam carrying multiple spring––mass systems. Hamdan MN, Jubran BA (1991) Free and forced vibrations of a restrained cantilever beam carrying a concentrated mass. Wu J-S, Hsu T-F (2007) Free vibration analyses of simply supported beams carrying multiple point masses and spring-mass systems with mass of each helical spring considered. 2013 2nd international conference on civil engineering (ICCEN 2013), Stockholm, Sweden 5, Part 2 of, Montreal, CanadaĬhalah-Rezgui L, Chalah F, Falek K, Bali A, Nechnech A (2013) Transverse vibration analysis of uniform beams under various ends restraints. J Test Eval JTEVA 25(5):522–524įalek K, Rezgui L, Chalah F, Bali A, Nechnech A (2013) Structural element vibration analysis. Murphy JF (1997) Transverse vibration of a simply supported beam with symmetric overhang of arbitrary length. SIAM Rev 40:1–39Ĭhu MT, Gene HG (2005) Inverse eigenvalue problems theory, algorithms, and applications. Kluwer Academic Publications, DordrechtĬhu MT (1992) Inverse eigenvalue problems. Gladwell GML (2004) Inverse problems in vibrations, 2nd edn. Meenakshi Sundaram M, Ananthasuresh GK (2012) A note on the inverse mode shape problem for bars, beams, and plates. Paz M (2000) Structural dynamics theory and computation. J Sound Vib 225(5):935–988Ĭlough RW, Penzien J (2003) Dynamics of structures, 3rd edn. Han SM, Benaroya H, Wei T (1999) Dynamics of transversely vibrating beams: using four engineering theories. Wilson EL (2008) Three dimensional static and dynamic analysis of structures, 3 rd edn. Prentice-Hall, Englewood Cliffsīathe KJ (1996) Finite element procedures. Keywordsīathe KJ, Wilson EL (1976) Numerical methods in finite element analysis. The results as found are in agreement with analytical ones and after introducing the rotational restraint at the right-hand end, an intermediate behavior is initiated by varying the s/L (span length/beam length) ratio, allowing a simplified extraction of the fundamental vibration frequency for various values of K r (rotational restraint). When the rotational restraint value increases the beam is considered first pinned-pinned and then pinned-fixed behavior is obtained. It is compared to theoretical, energetic Rayleigh method results and those due to the finite element method for the simply supported beam, pinned-clamped and free-fixed beam (cantilever beam). In these two studied cases, the rotational restraint is not considered. The first step of validation is relative to the extreme situations where either the overhang or the intermediate span length is zero (span length approx. The purpose of this investigation consists of treating similar beam cases with and without a rotational restraint at one node. Many situations are studied using the finite element method based on the Euler-Bernoulli assumptions to analyze beams vibration, without elastic restraints. In this study, a beam with one overhang, having a rotational restraint at one pinned end and a support of variable abscissa is investigated. To carry out a dynamic analysis of vibrating systems, different methods exist and numerical methods take a large place.