Research on the application of the parameter freezing precise exponential integrator in vehicle-road coupling vibration

doi:10.1007/s10483-025-3220-7

摘要/Abstract

Abstract:

The vehicle-road coupling dynamics problem is a prominent issue in transportation, drawing significant attention in recent years. These dynamic equations are characterized by high-dimensionality, coupling, and time-varying dynamics, making the exact solutions challenging to obtain. As a result, numerical integration methods are typically employed. However, conventional methods often suffer from low computational efficiency. To address this, this paper explores the application of the parameter freezing precise exponential integrator to vehicle-road coupling models. The model accounts for road roughness irregularities, incorporating all terms unrelated to the linear part into the algorithm's inhomogeneous vector. The general construction process of the algorithm is detailed. The validity of numerical results is verified through approximate analytical solutions (AASs), and the advantages of this method over traditional numerical integration methods are demonstrated. Multiple parameter freezing precise exponential integrator schemes are constructed based on the Runge-Kutta framework, with the fourth-order four-stage scheme identified as the optimal one. The study indicates that this method can quickly and accurately capture the dynamic system's vibration response, offering a new, efficient approach for numerical studies of high-dimensional vehicle-road coupling systems.

Key words: vehicle-road coupled dynamics, dynamic response, parameter freezing precise exponential integrator, Newmark-β integration

中图分类号:

O242

. [J]. Applied Mathematics and Mechanics (English Edition), 2025, 46(2): 373-390.

Yu ZHANG, Chao ZHANG, Shaohua LI, Shaopu YANG. Research on the application of the parameter freezing precise exponential integrator in vehicle-road coupling vibration[J]. Applied Mathematics and Mechanics (English Edition), 2025, 46(2): 373-390.

图/表 17

Parameter	Unit	Numerical value	Parameter	Unit	Numerical value
$m 1$	kg	190	$L$	m	100
$m 2$	kg	10 109	$b$	m	6
$k 1$	$N ⋅ m − 1$	36 000 000	$h$	m	0.1
$k 2$	$N ⋅ m − 1$	9 000 000	$E$	GPa	$1.6 × 109$
$c 1$	$N ⋅ s ⋅ m − 1$	700	$ρ$	$kg ⋅ m − 3$	$2.5 × 103$
$c 2$	$N ⋅ s ⋅ m − 1$	80 000	$k r$	$N ⋅ m − 2$	$4.8 × 107$
			$c r$	$N ⋅ s ⋅ m − 2$	$3 × 105$

FPEI4-4 time step obtained $t$ /s	Multiple	Calculation time $t$ /s		Error level of the result
FPEI4-4 time step obtained $t$ /s	Multiple	FPEI4-4	Newmark- $β$	Error level of the result
0.001	10	338	242	Small
0.01	100	16	242	Small
0.025	250	7	242	Large

Modal truncation order $N M$	Calculation time $t$ /s		Error level of the result
Modal truncation order $N M$	FPEI4-4	Newmark- $β$	Error level of the result
50	2	26	Small
80	4	64	Small
100	7	104	Small
150	16	242	Small

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