Abstract
This article proposes a new orthogonal basis for the spatial discretization tracking the dynamic response of shear deformable beams. The corresponding initial boundary value differential equations of motion are dealt with focusing on Timoshenko and Reddy–Bickford beam theories. The presented technique takes advantage of a compatible trigonometric set of functions defining the rotation field in combination with orthogonal splines for the transverse deformation. A broad survey is conducted gaining the beam natural frequencies in free vibration; the forced vibration of the beam is attacked considering a traveling inertial body interacting with the base beam. For different beam end-fixity cases, the orthogonal basis could be straightforwardly constructed representing a rapid convergence. In this regard, a remedy is achieved for the inconvenient procedure of creating the shape functions in other competing methodologies.
Similar content being viewed by others
References
Frýba L (1999) Vibration of solids and structures under moving loads, 3rd edn. Thomas Telford, London
Olsson M (1991) On the fundamental moving load problem. J Sound Vib 145:299–307
Ouyang H (2011) Moving-load dynamic problems: A tutorial (with a brief overview). Mech Syst Signal Process 25:2039–2060
Eftekhari SA, Jafari AA (2014) A variational formulation for vibration problem of beams in contact with a bounded compressible fluid and subjected to a traveling mass. Arab J Sci Eng 39:5153–5170
Akin JE, Mofid M (1989) Numerical solution for response of beams with moving mass. J Struct Eng 115:120–131
Yang YB, Yau JD, Hsu LC (1997) Vibration of simple beams due to trains moving at high speeds. Eng Struct 19:936–944
Rao GV (2000) Linear dynamics of an elastic beam under moving loads. ASME J Vib Acoust 122:281–289
Yavari A, Nouri M, Mofid M (2002) Discrete element analysis of dynamic response of Timoshenko beams under moving mass. Adv Eng Softw 33:143–153
Nikkhoo A, Kananipour H (2014) Numerical solution for dynamic analysis of semicircular curved beams acted upon by moving loads. Proc IMechE Part C J Mech Eng Sci. doi:10.1177/0954406213518908
Kargarnovin MH, Ahmadian MT, Talookolaei RAJ (2012) Dynamics of a delaminated Timoshenko beam subjected to a moving oscillatory mass. Mech Based Des Struct Mach Int J 40:218–240
Ghannadiasl A, Mofid M (2013) Dynamic Green Function for response of Timoshenko beam with arbitrary boundary conditions. Mech Based Des Struct Mach Int J 42:97–110
Eftekhar Azam S, Mofid M, Afghani Khoraskani R (2013) Dynamic response of Timoshenko beam under moving mass. Scientia Iranica, Transaction A: Civil Engineering. doi:10.1016/j.scient.2012.11.003
Ahmadi M, Nikkhoo A (2014) Utilization of characteristic polynomials in vibration analysis of non-uniform beams under a moving mass excitation. Appl Math Modell 38:2130–2140
Bhat R (1986) Transverse vibrations of a rotating uniform cantilever beam with tip mass as predicted by using beam characteristic orthogonal polynomials in the Rayleigh-Ritz method. J Sound Vib 105:199–210
Leissa AW, Qatu MS (2011) Vibration of continuous systems. McGraw Hill, New York
Ebrahimzadeh Hassanabadi M, Nikkhoo A, Vaseghi Amiri J, Mehri B (2013) A new orthonormal polynomial series expansion method in vibration analysis of thin beams with non-uniform thickness. Appl Math Modell 37:8543–8556
Wang C, Reddy JN, Lee K (2000) Shear deformable beams and plates: relationships with classical solutions. Elsevier BV
Chakraverty S (2010) Vibration of plates. CRC press
Brogan WL (1991) Modern control theory. Prentice-Hall, New Jersey
Nikkhoo A, Rofooei F, Shadnam M (2007) Dynamic behavior and modal control of beams under moving mass. J Sound Vib 306:712–724
Nikkhoo A (2014) Investigating the behavior of smart thin beams with piezoelectric actuators under dynamic loads. Mech Syst Signal Process 45:513–530
Lee J, Schultz WW (2004) Eigenvalue analysis of Timoshenko beams and axisymmetric Mindlin plates by the pseudospectral method. J Sound Vib 269:609–621
Kiani K, Nikkhoo A, Mehri B (2009) Prediction capabilities of classical and shear deformable beam models excited by a moving mass. J Sound Vib 320:632–648
Author information
Authors and Affiliations
Corresponding author
Additional information
Technical Editor: Fernando Alves Rochinha.
Rights and permissions
About this article
Cite this article
Nikkhoo, A., Farazandeh, A. & Ebrahimzadeh Hassanabadi, M. On the computation of moving mass/beam interaction utilizing a semi-analytical method. J Braz. Soc. Mech. Sci. Eng. 38, 761–771 (2016). https://doi.org/10.1007/s40430-014-0277-1
Received:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s40430-014-0277-1