On the viscoelastic beam subjected to moving mass. (English) Zbl 1423.74503
Summary: Two methods are presented that can be used to determine the dynamic behavior of viscoelastic beams with different boundary conditions, carrying a moving mass. An analytical-numerical formulation that transforms the governing differential equation in viscoelastic media into a set of ordinary differential equations and thereafter a discrete element model based on assumption that continuous viscoelastic beam can be replaced by a system of rigid bars and joints which resist relative rotation of attached bars. The physical properties of the joints can be found through considering the viscoelastic model of beams material. Correctness of results has been ascertained by a comparison, made between the above two techniques and good agreements has been achieved.
MSC:
| 74K10 | Rods (beams, columns, shafts, arches, rings, etc.) |
| 74B99 | Elastic materials |
| 74S30 | Other numerical methods in solid mechanics (MSC2010) |
Keywords:
viscoelastic beam; moving mass; Kelvin model; numerical analytical method; discrete element modelReferences:
| [1] | Jeffcott, H. H.: On the vibration of beams under the action of moving loads, Philos mag ser 7, No. 8, 66 (1929) · JFM 55.0460.03 |
| [2] | Steuding, H.: Die schwinging von tragern bei bewegten lasten, Ingen arch 5, 275 (1934) · JFM 60.0715.02 · doi:10.1007/BF02084154 |
| [3] | Odman STA. Differential equation for calculation of vibrations produced in load bearing structures by moving loads. Preliminary publications International Assn. for bridge and structural engineering, 3rd congress, Liege; 1948. |
| [4] | Pestel, E.: Tragwerksauslenkung unter bewegter last, Ingen arch 19, 378 (1951) · Zbl 0044.20901 · doi:10.1007/BF00534809 |
| [5] | Stanisic, M. M.; Hardin, J. C.: On response of beams to an arbitrary number of moving masses, Franklin inst 287, 115 (1969) |
| [6] | Akin, J. E.; Mofid, M.: Numerical solution for response of beams with moving mass, ASCE J struct mech 115, No. 1, 120-131 (1989) |
| [7] | Mofid, M.; Shadnaam, M.: On dynamic response of rectangular plate with moving mass, Thin wall struct 39, 797-806 (2001) |
| [8] | Mofid, M.; Akin, J. E.: Discrete element response of beams with traveling mass, Adv eng softw 25, 321-331 (1995) |
| [9] | Mofid, M.; Shadnaam, M.: On the response of beams with internal hinges, under moving mass, Adv eng softw 31, 323-328 (2000) |
| [10] | Yavari, A.; Mofid, M.: Discrete element analysis of dynamic response of Timoshenko beams under moving mass, Adv eng softw 33, 143-153 (2001) · Zbl 1042.68692 · doi:10.1016/S0965-9978(02)00003-0 |
| [11] | Bowe, C. J.; Mullarkey, T. P.: Unsprung wheel – beam interactions using modal and finite element models, Adv eng softw 39, 911-922 (2008) · Zbl 1234.74052 |
| [12] | Vicat, L. T.: Note sur lallognement progressive du fil the fer soumis a diverses tensions, Ann pnnts chausees mmem docum 7 (1834) |
| [13] | Christensen, R. M.: Theory viscoelasticity, (1982) · Zbl 0511.65061 |
| [14] | Renady, M.; Hrus, W.; Nohel, W. J.: Mathematical problems in viscolasticity, (1987) · Zbl 0719.73013 |
| [15] | Gurtin, M. E.; Strengberg, E.: On the linear theory of viscoelasticity, Arch ration mech anal 11, 291-356 (1962) · Zbl 0107.41007 · doi:10.1007/BF00253942 |
| [16] | Bland, D. R.: The theory of linear viscoelasticity, (1960) · Zbl 0108.38501 |
| [17] | Flugge, W.: Viscoelasticity, (1967) |
| [18] | Golden, J. M.; Graham, G. A.: Boundary value problems in linear viscoelasticity, (1988) · Zbl 0655.73021 |
| [19] | Young, D.; Flegar, R.: Table of characteristic functions representing normal modes of vibration of beam, (1949) |
| [20] | Shames, I. H.; Cozzarelli, F. A.: Elastic and inelastic stress analysis, (1983) · Zbl 0759.73002 |
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.
