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A z and T 2 m -frequency curves of different mount frequency under small preload ( B 1⁄4 0 : 9 g, Á 1⁄4 1 mm).
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Piecewise-linear isolators are widely used in spacecraft for satisfying ever more stringent vibration requirements of high precision payloads. This paper focuses on ground tests of such isolators, with special consideration of gravitational asymmetry and mount flexibility. With asymmetrical equivalent isolator parameters derived with the extended e...
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... Here, ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi the mount frequency ! 2 is defined as ð m 1 þ m 2 Þ = k 2 , which is chosen as 80 Hz, 100 Hz, 120 Hz and 100,000 Hz (rigid), respectively. The excitation level is B 1⁄4 0 : 9 g, and the clearance size is Á 1⁄4 0 : 1 mm for the large preload and Á 1⁄4 1 mm for the small preload. The responses of relative displacement A z defined by equation (9) and absolute acceleration transfer function of the upper stage mass T m defined by equation (42), respectively, for both preloads are shown in Figures 10 and 11, respectively. As shown in Figure 10, under the condition of small preload the primary resonant peaks for different mount frequencies are almost the same, while a softer mount has a lower second resonant frequency but higher resonant peak in the range of 100 Hz $ 200 Hz. However for the case of a large preload as shown in Figure 11, the mount flexibility greatly affects the primary resonant peaks of A z and T m 2 , and a lower mount frequency means a higher resonant peak. Therefore, the mount flexibility has significant influence on the frequency responses in a different way and parameter study is necessary. Figures 12 and 13 identify some features of the resonant responses: 1. The mount flexibility has stronger influence on the large preload (Figure 13) than on the small preload (Figure 12) when ! is in the range of 80 Hz $ 200 Hz. 2. With a given mount frequency ! 2 , for the case of a small preload (Figure 12), the resonant amplitude of T m 2 (denoted as T m 2 P ) in the nonlinear region decreases the resonant along frequency with the (denoted excitation as À f amplitude m 2 Á P ) increases. but However the large preload does not show similar features, and its response is a highly nonlinear func- 3. tion T m 2 P of and the À excitation. f m 2 Á P tend to become stable gradually as the increase of mount frequency ! 2 , and after 150 Hz the changes are negligible no matter what the excitation amplitude is (Figure 13). In the research stage, a vibration isolator is generally studied with a shake table, i.e. tested on a rigid mount, but in the application stage, an important test for the isolator is the whole spacecraft structure test, i.e. tested on a flexible mount. In this part of the section, we will study the differences in the test results on these two different mounts from the aspects of resonant frequency and resonant amplitude. The relative differences of the resonant amplitude and resonant frequency are defined respectively ...
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Citations
... The former can reduce axial support stiffness, while the latter can reduce the peak disturbance value. Wang and Zheng [159] proposed a transfer function method with two steps to improve the efficiency of parameter optimization design. Kown et al. [160] braided a superelastic shape-memory alloy wire into an annular structure for axial vibration isolation of RWAs. ...
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... Piece-wise linear transfer functions are widely proposed and adopted in literature [24] to perform robust model reduction of systems with non-linear or badly scaled dynamics [25,26]. ...
Diffusion of electric and hybrid vehicles is accelerating the development of innovative braking technologies. Calibration of accurate models of a hydraulic brake plant involves availability of large amount of data whose acquisition is expensive and time consuming. Also, for some applications, such as vehicle simulators and hardware in the loop test rig, a real-time implementation is required. To avoid excessive computational loads, usage of simplified parametric models is almost mandatory. In this work, authors propose a simplified functional approach to identify and simulate the response of a generic hydraulic plant with a limited number of experimental tests. To reproduce complex nonlinear behaviours that are difficult to be reproduced with simplified models, piecewise transfer functions with scheduled poles are proposed. This innovative solution has been successfully applied for the identification of the brake plant of an existing vehicle, a Siemens prototype of instrumented vehicle called SimRod, demonstrating the feasibility of proposed method.
... Moreover, the stiffness or damping characteristics of nonlinear systems can be satisfactorily approximated by piecewise linear functions [1][2][3]. The asymmetric damping or stiffness characteristics [4][5][6], the vibration control strategies [7][8][9][10][11], mechanical systems with controllable dry friction [12][13][14], semi-active on-off dynamic vibration absorbers [15,16] are examples of practical applications of piecewise linear systems. ...
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... The objective of this paper is to find complete steady-state solutions for nonlinear structures with many DOFs under external excitations. An inverse solution technique is proposed and currently it could be applied to the primary harmonic solutions of multiple degree-of-freedom (MODF) structures with one local nonlinear component, which has wide applications such as nonlinear isolator [29][30][31][32] or nonlinear damper [22], nonlinear vibration absorber or nonlinear energy sink [11][12][13][14][15][16][17][18]21,33], joint [23,24], clearance element [34] and delayed feedback control of nonlinear structures [35]. In these systems, the primary structure usually has many DOFs, while the number of nonlinear element is only one. ...
An inverse solution technique with the ability of obtaining complete steady-state primary harmonic responses of local nonlinear structures in the frequency domain is proposed in the present paper. In this method, the nonlinear dynamic equations of motion is first condensed from many to only one algebraic amplitude–frequency equation of relative motion. Then this equation is transformed into a polynomial form, and with its frequency as the unknown variable, the polynomial equation is solved by tracing all the solutions of frequency with the increase of amplitude. With this solution technique, some complicated dynamic behaviors such as sharp tuning, anomalous jumps, breaks in responses and detached resonance curves could be obtained. The proposed method is demonstrated and validated through a finite element beam under force excitations and a lumped parameter model with a local nonlinear element under base excitations. The phenomenon of detached resonance curves in the frequency response and its coupling effects with multiple linear modes in the latter example are observed.
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