
AIMS Mathematics, 2019, 4(3): 751762. doi: 10.3934/math.2019.3.751.
Research article Topical Section
Export file:
Format
 RIS(for EndNote,Reference Manager,ProCite)
 BibTex
 Text
Content
 Citation Only
 Citation and Abstract
A generalized mathematical model for a class of mechanical systems with lumped and distributed parameters
1 Chair of Applied Mathematics, East Siberian State University of Technology and Management, UlanUde, 670013, Russia
2 Institute of Mathematics and Computer Science, Department of Applied Mathematics and differential equations, Buryat State University, UlanUde, 670000, Russia
Received: , Accepted: , Published:
Topical Section: Mathematical modeling
Keywords: mechanical systems; system of rigid bodies; generalized mathematical model; EulerBernoulli beam; hybrid systems of differential equations; Hamiltonian variation principle
Citation: Arsalan D. Mizhidon. A generalized mathematical model for a class of mechanical systems with lumped and distributed parameters. AIMS Mathematics, 2019, 4(3): 751762. doi: 10.3934/math.2019.3.751
References:
 1.A. D. Mizhidon, K. A. Mizhidon, Eigenvalues of boundary value problem for a hybrid system of differential equations, Siberian Electronic Mathematical Reports, 13 (2016), 911922.
 2.D. W. Chen, The exact solution for free vibration of uniform beams carrying multiple twodegreeoffreedom springmass systems, J. Sound Vib., 295 (2006), 342361.
 3.T. P. Chang, C. Y. Chang, Vibration analysis of beams with a twodegreeoffreedom springmass system, Int. J. Solids Struct., 35 (1998), 383401.
 4.P. D. Cha, Free vibrations of a uniform beam with multiple elastically mounted twodegreeoffreedom systems, J. Sound Vib., 307 (2007), 386392.
 5.J.J. Wu, A. R. Whittaker, The natural frequencies and mode shapes of a uniform cantilever beam with multiple twoDOF springmass systems, J. Sound Vib., 227 (1999), 361381.
 6.S. Naguleswaran, Transverse vibrations of an EulerBernoulli uniform beam carrying several particles, Int. J. Mech. Sci., 44 (2002), 24632478.
 7.S. Naguleswaran, Transverse vibration of an EulerBernoulli uniform beam on up a five resilient supports including ends, J. Sound Vib., 261 (2003), 372384.
 8.H. Su, J. R. Banerjee, Exact natural frequencies of structures consisting of two part beammass systems, Struct. Eng. Mech., 19 (2005), 551566.
 9.J.S. Wu, Alternative approach for free vibration of beams carrying a number of twodegree of freedom springmass systems, J. Struct.Eng., 128 (2002), 16041616.
 10.J.S. Wu, H.M. Chou, A new approach for determining the natural frequencies and mode shapes of a uniform beam carrying any number of spring masses, J. Sound Vib., 220 (1999), 451468.
 11.J.S. Wu, D.W. Chen, Dynamic analysis of a uniform cantilever Beam carrying a number of elastically mounted point masses with dampers, J. Sound Vib., 229 (2000), 549578.
 12.S. Kukla, B. Posiadala, Free vibrations of beams with elastically mounted masses, J. Sound Vib., 175 (1994), 557564.
 13.S. Kukla, The green function method in frequency analysis of a beam with intermediate elastic supports, J. Sound Vib., 149 (1991), 154159.
 14.A. D. Mizhidon, Theoretical foundations of the study of a certain class of hybrid systems of differential equations, Itogi Nauki i Tekhniki. Seriya "Sovrem. Mat. Pril. Temat. Obz.", 155 (2018), 3864.
Reader Comments
© 2019 the Author(s), licensee AIMS Press. This is an open access article distributed under the terms of the Creative Commons Attribution Licese (http://creativecommons.org/licenses/by/4.0)
Associated material
Metrics
Other articles by authors
Related pages
Tools
your name: * your email: *