scholarly journals Strategies for Analyzing Random Vibration of Jointed Structures

2013 ◽  
Author(s):  
Daniel J. Segalman ◽  
Michael J. Starr ◽  
Michael A. Guthrie
Keyword(s):  
Constitutive Model ◽  
Mathematical Models ◽  
Dynamic Analysis ◽  
Random Vibration ◽  
Nonlinear Behavior ◽  
System Response ◽  
Equivalent Linearization ◽  
Nonlinear Structures ◽  
Random Loads ◽  
Previous Approximation

Development of mathematical models for built-up structures, particularly those with many interfaces, is still primitive. This limitation is particularly evident when complex loads and load histories are considered, an example of which is random vibration. Two steps in simplifying this problem are explored here. First, the system response is approximated as that of the superposition of numerous decoupled modes, the coordinates of which evolve according to a constitutive model designed to capture the nonlinearity of the structure. Second, because among the categories of load for which dynamic analysis on nonlinear structures is particularly difficult is that of random loads and the resulting random vibration, and given the previous approximation, it is natural to apply the method of stochastic equivalent linearization to the governing equation of each mode. Both of these approximations are explored for the case where the nonlinear behavior of the interfaces is represented by a Masing-Prandtl-Ishlinskii-Iwan model employing a Palmov kernel.

Response Analysis of Secondary Systems With Nonlinear Supports

1991 ◽  
Vol 113 (4) ◽  
pp. 524-531 ◽  
Author(s):  
T. Igusa ◽  
R. Sinha
Keyword(s):  
Random Vibration ◽  
Natural Frequencies ◽  
Hysteresis Loops ◽  
Nonlinear Behavior ◽  
Equivalent Linearization ◽  
Response Analysis ◽  
Analysis Method ◽  
Secondary System ◽  
Secondary Systems ◽  
Insight Into

This paper introduces a simplified random vibrations analysis method of linear secondary systems with nonlinear supports. The method separates, as much as possible, the nonlinear analysis of the supports from the linear analysis of the remainder of the secondary system. Equivalent linearization is used to generate response-dependent linear properties of the supports directly from hysteresis loops. These properties are then combined with the properties of the secondary system, and a response analysis is performed using mode combination. The analysis procedure is simpler than standard random vibration methods, and for narrow-band responses, it accurately models nonlinear behavior. In addition, the procedure uses equivalent modal quantities, such as natural frequencies and damping ratios, which provide insight into the effects of the nonlinear supports on the secondary system.

scholarly journals Force appropriation of nonlinear structures

2018 ◽  
Vol 474 (2214) ◽  
pp. 20170880 ◽  
Author(s):  
L. Renson ◽  
T. L. Hill ◽  
D. A. Ehrhardt ◽  
D. A. W. Barton ◽  
S. A. Neild
Keyword(s):  
Mathematical Models ◽  
Normal Modes ◽  
Nonlinear Normal Modes ◽  
System Response ◽  
Nonlinear Structures ◽  
Input Force ◽  
Nonlinear Normal

Nonlinear normal modes (NNMs) are widely used as a tool for developing mathematical models of nonlinear structures and understanding their dynamics. NNMs can be identified experimentally through a phase quadrature condition between the system response and the applied excitation. This paper demonstrates that this commonly used quadrature condition can give results that are significantly different from the true NNM, in particular, when the excitation applied to the system is limited to one input force, as is frequently used in practice. The system studied is a clamped–clamped cross-beam with two closely spaced modes. This paper shows that the regions where the quadrature condition is (in)accurate can be qualitatively captured by analysing transfer of energy between the modes of the system, leading to a discussion of the appropriate number of input forces and their locations across the structure.

scholarly journals Thermodynamic compatibility conditions of a new class of hysteretic materials

2021 ◽  
Author(s):  
Salvatore Sessa
Keyword(s):  
Constitutive Model ◽  
Dynamic Analysis ◽  
Closed Form ◽  
Iterative Procedure ◽  
Displacement Amplitude ◽  
Compatibility Conditions ◽  
Algebraic Functions ◽  
New Class ◽  
Thermodynamic Compatibility ◽  
Constitutive Parameters

AbstractThe thermodynamic compatibility defined by the Drucker postulate applied to a phenomenological hysteretic material, belonging to a recently formulated class, is hereby investigated. Such a constitutive model is defined by means of a set of algebraic functions so that it does not require any iterative procedure to compute the response and its tangent operator. In this sense, the model is particularly feasible for dynamic analysis of structures. Moreover, its peculiar formulation permits the computation of thermodynamic compatibility conditions in closed form. It will be shown that, in general, the fulfillment of the Drucker postulate for arbitrary displacement ranges requires strong limitations of the constitutive parameters. Nevertheless, it is possible to determine a displacement compatibility range for arbitrary sets of parameters so that the Drucker postulate is fulfilled as long as the displacement amplitude does not exceed the computed threshold. Numerical applications are provided to test the computed compatibility conditions.

Nonlinear Finite Element Analysis of Super-Long Pile and Soil Interaction in Soft Soil

2011 ◽  
Vol 201-203 ◽  
pp. 1601-1605 ◽  
Author(s):  
Shang Ping Chen ◽  
Wen Juan Yao ◽  
Sheng Qing Zhu
Keyword(s):  
Finite Element ◽  
Constitutive Model ◽  
Soft Soil ◽  
Three Dimensional ◽  
Nonlinear Behavior ◽  
Element Model ◽  
Element Analysis ◽  
Friction Resistance ◽  
Tip Resistance ◽  
Side Friction

In this paper, a nonlinear three-dimensional finite element model for super-long pile and soil interaction is established. In this model, contact elements are applied to simulate the nonlinear behavior of interaction of super-long pile and soil. A nonlinear elastic constitutive model for concrete is employed to analyze stress-strain relation of pile shaft under the axial load and the Duncan-Chang’s nonlinear constitutive model is used to reflect nonlinear and inelastic properties of soil. The side friction resistance, axial force, pile-tip resistance, and developing trend of soil plastic deformation are obtained and compared with measured results from static load tests. It is demonstrated that a super-long pile has the properties of degradation of side friction resistance and asynchronous action between side and pile-tip resistance, which is different from piles with a short to medium length.

Dynamic Shock Analysis of Shipboard Equipment

1967 ◽  
Vol 4 (04) ◽  
pp. 331-354
Author(s):  
R. L. Harrington ◽  
W. S. Vorus
Keyword(s):  
Mathematical Models ◽  
Dynamic Analysis ◽  
Analysis Method ◽  
Dynamic Analyses ◽  
Shock Resistance ◽  
Computational Procedures

A description and evaluation of the dynamic analysis method of determining the shock resistance of shipboard equipment is given. Development of equipment mathematical models is treated in detail, and the computational procedures used in conducting dynamic analyses are illustrated. Considerations in the preparation of dynamic-analysis reports are discussed. Discussers R. S. Adelizzi G. W. Bishop V. T. Boatwright K. J. Calvin C. Dotson Capt. H. C. Field, Jr., USND. W. Ginter O. Gould D. M. Gray K. Gyswyt R. T. Hawley RADM L. V. Honsinger, USN(Ret.) C. Lee J. C. Lester C. Li W. A. Littlejohn N. J. Monroe A. Morrone B. Novak E. W. Palmer C. G. Puffenburger L. L. Salter H.M. Schauer J. R. Sullivan J. D. Swannack C. Y. Tiao H. H. Ward W. P. Welch J. B. Woodward, III

Characterization of Nonlinear Rattling Behavior of a Gear Pair Through a Validated Torsional Model

2021 ◽  
Author(s):  
Ata Donmez ◽  
Ahmet Kahraman
Keyword(s):  
Piecewise Linear ◽  
Nonlinear Behavior ◽  
Severity Index ◽  
System Response ◽  
Gear Pair ◽  
Computationally Efficient ◽  
Linear Solution ◽  
Set Up ◽  
The Impact ◽  
Gear Rattle

Abstract Dynamic response of a gear pair subjected to input and output torque or velocity fluctuations is examined analytically. Such motions are commonly observed in various powertrain systems and identified as gear rattle or hammering motions with severe noise and durability consequences. A reduced-order torsional model is proposed along with a computationally efficient piecewise-linear solution methodology to characterize the system response including its sensitivity to excitation parameters. Validity of the proposed model is established through comparisons of its predictions to measurements from a gear rattle experimental set-up. A wide array of nonlinear behavior is demonstrated through presentation of periodic and chaotic responses in the forms of phase plots, Poincaré maps, and bifurcation diagrams. The severity of the resultant impacts on the noise outcome is also assessed through a rattle severity index defined by using the impact velocities.

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