# Dynamic Characteristics Analysis of a Rigid Body System with Spatial Multi-Point Supports
###### Abstract  
This paper presents the dynamic characteristics analysis of a rigid body system with spatial multi-point elastic supports, as well as the sensitivity analysis of support parameters. A rigid object is characterized by six degrees-of-freedom (DOFs) motions and considering the spatial location vector decomposition of elastic supports, a rigid body system dynamic model with spatial multi-point elastic supports is derived via the Lagrangian energy method. The system modal frequencies are calculated, and to be verified by finite element modal analysis results. Next, based on the above-mentioned model, system modal frequencies are obtained under different support locations, where the support stiffness components are different. Interpolate the stiffness components corresponding to each support location, calculate system modal frequencies, and the response surface model (RSM) for system modal frequencies is established. Further, based on the RSM modal analysis results, the allowable support location for the system modal insensitive area can be obtained. At last, a lubricating oil-tank system with four supports is taken as an example, and the effects of support spatial locations and stiffness components on the system inherent characteristics are discussed. This present work can provide a basis for the dynamic design of the spatial location and stiffness for this type of installation structures. spatial multi-point supports; system dynamic model; support stiffness decomposition; response surface model; parameter sensitivity analysis +
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spatial multi-point elastic supports is extensive, and it has been highly valued in many fields recently. At present, few studies on the dynamics of a lubrication oil tank-mounting structure system with spatial multi-point elastic supports have been documented, and related studies mainly involve automotive powertrain multi-point mounting system, marine power plant and its vibration isolation structure, and aircraft engine nacelle suspension. The related research work is reviewed as follows. Many achievements have been made in the research on automobile powertrain system dynamics. The core idea of dynamics and optimization design of automobile engine powertrain and its mounting system is to realize the reasonable distribution of powertrain modal frequency and the modal decoupling of the mounting system under excitation, to reduce the vibration transmission rate between the powertrain and the frame, etc. [4; 5; 6]. Only rigid-body modes of the powertrain are considered, the torque roll axis (TRA) decoupling dynamics equation was established by [PERSON] and [PERSON] [7], and the spatial multi-point mounting schemes of an automotive engine gearbox system with oscillating torques excitation was obtained. [PERSON] and [PERSON] [8] took mount rate ratios, mount locations, and orientation angles as key design parameters to investigate the modal characteristics of the multi-point rigid body system and its TRA decoupling problem. [PERSON] et al. [9] established a dynamic model of the engine mounting system and took the mounting stiffness coefficient and orientations of individual mount as design parameters to optimize the support stiffness value obtained via the modal sensitivity method. [PERSON] et al. [10] demonstrated that the performance of the whole engine mounting system not only depended on the performance of individual mounts, but the multi-point supports of the whole system as well, and it is of need to further consider the nonlinear characteristics of the supports. The high-power diesel engine-generator set for locomotives or ships is typically a rigid body system with multi-point supports, and it has the characteristics of multi-point elastic supports in space, multiple source excitation, wide frequency domain, complex system dynamics, and is prone to coupled vibrations.