The Effect of the Impact Model on Vibration Response of Discrete and Continuous Systems

2012 ◽  
Author(s):  
M. R. Brake
Keyword(s):  
Constitutive Model ◽  
Coefficient Of Restitution ◽  
Degree Of Freedom ◽  
Impact Dynamics ◽  
Impact Model ◽  
Single Degree Of Freedom ◽  
Elastic Plastic ◽  
Single Degree ◽  
Contact Models ◽  
The Impact

Impact is a phenomenon that is ubiquitous in mechanical design; however, the modeling of impacts in complex systems is often a simplified, imprecise process. In many high fidelity finite element simulations, the number of elements required to accurately model the constitutive properties of an impact event is impractical. As a result, rigid body dynamics with approximate representations of the impact dynamics are commonly used. These approximations can include a constant coefficient of restitution, an artificially large penalty stiffness, or a single degree of freedom constitutive model for the impact dynamics that is specific to the type of materials involved (elastic, plastic, viscoelastic, etc.). In order to understand the effect of the impact model on the system’s dynamics, simulations are conducted to investigate a single degree of freedom, two degrees of freedom, and continuous system each with rigid stops limiting the amplitude of vibration. Five contact models are considered: a coefficient of restitution method, a penalty stiffness method, two similar elastic-plastic constitutive models, and a dissimilar elastic-plastic constitutive model. Frequency sweeps show that simplified contact models can lead to incorrect assessments of the system’s dynamics and stability. In the worst case, periodic behavior can be predicted in a chaotic regime. Additionally, the choice of contact model can significantly affect the prediction of wear and damage in the system.

The Dynamics of a Nonharmonically Excited System Having Rigid Amplitude Constraints

1992 ◽  
Vol 59 (3) ◽  
pp. 693-695 ◽  
Author(s):  
Pi-Cheng Tung
Keyword(s):  
Dynamic Response ◽  
Bifurcation Analysis ◽  
Piecewise Linear ◽  
Coefficient Of Restitution ◽  
Degree Of Freedom ◽  
Linear Oscillator ◽  
Chaotic Motions ◽  
Single Degree Of Freedom ◽  
Single Degree ◽  
Excited System

We consider the dynamic response of a single-degree-of-freedom system having two-sided amplitude constraints. The model consists of a piecewise-linear oscillator subjected to nonharmonic excitation. A simple impact rule employing a coefficient of restitution is used to characterize the almost instantaneous behavior of impact at the constraints. In this paper periodic and chaotic motions are found. The amplitude and stability of the periodic responses are determined and bifurcation analysis for these motions is carried out. Chaotic motions are found to exist over ranges of forcing periods.

Predicting the Impact Response of a Nonlinear Single-Degree-of-Freedom Shock-Absorbing System From the Measured Step Response

1997 ◽  
Vol 119 (3) ◽  
pp. 221-227 ◽  
Author(s):  
S. N. Robinovitch ◽  
W. C. Hayes ◽  
T. A. McMahon
Keyword(s):  
High Energy ◽  
Degree Of Freedom ◽  
Step Response ◽  
Single Degree Of Freedom ◽  
Single Degree ◽  
Impact Forces ◽  
Standard Linear Solid ◽  
Standard Linear ◽  
The Impact ◽  
Measured Response

We measured the step response of a surrogate human pelvis/impact pendulum system at force levels between 50 and 350 N. We then fit measured response curves with four different single-degree-of-freedom models, each possessing a single mass, and supports of the following types: standard linear solid, Voigt, Maxwell, and spring. We then compared model predictions of impact force during high-energy collisions (pendulum impact velocity ranging from 1.16 to 2.58 m/s) to force traces from actual impacts to the surrogate pelvis. We found that measured peak impact forces, which ranged from 1700 to 5600 N, were best predicted by the mass-spring, Maxwell, and standard linear solid models, each of which had average errors less than 3 percent. Reduced accuracy was observed for the commonly used Voigt model, which exhibited an average error of 10 percent. Considering that the surrogate pelvis system used in this study exhibited nonlinear stiffness and damping similar to that observed in simulated fall impact experiments with human volunteers, our results suggest that these simple models allow impact forces in potentially traumatic falls to be predicted to within reasonable accuracy from the measured response of the body in safe, simulated collisions.

Pressure-Impulse Diagrams for Blast Loaded Continuous Beams Based on Dimensional Analysis

2013 ◽  
Vol 80 (5) ◽  
Author(s):  
A. S. Fallah ◽  
E. Nwankwo ◽  
L. A. Louca
Keyword(s):  
Structural Model ◽  
Continuous System ◽  
Degree Of Freedom ◽  
Pulse Loading ◽  
Single Degree Of Freedom ◽  
Pressure Impulse ◽  
Elastic Plastic ◽  
Single Degree ◽  
Continuous Beams ◽  
Shape Effects

Pressure-impulse diagrams are commonly used in preliminary blast resistant design to assess the maxima of damage related parameter(s) in different types of structures as a function of pulse loading parameters. It is well established that plastic dynamic response of elastic-plastic structures is profoundly influenced by the temporal shape of applied pulse loading (Youngdahl, 1970, “Correlation Parameters for Eliminating the Effect of Pulse Shape on Dynamic Plastic Deformation,” ASME, J. Appl. Mech., 37, pp. 744–752; Jones, Structural Impact (Cambridge University Press, Cambridge, England, 1989); Li, and Meng, 2002, “Pulse Loading Shape Effects on Pressure–Impulse Diagram of an Elastic–Plastic, Single-Degree-of-Freedom Structural Model,” Int. J. Mech. Sci., 44(9), pp. 1985–1998). This paper studies pulse loading shape effects on the dynamic response of continuous beams. The beam is modeled as a single span with symmetrical semirigid support conditions. The rotational spring can assume different stiffness values ranging from 0 (simply supported) to ∞ (fully clamped). An analytical solution for evaluating displacement time histories of the semirigidly supported (continuous) beam subjected to pulse loads, which can be extendable to very high frequency pulses, is presented in this paper. With the maximum structural deflection, being generally the controlling criterion for damage, pressure-impulse diagrams for the continuous system are developed. This work presents a straightforward preliminary assessment tool for structures such as blast walls utilized on offshore platforms. For this type of structures with semirigid supports, simplifying the whole system as a single-degree-of-freedom (SDOF) discrete-parameter model and applying the procedure presented by Li and Meng (Li and Meng, 2002, “Pulse Loading Shape Effects on Pressure–Impulse Diagram of an Elastic–Plastic, Single-Degree-of-Freedom Structural Model,” Int. J. Mech. Sci., 44(9), pp. 1985–1998; Li and Meng, 2002, “Pressure-Impulse Diagram for Blast Loads Based on Dimensional Analysis and Single-Degree-of-Freedom Model,” J. Eng. Mech., 128(1), pp. 87–92) to eliminate pulse loading shape effects on pressure-impulse diagrams would be very conservative and cumbersome considering the support conditions. It is well known that an SDOF model is a very conservative simplification of a continuous system. Dimensionless parameters are introduced to develop a unique pulse-shape-independent pressure-impulse diagram for elastic and elastic-plastic responses of continuous beams.

scholarly journals The Effect of the Contact Model on the Design of Mechanical Systems

2012 ◽  
Author(s):  
M. R. Brake ◽  
D. S. Aragon ◽  
D. J. VanGoethem ◽  
H. Sumali
Keyword(s):  
Constant Coefficient ◽  
Degrees Of Freedom ◽  
Mechanical Systems ◽  
Constitutive Models ◽  
Coefficient Of Restitution ◽  
Rigid Body Dynamics ◽  
Contact Model ◽  
Elastic Plastic ◽  
Contact Models ◽  
The Impact

Impact is a wide-spread phenomenon in mechanical systems that can have a significant effect on the system’s dynamics, stability, wear, and damage. The simulation of impact in complex, mechanical systems, however, is often too computationally intensive for high fidelity finite element analyses to be useful as design tools. As a result, rigid body dynamics and reduced order model simulations are often used, with the impact events modeled by ad hoc methods such as a constant coefficient of restitution or a penalty stiffness. The consequences of the choice of contact model are studied in this paper for a representative multiple-degrees of freedom mechanical system. Four contact models are considered in the analysis: a constant coefficient of restitution model, two similar elastic-plastic constitutive models, and one dissimilar elastic-plastic constitutive model. The predictions of wear, mechanical failure, and stability are assessed for each of the contact models, and the subsequent effect on the system design is investigated. These results emphasize the importance of choosing a realistic contact model when simulations are being used to drive the design of a system.

The Role of Epistemic Uncertainty of Contact Models in the Design of Mechanical Systems

2013 ◽  
Author(s):  
M. R. Brake
Keyword(s):  
Constant Coefficient ◽  
Epistemic Uncertainty ◽  
Piecewise Linear ◽  
Mechanical Systems ◽  
Coefficient Of Restitution ◽  
Rigid Body Dynamics ◽  
Contact Model ◽  
Elastic Plastic ◽  
Contact Models ◽  
The Impact

Impact is a wide-spread phenomenon in mechanical systems that can have a significant effect on the systems dynamics, stability, wear, and damage. The simulation of impact in complex, mechanical systems, however, is often too computationally intensive for high fidelity finite element analyses to be useful as design tools. As a result, rigid body dynamics and reduced order model simulations are often used, with the impact events modeled by ad hoc methods such as a constant coefficient of restitution or penalty stiffness. The effect of epistemic uncertainty in the choice of contact model is investigated in this paper for a representative multiple-degree of freedom mechanical system. Five contact models are considered in the analysis: a constant coefficient of restitution model, a piecewise-linear stiffness and damping (i.e. Kelvin-Voight) model, two similar elastic-plastic constitutive models, and one dissimilar elastic-plastic constitutive model. The predictions of wear and mechanical failure are assessed for each of the contact models. The ramifications of the choice of the contact model for an optimization study of the system’s geometric design are also presented. These results emphasize the importance of choosing an accurate contact model when simulations are being used to drive the design of a system.

scholarly journals Optimization of Multiple Tuned Mass Damper (MTMD) Parameters for a Primary System Reduced to a Single Degree of Freedom (SDOF) through the Modal Approach

2021 ◽  
Vol 11 (4) ◽  
pp. 1389
Author(s):  
Piotr Wielgos ◽  
Robert Geryło
Keyword(s):  
Degrees Of Freedom ◽  
Research Work ◽  
System Optimization ◽  
Degree Of Freedom ◽  
Primary System ◽  
Single Degree Of Freedom ◽  
Modal Approach ◽  
Single Degree ◽  
Novel Approach ◽  
The Impact

The research paper presents a novel approach toward constructing motion equations for structures with attached MTMDs (multiple tuned mass dampers). A primary system with MDOF (multiple dynamic degrees of freedom) was reduced to an equivalent system with a SDOF (single degree of freedom) through the modal approach, and equations from additional MTMDs were added to a thus-created system. Optimization based on ℌ2 and ℌ∞ for the transfer function associated with the generalized displacement of an SDOF system was applied. The research work utilized GA (genetic algorithms) and SA (simulated annealing method) optimization algorithms to determine the stiffness and damping parameters for individual TMDs. The effect of damping and stiffness (MTMD tuning) distribution depending on the number of TMDs was also analyzed. The paper also reviews the impact of primary system mass change on the efficiency of optimized MTMDs, as well as confirms the results of other authors involving greater MTMD effectiveness relative to a single TMD.

scholarly journals Optimization of Multiple Tuned Mass Damper (MTMD) Parameters for a Primary System Reduced to a Single Degree of Freedom (SDOF) Through the Modal Approach

2020 ◽  
Author(s):  
Piotr Wielgos ◽  
Robert Geryło
Keyword(s):  
Degrees Of Freedom ◽  
Research Work ◽  
System Optimization ◽  
Degree Of Freedom ◽  
Primary System ◽  
Single Degree Of Freedom ◽  
Modal Approach ◽  
Single Degree ◽  
Stiffness And Damping ◽  
The Impact

The research paper presents a new approach towards constructing motion equations for structures with attached MTMDs (multiple tuned mass dampers). A primary system, with MDOF (multiple dynamic degrees of freedom) was reduced to an equivalent system with a SDOF (single degree of freedom) through the modal approach, and equations from additional MTMDs were added to a thus-created system. Optimization based on H2 and H∞ for the transfer function associated with the generalized displacement of an SDOF system. The research work utilized GA (genetic algorithms) and SA (simulated annealing method) optimization algorithms to determine the stiffness and damping parameters for individual TMDs. The effect of damping and stiffness (MTMD tuning) distribution depending on the number of TMDs was also analyzed. The paper also reviews the impact of primary system mass change on the efficiency of optimized MTMDs, as well as confirms the results of other authors involving greater MTMD effectiveness relative to a single TMD.

Nonlinearities in Experimental System Identification of a Piezocomposite Beam Model

2017 ◽  
Author(s):  
Patrick S. Heaney ◽  
Onur Bilgen
Keyword(s):  
System Identification ◽  
Electromechanical Coupling ◽  
Degree Of Freedom ◽  
Parameter Estimates ◽  
Beam Model ◽  
Single Degree Of Freedom ◽  
Testing Procedures ◽  
Single Degree ◽  
Constitutive Relationships ◽  
The Impact

Piezocomposite beams are often modeled using linear constitutive equations describing the electromechanical coupling of the material. In nearly all experimental identification processes, nonlinearities in these equations are ignored, which can lead to significant errors in the identified models. Following a common practice in the literature, a piezocomposite cantilever beam is modeled as a single degree of freedom system, with strain induced harmonic excitation governed by linear piezoelectric constitutive relationships. The validity of the linear property assumptions is investigated. It is experimentally demonstrated that the relationship between input and response of the beam is significantly nonlinear. The impact of this nonlinear behavior on the parameter identification of the system is shown for three different testing methods, (1) Open Loop Excitation, (2) Constant Input, and (3) Constant Response. For each method, the command amplitude is varied which yields different parameter estimates for the single degree of freedom beam model. These results demonstrate that the assumed linear constitutive relationships lead to parameter estimates which are only accurate for the specific testing method and the specific commanded input or response amplitude, even under highly controlled testing procedures. The paper concludes with comments on the system identification of a single degree of freedom model given this nonlinear system behavior.

Sign in / Sign up

Export Citation Format

Share Document