Generalized Cause-and-Effect Analyses for the Prototypic Nonlinear Mass–Spring–Damper System Using Volterra Kernels

2012 ◽  
Vol 135 (1) ◽  
Author(s):  
Ashraf Omran ◽  
Brett Newman
Keyword(s):  
Parametric Study ◽  
Volterra Series ◽  
System Response ◽  
System Behavior ◽  
Volterra Kernels ◽  
Numerical Examples ◽  
Frequency Domains ◽  
Variational Expansion ◽  
Mass Spring ◽  
Bilinear Terms

This paper develops generalized analytical first and second Volterra kernels for the prototypic nonlinear mass–spring–damper system. The nonlinearity herein is mathematically considered in quadratic and bilinear terms. A variational expansion methodology, one of the most efficient analytical Volterra techniques, is used to develop an analytical two-term Volterra series. The resultant analytical first and second kernels are visualized in both the time and the frequency domains followed by a parametric study to understanding the influence of each nonlinear/linear term appearing in the kernel structure. An analytical nonlinear step and periodic responses are also conducted to characterize the overall system response from the fundamental components. The developed analytical responses provide an illumination for the source of differences between nonlinear and linear responses. Feasibility of the proposed implementation is assessed by numerical examples. The developed kernel-based model shows the ability to predict, understand, and analyze the system behavior beyond that attainable by the linear-based model.

A Theory of Post-Stall Transients in Axial Compression Systems: Part II—Application

1986 ◽  
Vol 108 (2) ◽  
pp. 231-239 ◽  
Author(s):  
E. M. Greitzer ◽  
F. K. Moore
Keyword(s):  
Axial Compression ◽  
Parametric Study ◽  
Pressure Rise ◽  
Transient Behavior ◽  
Rotating Stall ◽  
Future Research ◽  
System Response ◽  
System Behavior ◽  
Flow Pressure ◽  
The Impact

Using the theory developed in Part I, calculations have been carried out to show the evolution of the mass flow, pressure rise, and rotating-stall cell amplitude during compression system post-stall transients. In particular, it is shown that the unsteady growth or decay of the stall cell can have a significant effect on the instantaneous compressor pumping characteristic and hence on the overall system behavior. A limited parametric study is carried out to illustrate the impact of different system features on transient behavior. It is shown, for example, that the ultimate mode of system response, surge or stable rotating stall, depends not only on the B parameter, but also on the compressor length-to-radius ratio. Small values of the latter quantity tend to favor the occurrence of surge, as do large values of B. Based on the analytical and numerical results, some specific topics are suggested for future research on post-stall transients.

Analytical Response for the Prototypic Nonlinear Mass-Spring-Damper System

2010 ◽  
Author(s):  
Ashraf Omran ◽  
Brett Newman
Keyword(s):  
Step Response ◽  
System Response ◽  
System Behavior ◽  
Nonlinear Solution ◽  
Departure Time ◽  
Analytical Response ◽  
Analytical Step ◽  
Expansion Theory ◽  
Mass Spring ◽  
Symmetric Response

In this paper, a procedure to analytically develop an approximate nonlinear solution for the prototypic nonlinear mass-spring-damper system based on multi-dimensional convolution expansion theory is offered. An analytical nonlinear step response is also conducted to characterize the overall system response. The developed analytical step response provides an illumination for the source of differences between nonlinear and linear responses such as initial departure time, differences in settling times and steady value, and non-symmetric response. Feasibility of the proposed implementation is assessed by a numerical example. The developed kernel-based model shows the ability to predict, understand, and analyze the system behavior beyond that attainable by linear-based model.

scholarly journals Vibro-Acoustical Sensitivities of Stiffened Aircraft Structures Due to Attached Mass-Spring-Dampers with Uncertain Parameters

Aerospace ◽  
2021 ◽  
Vol 8 (7) ◽  
pp. 174
Author(s):  
Johannes Seidel ◽  
Stephan Lippert ◽  
Otto von Estorff
Keyword(s):  
System Response ◽  
Fuzzy Arithmetic ◽  
Parameter Uncertainties ◽  
Excitation Spectra ◽  
Radiated Noise ◽  
Linking Elements ◽  
Manufacturing Tolerances ◽  
Suitable Framework ◽  
Mass Spring ◽  
The Impact

The slightest manufacturing tolerances and variances of material properties can indeed have a significant impact on structural modes. An unintentional shift of eigenfrequencies towards dominant excitation frequencies may lead to increased vibration amplitudes of the structure resulting in radiated noise, e.g., reducing passenger comfort inside an aircraft’s cabin. This paper focuses on so-called non-structural masses of an aircraft, also known as the secondary structure that are attached to the primary structure via clips, brackets, and shock mounts and constitute a significant part of the overall mass of an aircraft’s structure. Using the example of a simplified fuselage panel, the vibro-acoustical consequences of parameter uncertainties in linking elements are studied. Here, the fuzzy arithmetic provides a suitable framework to describe uncertainties, create combination matrices, and evaluate the simulation results regarding target quantities and the impact of each parameter on the overall system response. To assess the vibrations of the fuzzy structure and by taking into account the excitation spectra of engine noise, modal and frequency response analyses are conducted.

Analytical Determination of Shock Response Spectra for an Impulse-Loaded Proportionally Damped System

Volume 1 ◽  
2004 ◽  
Author(s):  
R. David Hampton ◽  
Nathan S. Wiedenman ◽  
Ting H. Li
Keyword(s):  
Transient Response ◽  
Shock Loading ◽  
Response Spectrum ◽  
Response Spectra ◽  
Analytical Determination ◽  
System Response ◽  
Mechanical Shock ◽  
Shock Response ◽  
Mass Spring ◽  
The Impact

Many military systems must be capable of sustained operation in the face of mechanical shocks due to projectile or other impacts. The most widely used method of quantifying a system’s vibratory transient response to shock loading is called the shock response spectrum (SRS). The system response for which the SRS is to be determined can be due, physically, either to a collocated or to a noncollocated shock loading. Taking into account both possibilities, one can define the SRS as follows: the SRS presents graphically the maximum transient response (output) of an imaginary ideal mass-spring-damper system at one point on a flexible structure, to a particular mechanical shock (input) applied to an arbitrary (perhaps noncollocated) point on the structure, as a function of the natural frequency of the imaginary mass-spring-damper system. For a response point sufficiently distant from the impact area, many Army platforms (such as vehicles) can be accurately treated as linear systems with proportional damping. In such cases the output due to an impulsive mechanical-shock input can be decomposed into exponentially decaying sinusoidal components, using normal-mode orthogonalization. Given a shock-induced loading comprising such components, this paper provides analytical expressions for the various common SRS forms. The analytical approach to SRS-determination can serve as a verification of, or an alternative to, the numerical approaches in current use for such systems. No numerical convolution is required, because the convolution integrals have already been accomplished analytically (and exactly), with the results incorporated into the algebraic expressions for the respective SRS forms.

scholarly journals On the detection of a nonlinear damage in an uncertain nonlinear beam using stochastic Volterra series

2019 ◽  
Vol 19 (4) ◽  
pp. 1137-1150 ◽  
Author(s):  
Luis GG Villani ◽  
Samuel da Silva ◽  
Americo Cunha ◽  
Michael D Todd
Keyword(s):  
Volterra Series ◽  
Novelty Detection ◽  
Nonlinear Behavior ◽  
System Response ◽  
Baseline Model ◽  
Nonlinear Beam ◽  
Stochastic Version ◽  
Nonlinear Components ◽  
Baseline State ◽  
Data Variation

In the present work, two issues that can complicate a damage detection process are considered: the uncertainties and the intrinsically nonlinear behavior. To deal with these issues, a stochastic version of the Volterra series is proposed as a baseline model, and novelty detection is applied to distinguish the condition of the structure between a reference baseline state (presumed “healthy”) and damaged. The studied system exhibits nonlinear behavior even in the reference condition, and it is exposed to a type of damage that causes the structure to display a nonlinear behavior with a different nature than the initial one. In addition, the uncertainties associated with data variation are taken into account in the application of the methodology. The results confirm that the monitoring of nonlinear coefficients and nonlinear components of the system response enables the method to detect the presence of the damage earlier than the application of some linear-based metrics. Besides that, the stochastic treatment enables the specification of a probabilistic interval of confidence for the system response in an uncertain ambient, thus providing more robust and reliable forecasts.

Component Based Modeling of Electromechanical Systems

2005 ◽  
Author(s):  
Shilpa A. Vaze ◽  
Prakash Krishnaswami ◽  
James DeVault
Keyword(s):  
Design Sensitivity ◽  
Differential Algebraic Equations ◽  
Single Step ◽  
System Response ◽  
Algebraic Equations ◽  
System Behavior ◽  
Governing Equations ◽  
Electromechanical Systems ◽  
System Equations ◽  
Saturation Effects

Simulation methods for electromechanical systems should accommodate their interdisciplinary nature and the fact that these systems often display qualitative changes in system behavior during operation, such as saturation effects and changes in kinematic structure. Current approaches are either based on deriving the system equations by applying a single formulation to all problem domains, or they are based on trying to integrate different software packages/modules to solve the interdisciplinary problem. In this paper, we present a component-based approach which allows the governing equations of each component to be defined in terms of its natural variables. The different component equations are then brought together to form a single system of differential-algebraic equations (DAE’s), which can be numerically solved to obtain the system response. The fact that we have an explicit, unified form of the system governing equations means that this formulation can be easily extended to design sensitivity analysis and optimization of electromechanical systems (EMS). The formulation includes monitor functions which can be used to detect when a qualitative system change has occurred, and to switch to a new set of governing equations to reflect this change. A single step integrator is used to make it easier to switch to a new system behavior, since this will always require a restart of the integrator. There is considerable flexibility in how the components can be defined, and connections between components are themselves modeled as special types of components. Examples of components from the mechanical and electrical side are presented, and two numerical examples are solved to illustrate the efficacy of the proposed method. One example is a link that is driven by a DC motor through a gearbox. The results of this example were verified against Simulink, and good agreement was observed. The second example is a motor driven slider-crank mechanism. The method can be extended to include components from any domain, such as hydraulics, thermal, controls, etc., as long as the governing equations can be written as DAE’s.

On the Inverse Multiplicative Eigenvalue Problem With an Engineering Application

1995 ◽  
Author(s):  
Dmitri D. Sivan ◽  
Yitshak M. Ram
Keyword(s):  
Eigenvalue Problem ◽  
Closed Form ◽  
Engineering Application ◽  
Iterative Approach ◽  
Numerical Examples ◽  
Practical Applications ◽  
Spring System ◽  
The Masses ◽  
Three Degree Of Freedom ◽  
Mass Spring

Abstract The problem of determining the masses of a mass-spring system is an inverse multiplicative eigenvalue problem. Generally, the solutions of this problem are not yet fully characterised. Since all known methods of solution follow an iterative approach, the possibility of developing a closed-form algorithm is examined. Although such method is found for the two and three degree-of-freedom systems, it appears to be impractical for higher order systems. Two well known existing algorithms are then examined numerically. Both converge locally at a quadratic rate. However, for practical applications, a globally converging algorithm may be more effective. In this paper a new, linearly converging algorithm is advised. The three methods are then tested on some selected numerical examples, and their performances compared.

Dynamics Analysis and Numerical Simulation of Large-Scale Hydraulic Cylinder Actuators

2020 ◽  
Vol 900 ◽  
pp. 14-19
Author(s):  
Van Thuan Truong ◽  
Yunn Lin Hwang ◽  
Jung Kuang Cheng ◽  
Khanh Duong Tran
Keyword(s):  
Numerical Simulation ◽  
Fluid Mechanics ◽  
Large Scale ◽  
Hydraulic Cylinder ◽  
Equivalent Model ◽  
System Response ◽  
Viscous Damping ◽  
Dynamics Analysis ◽  
Mass Spring ◽  
Actuator Design

This research presents a dynamic analysis of a large-scale hydraulic cylinder actuator via numerical simulation. A model of the actuator built with dynamically parameters is implemented basing on fluid mechanics and vibration theories. In which, coefficients of viscous damping and stiffness generated by compressibility and viscous characteristics of hydraulic oil are considered. Hence, the large-scale hydraulic cylinder actuator can be investigated via an equivalent model of mass-spring-damper. In order of obtaining the system response, numerical simulation is done with some realistic actuator parameter sets. The results are consistent with reality and can be used as valuable fundamental for large-scale hydraulic cylinder actuator design.

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