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.

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.

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.

Practical aspects of heat conduction simulation in household heating optimization tasks

2019 ◽  
Vol 5 (2) ◽  
pp. 9-22
Author(s):  
Jan Tadeusz Duda
Keyword(s):  
Heat Conduction ◽  
State Space ◽  
State Space Model ◽  
Step Response ◽  
Space Model ◽  
Optimization Task ◽  
Modeling Errors ◽  
Analytical Step ◽  
Analytical Formulae ◽  
Heating Optimization

Mathematical model selection for simulation heat conduction processes in household heating optimization task is considered. The essence of the matter is that the heat transfer dynamics properties are very diversified, so simulation procedure formulae and parameters should be properly selected to avoid excessive modeling errors with reasonable calculation time being held. The typical state-space model and analytical formulae for step response of the heat conduction across a homogeneous wall are presented and compared in terms of modeling errors. Formal and numerical problems of heat losses simulation are discussed. Semi-analytical step-response formulae for multilayer walls are derived and their accuracy is compared with effects of simulation based on the state-space model. Some recommendations for time and space discetization parameters are given.

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.

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.

Root Locus Diagrams and the Effect of Zeros on System Response

1997 ◽  
Vol 34 (1) ◽  
pp. 48-69 ◽  
Author(s):  
J. C. Peyton Jones ◽  
D. P. Atherton
Keyword(s):  
Step Response ◽  
System Response ◽  
Minimum Phase ◽  
Root Locus ◽  
Graphical Notation ◽  
Response Characteristics ◽  
Pole Dominance ◽  
Phase Systems ◽  
Insight Into

New expressions, and a graphical notation are introduced to quantify the effect of zeros on step response characteristics. The expressions, which also hold for non-minimum phase systems, are illustrated geometrically in the s-plane, and give a more accurate insight into a concept of pole dominance than the standard ‘pure-pole’ approximations.

Application of adaptive sliding mode control for nonlinear systems with unknown polynomial bounded uncertainties

2017 ◽  
Vol 40 (13) ◽  
pp. 3721-3735 ◽  
Author(s):  
Jiang Zhu ◽  
Karim Khayati
Keyword(s):  
Nonlinear Systems ◽  
Sliding Mode Control ◽  
Sliding Mode ◽  
Adaptive Sliding Mode Control ◽  
System Response ◽  
Adaptive Sliding Mode ◽  
Mode Control ◽  
Spring System ◽  
Adaptation Law ◽  
Mass Spring

In this paper, we discuss the application of a novel switching integral-exponential-adaptation-law-based adaptive sliding mode control design for a wide class of nonlinear systems with unknown polynomial bounds on the uncertainty norm. A robust finite time convergence, i.e. finite stability, is obtained with low chatter on control actions and a fast-transient performance for adaptive sliding mode control handling the multi-input multi-output nonlinear systems with uncertainties of amplitudes bounded within unknown polynomials in the state vector norm. The exponential term of the proposed adaptation law targets the reduction of the chatter levels of the sliding mode by significantly reducing the gain overestimation while simultaneously suppressing the overshoot by speeding up the system response to the uncertainties. It also prevents the instability issues which encounters the classic integral-gain-law-based adaptive sliding mode control when underestimating its initial gain or gain rate parameter. A simple example illustrates the motivation and feasibility of the proposed adaptive sliding mode control. The applications on a nonlinear mass–spring system and on a two degree of freedom electromechanical rotative plant demonstrate the effectiveness of the proposed design.

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