 | | Mechanics of Solids
A Journal of Russian Academy of Sciences | | Founded
in January 1966
Issued 6 times a year
Print ISSN 0025-6544
Online ISSN 1934-7936 |
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| I. I. Ivanchenko, "Design of framed structures modeling bridges for moving loads," Mech. Solids. 36 (4), 121-132 (2001) |
| Year |
2001 |
Volume |
36 |
Number |
4 |
Pages |
121-132 |
| Title |
Design of framed structures modeling bridges for moving loads |
| Author(s) |
I. I. Ivanchenko (Moscow) |
| Abstract |
We suggest a new method for the design of framed systems for massive
moving loads. To solve this problem for a beam
with a load moving on it, two methods have been basically applied.
(These methods can be also extended to other structures.) The first
method involves the generalized coordinates to be introduced by expanding
the deflection of the beam in terms of its natural vibration modes and reduces
the problem to the solution of a system of ordinary differential equations
with variable coefficients [1-3]. The second method involves the decomposition
of the beam-load system and reduces the problem to solving an integral
equation for the dynamic response of the load [4, 5]. In the methods
of [1-3], the increase in the number of modes to be preserved implies an
increase in the order of the system of differential equations. The methods
of [4, 5] face difficulties associated with the conditional stability of
difference schemes. A method that combines these two approaches and removes
their drawbacks is presented in [6] for beams. This method fairly simply
takes into account any number of natural vibration modes in the deflection
expansion and uses the system of governing equations that has a minimal number
of unknowns (as is the case for the method of integral equations [4, 5])
and can be integrated by means of an unconditionally stable scheme. In the method
suggested in the present paper, these advantages are preserved for the case
of design of framed systems for moving loads with nonzero mass.
In the design of bridges, framed structures are utilized to model various
load bearing components, including the solid superstructure, frame trestles, and trusses.
The traditional approaches to the design of framed structures for a moving load
utilize finite elements (FM), with polynomials being used to approximate
displacements [7-9]. As is the case for the classical problem of the motion
of a load along a beam, both of the cited approaches taking into account
the moving load can be applied to framed structures, with the specific features
of their numerical implementation being preserved. Both these methods utilize
finite elements either for solving an auxiliary eigenvalue problem
or for the construction of the governing equations to be integrated directly.
These approaches are reduced to the construction of discrete analogues
for the Inglis method [7] and for the method of integral equations [9].
Both these methods require fine spatial discretization of the structure,
since the analysis of systems subjected to impulsive, rapidly moving
or vibrational loads requires a great number of vibration modes to be
taken into account. However, the extension of the frequency spectrum,
as has been mentioned, increases the order of the system of the governing
equations. We aim in the present paper at the removal of this drawback.
The method suggested for framed structures combines the two cited
approaches and utilizes also the method developed earlier for the design
of beams for a moving load [6] and the finite element technique for
the design of distributed framed structures for transient excitations,
including massless moving loads [10]. To take into account a moving load
that has mass, finite (boundary) elements of large length are suggested,
with the displacements being approximated by linear functions
and trigonometric (Fourier) series. The direct integration of the governing
system leads at each step to a system of linear equations for only the
accelerations at the nodes, including the nodes of the framed structure
and the nodes at the points of contact of the structure with the moving load.
In this approach, the increase in the number of the spatial discretization
elements does not increase the order of the system of the governing
equations, and the iterative procedure constructed on the basis of the
mixed method of the structural mechanics is unconditionally stable with
respect to time and permits one to determine the fields of forces,
displacements, and dynamic pressure of moving loads acting on bridges. The
moving loads modeling high-speed trains and automobiles can be considered. |
| References |
| 1. | C. E. Inglis, Mathematical Treatise in Vibrations in Railway Bridges,
University Press, Cambridge, 1934. |
| 2. | V. V. Bolotin, "Analysis of vibrations of bridges under the action
of a moving load," Izv. AN SSSR. OTN. Mekhanika i Mashinostroenie,
No 4, pp. 109-115, 1961. |
| 3. | N. G. Bondar', Yu. G. Koz'min, V. P. Tarasenko, et al., Railway
Bridge-Vehicle Interaction [in Russian], Transport, Moscow, 1984. |
| 4. | A. P. Filippov and S. S. Kokhmanyuk, Dynamic Action of Moving
Loads on Rods [in Russian], Naukova Dumka, Kiev, 1967. |
| 5. | S. S. Kokhmanyuk, E. G. Yanyutin, and L. G. Romanenko,
Vibrations of Deformable Systems under Impulsive and Moving Loads [in Russian],
Naukova Dumka, Kiev, 1980. |
| 6. | I. I. Ivanchenko, "On the action of a moving load on bridges,"
Izv. AN. MTT, No. 6, pp. 180-185, 1997. |
| 7. | T. Borowicz, "Wyteženie belek pod obsiaženiem ruchomym,"
Arch. Inž. Lad., Vol. 24, No. 2, pp. 219-235, 1978. |
| 8. | V. K. Garg, K. H Chu, and T. L. Wang, "A study of railway/vehicle
interaction and elevation of fatigue life," Earthquake Engineering and
Structural Dynamics, Vol. 13, pp. 687-709, 1985. |
| 9. | N. N. Shaposhnikov, S. K. Kashaev, V. B. Babaev, and A. A. Dolganov,
"Design of structures for moving loads with the help of the finite-element
method," Stroitel'naya Mekhanika i Raschet Sooruzhenii, No. 1,
pp. 59-52, 1986. |
| 10. | I. I. Ivanchenko, "Design of framed systems with distributed
parameters for impulsive and moving loads," Prikladnaya Mekhanika,
Vol. 24, No. 9, pp. 109-118, 1988. |
| 11. | L. A. Rozin, Variational Statements of Problems for
Elastic Systems [in Russian], Izd-vo LGU, Leningrad, 1978. |
| 12. | I. I. Ivanchenko, "On the dynamic analysis of bridges
for a moving load in the form of a railway train,"
Stroitel'naya Mekhanika i Raschet Sooruzhenii, No. 6, pp. 26-31, 1989. |
| 13. | S. V. Vershinskii, V. N. Danilov, and V. D. Khusidov,
Dynamics of a Railway Vehicle [in Russian], Transport, Moscow, 1991. |
| 14. | A. Ya. Kogan, A. A. L'vov, and M. A. Levinzon,
"Characteristics of railway vehicles and track irregularities
for velocities not exceeding 350km/h," Vestnik VNIIZhT,
No. 3, pp. 10-14, 1991. |
|
| Received |
08 December 1998 |
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