Dynamic Response Of Mechanical Systems Research Articles

Material Damping Estimation within Low-, Medium- and High-Frequency Ranges

When considering the dynamic response of mechanical systems, material damping is a main factor to account for. It largely affects phenomena at different time scales, from the transient response of the system, to its modal response, up to the acoustic wave propagation within the bulk and at the contact interfaces. Nevertheless, despite the key role of the material damping in the mechanical response, its estimation within a wide frequency range is still a challenge, when considering the existing technics. Moreover, the material damping varies largely with respect to frequency and the actual approaches for its estimation are limited within restricted frequency ranges. An approach for estimating the material damping within the overall frequency range does not exist in the literature. This paper proposes an approach where structural and acoustic technics are combined with an energy statistical approach, for identifying the trend of material damping within a larger frequency range. The approach is here applied to polycarbonate (PC) material. The results highlighted that the material damping in the low–medium frequency range (1[Formula: see text]Hz-several kHz) fits with the Rayleigh damping model. On the other hand, the damping in the higher frequency range (106 Hz) showed a stabilization with the increase of the frequency.

A Machine Learning-Based Surrogate Finite Element Model for Estimating Dynamic Response of Mechanical Systems

A Machine Learning-Based Surrogate Finite Element Model for Estimating Dynamic Response of Mechanical Systems

A novel test rig to study the effect of fretting wear on the forced response dynamics with a friction contact

This paper presents a novel test rig to study the effect of fretting wear and of the contact surface evolution on the forced response of systems with dry friction contact. This rig allows simulating contacts similar to the type of contacts present between the shrouds at the blade tip. Several research groups have been studying how fretting wear affects the dynamic response of mechanical systems, developing numerical prediction tools that consider dry friction contact and nonlinearity. The aim of this work is to experimentally study the evolution of contact interfaces and how this evolution affects the system dynamics. Experimental results will aid to validate the numerical predictions. The test rig developed for this activity is made of a cantilever beam fixed at one end and with a friction contact at the free end. The contact couple is made of two replaceable specimens. The contact is loaded via a lifting mechanism through a screw with fine thread. Fretting wear test was performed at a constant frequency and force amplitude, exciting the beam with an electromagnetic shaker. To emphasize the change of the dynamic response, frequency sweeps were performed at various intervals during the wear test. The full range test with ‘changing preload’ due to progressing wear was performed until a full loss of contact. This paper describes the test rig design, intent, set-up, instrumentation, test plan and results. Results include the frequency response curves for unworn contact, wear profiles at multiple intervals and the effect of wear on the frequency response. Though energy dissipation per cycle is quite small, wear leads to material loss at the contact with a sufficiently large number of cumulative cycles and substantially affects the dynamic response. Results collected in this research activity are of particular importance to validate numerical tool that aim to simulate the dynamic behaviour of systems with dry friction contacts that undergo material loss caused by wear.

On two improved numerical algorithms for vibration analysis of systems involving fractional derivatives

Zhang and Shimizu (1998) proposed a numerical algorithm based on Newmark method to calculate the dynamic response of mechanical systems involving fractional derivatives. On the basis of Runge-Kutta-Nyström method and Newmark method, the present study proposes two new numerical algorithms, namely, the improved Newmark algorithm using the second order derivative and the improved Runge-Kutta-Nyström algorithm using the second order derivative to solve the fractional differential equations of vibration systems. The accuracy of new algorithms is investigated in detail by numerical simulation. The simulation result demonstrated that the Runge-Kutta-Nyström algorithm using the second order derivative for the vibration analysis of systems involving fractional derivatives is more effective than the Newmark algorithm of Zhang and Shimizu.

Generalized Modal Amplitude Stability Analysis for the prediction of the nonlinear dynamic response of mechanical systems subjected to friction-induced vibrations

The numerical prediction of the dynamic behaviour of mechanical systems subjected to friction-induced vibrations is still a tedious problem. Different methodologies exist nowadays to study it. The first one is the complex eigenvalue analysis, which is widely used by the scientists and the industrials to predict the appearance of instabilities despite its disadvantages. Other methodologies, namely temporal integration and frequential approaches, have been developed to determine the transient and/or the steady-state response to assess the history of the dynamic response, and so to identify the unstable modes involved in the nonlinear dynamic response as well as the vibration levels. However, because of their complex implementation, their high numerical cost and sometimes the strong assumptions made on the form of the solutions, these methods are not widely and currently used in industry. To cope with the limitations of the CEA, namely the over- or under-predictability and the lack of information about modal participations in the nonlinear dynamic response, developing complementary tools is necessary. Thus, this paper is devoted to the extension and generalization of a nonlinear approach, called the modal amplitude stability analysis, to the multi-instability case. The method, called the Generalized Modal Amplitude Stability Analysis (GMASA), allows to identify the evolutions and contributions of unstable modes involved in the nonlinear self-sustaining vibration response and to estimate the limit cycles. The method is applied on a phenomenological system for which it is easy to provide an understanding of the unstable mode(s) contribution to the nonlinear dynamic response of the system and for which the calculations can be performed with reasonable computational times. Thus, the efficiency and validity of the GMASA approach are investigated by comparing the GMASA results with those of the reference results based on temporal approach.

Macroscopic dynamic response of mechanical systems involving composites and effect of inner structure on damping properties

The paper deals with relation between inner structure of the machine and the composite material used in it and macroscopic dynamic response. It presents the experimental results of testing the relation between inner composite material structure and damping properties presented by logarithmic decrement quantity. Moreover, the paper provides the case study of application the composite material layered structure to the flexographic printing machine and results of that applications presented by printing speed.

Direct sensitivity analysis of multibody systems with holonomic and nonholonomic constraints via an index-3 augmented Lagrangian formulation with projections

Optimizing the dynamic response of mechanical systems is often a necessary step during the early stages of product development cycle. This is a complex problem that requires to carry out the sensitivity analysis of the system dynamics equations if gradient-based optimization tools are used. These dynamics equations are often expressed as a highly nonlinear system of ordinary differential equations or differential-algebraic equations, if a dependent set of generalized coordinates with its corresponding kinematic constraints is used to describe the motion. Two main techniques are currently available to perform the sensitivity analysis of a multibody system, namely the direct differentiation and the adjoint variable methods. In this paper, we derive the equations that correspond to the direct sensitivity analysis of the index-3 augmented Lagrangian formulation with velocity and acceleration projections. Mechanical systems with both holonomic and nonholonomic constraints are considered. The evaluation of the system sensitivities requires the solution of a tangent linear model that corresponds to the Newton–Raphson iterative solution of the dynamics at configuration level, plus two additional nonlinear systems of equations for the velocity and acceleration projections. The method was validated in the sensitivity analysis of a set of examples, including a five-bar linkage with spring elements, which had been used in the literature as benchmark problem for similar multibody dynamics formulations, a point-mass system subjected to nonholonomic constraints, and a full-scale vehicle model.

A survey and comparison of several friction force models for dynamic analysis of multibody mechanical systems

This study is aimed at examining and comparing several friction force models dealing with different friction phenomena in the context of multibody system dynamics. For this purpose, a comprehensive review of present literature in this field of investigation is first presented. In this process, the main aspects related to friction are discussed, with particular emphasis on the pure dry sliding friction, stick–slip effect, viscous friction and Stribeck effect. In a simple and general way, the friction force models can be classified into two main groups, namely the static friction approaches and the dynamic friction models. The former group mainly describes the steady-state behavior of friction force, while the latter allows capturing more properties by using extra state variables. In the present study, a total of 21 different friction force models are described and their fundamental physical and computational characteristics are discussed and compared in details. The application of those friction models in multibody system dynamic modeling and simulation is then investigated. Two multibody mechanical systems are utilized as demonstrative application examples with the purpose of illustrating the influence of the various frictional approaches on the dynamic response of the systems. From the results obtained, it can be stated that both the choice of the friction force model and friction parameters involved can significantly affect the simulated/modeled dynamic response of mechanical systems with friction.

Dynamic response of mechanical systems to impulse process stochastic excitations: Markov approach

Methods for determination of the response of mechanical dynamic systems to Poisson and non-Poisson impulse process stochastic excitations are presented. Stochastic differential and integro-differential equations of motion are introduced. For systems driven by Poisson impulse process the tools of the theory of non-diffusive Markov processes are used. These are: the generalized Itô’s differential rule which allows to derive the differential equations for response moments and the forward integro-differential Chapman-Kolmogorov equation from which the equation governing the probability density of the response is obtained. The relation of Poisson impulse process problems to the theory of diffusive Markov processes is given. For systems driven by a class of non-Poisson (Erlang renewal) impulse processes an exact conversion of the original non-Markov problem into a Markov one is based on the appended Markov chain corresponding to the introduced auxiliary pure jump stochastic process. The derivation of the set of integro-differential equations for response probability density and also a moment equations technique are based on the forward integro-differential Chapman-Kolmogorov equation. An illustrating numerical example is also included.

Using scaled physical model for assessment of mechanical damping of power plant boiler structure

Summary To determine dynamic response of mechanical system is always a complex issue. One of the core inputs for such a task is a coefficient of logarithmic damping decrement. There is no way how to determine this coefficient analytically; it needs to be measured on the final product. There has been a large amount of dynamic tests carried out on common structures and the results have been incorporated in design codes. Nevertheless, power plant boiler structure differs significantly from common structures. To provide a large number of dynamic tests on real facility is very difficult for many reasons. Using a scaled model is a way how to achieve relevant data based on repeatable experiment.

A virtual prototype of a constrained extensible crank mechanism: Dynamic simulation and design

Dynamic response of mechanical systems containing rigid links connected by joints is affected by the velocity and mass of the systems components as well as by the presence of clearance or impact between components. Accurate simulations of such systems are increasingly important due to their wide application in engine design, knitting machinery or single and dual-arm robotic systems, as well as for their initial and optimised design. A virtual prototype of a newly developed extensible crank mechanism (applied to the design development of a bicycle crank) is presented in this article and its dynamical behaviour is analysed. The equations of motion of the extensible crank, constrained to either a circular or an elliptical path, are considered. Accurate simulation of the constrained extensible crank mechanism explores its performance and behaviour under the combined effect of different parameters such as clearance and impact. A three-dimensional finite element model is used to study the flexural behaviour of the extensible crank under the maximal loads that causes its motion.

Study of the effect of contact force model on the dynamic response of mechanical systems with dry clearance joints: computational and experimental approaches

The main objective of this work is to present a computational and experimental study on the contact forces developed in revolute clearance joints. For this purpose, a well-known slider-crank mechanism with a revolute clearance joint between the connecting rod and slider is utilized. The intra-joint contact forces that are generated at these clearance joints are computed by considering several different elastic and dissipative approaches, namely those based on the Hertz contact theory and the ESDU tribology-based cylindrical contacts, along with a hysteresis-type dissipative damping. The normal contact force is augmented with the dry Coulomb’s friction force. In addition, an experimental apparatus is used to obtained some experimental data in order to verify and validate the computational models. From the outcomes reported in this paper, it is concluded that the selection of the appropriate contact force model with proper dissipative damping plays a significant role in the dynamic response of mechanical systems involving contact events at low or moderate impact velocities.

Automatic generation of equations of motion for multibody system in discrete event simulation framework

In this paper, the development of a simulation program that can automatically generate equations of motion for mutibody systems in the discrete event simulation framework is presented. The need to analyze the dynamic response of mechanical systems that are under event triggered conditions is increasing. General mechanical systems can be defined as multibody systems that are collections of interconnected rigid bodies, consistent with various types of joints that limit the relative motion of pairs of bodies. For complex multibody systems, a systematic approach is required to efficiently set up the mathematical models. Therefore, a dynamics kernel was developed to automatically generate the equations of motion for multibody systems based on multibody dynamics. The developed dynamics kernel also provides the numerical solver for the dynamic analysis of multibody systems. The general multibody dynamics kernel cannot deal with discontinuous state variables, event triggered conditions, and state triggered conditions, though. To enable it to deal with multibody systems in discontinuous environments, the multibody dynamics kernel was integrated into a discrete event simulation framework, which was developed based on the discrete event system specification (DEVS) formalism. DEVS formalism is a modular and hierarchical formalism for modeling and analyzing systems under event triggered conditions, which are described by discontinuous state variables. To verify the developed program, it was applied to an block-lifting and transport simulation, and dynamic analysis of the system is carried out.

Two-substructure, time-domain transfer path analysis of transient dynamic response of mechanical systems with nonlinear coupling.

The traditional frequency domain transfer path analysis has become a popular method to detect and diagnose vehicle NVH problems. Unfortunately, due to its reliance on frequency transfer functions, the approach is strictly effective only for linear time-invariant system and steady-state response. This limitation prevents the method from being applied to transient and/or nonlinear behavior such as clunk, shudder, and tip-in and tip-out. In this paper, a novel time domain transfer path analysis is proposed to deal with a class of non-linear transient response problems. It combines the versatility of the transfer path analysis for tracking transmission of vibratory energy between substructures and generality of the time domain analysis for treating transient response that is also nonlinear in nature. The formulation that is derived by combining the spectral-based substructure method and a discrete, piecewise convolution theory is applied to a lumped parameter system, and the results are compared with output from a direct numerical integration of the nonlinear equations of motion. Comparison results show significant promise and appear to be usable for solving real-life vehicle problems that are highly transient with moderate level of nonlinearity present.

Design optimization for dynamic response of vibration mechanical system with uncertain parameters using convex model

The concept of uncertainty plays an important role in the design of practical mechanical system. The most common methods for solving uncertainty problems are to model the parameters as a random vector. A natural way to handle the randomness is to admit that a given probability density function represents the uncertainty distribution. However, the drawback of this approach is that the probability distribution is difficult to obtain. In this paper, we use the non-probabilistic convex model to deal with the uncertain parameters in which there is no need for probability density functions. Using the convex model theory, a new method to optimize the dynamic response of mechanical system with uncertain parameters is derived. Because the uncertain parameters can be selected as the optimization parameters, the present method can provide more information about the optimization results than those obtained by the deterministic optimization. The present method is implemented for a torsional vibration system. The numerical results show that the method is effective.

On a critique of a numerical scheme for the calculation of fractionally damped dynamical systems

Recently Yuan and Agrawal [L. Yuan and O.P. Agrawal, A numerical scheme for dynamic systems containing fractional derivatives, Journal of Vibration and Acoustics 124 (2002) 321–324] presented a new numerical scheme to calculate the dynamic response of mechanical systems, the damping forces of which are described by fractional derivatives. When solving the resulting equation of motion by time integration, it is necessary to store the entire displacement history of the system due to the non-local character of the fractional derivatives. The cited scheme appears to overcome this drawback by transforming the equation of motion with the fractional term into a set of ordinary differential equations. It can be shown that this scheme is equivalent to a classical spring-dashpot representation and thus does not imply the benefits derived from fractional-derivative models. In addition, it is less flexible and incorrectly predicts the asymptotic behavior.

Reply by Authors to M. Borri, M. Lanz, and P. Mantegazza

References Riff, R. and Baruch, M., Element Discretization of Hamilton's Law of Varying Action, AIAA Journal, Vol. 22, Sept. 1984, pp. 1310-1318. Baruch, M. and Riff, R., Hamilton Principle, Hamilton's Law, 6 Correct Formulations, ,414,4 Journal, Vol. 20, May 1982, pp. 687-692. Fried, I., Finite Element Analysis of Time Dependent Phenomena, AIAA Journal, Vol. 7, June 1969, pp. 1170-1173. Geradin, M., A Classification and Discussion of Integration Operators for Transient Structural Response, AIAA Paper 74-105, 1974. Borri, M., Ghiringhelli, G. L., Lanz, M., Mantegazza, P., and Merlini T., Dynamic Response of Mechanical Systems by a Weak Hamiltonian Formulation, Proceedings of the Symposium on Advances and Trends in Structures and Dynamics; also, Computers and Structures, Vol. 20, 1985, to be published.

Dynamic response of mechanical systems by a weak Hamiltonian formulation

The paper explains the appropriate use of Hamilton's Weak Principle (HWP) in the developement of consistent and efficient approximations for the determination of the response of mechanical systems. In particular it is shown how the HWP can be used to provide explicit and implicit integration formulae and to study the response and stability of nonlinear periodic systems. The discussion of the stability of the integration formula is also included. Some numerical examples show the result that can be obtained when the HWP is applied to some simple but significant response problems.