scholarly journals Constructing Equations of Motion for a Dynamic System from Modal Parameters

Author(s):  
Ehsan Sarshari ◽  
Nastaran Vasegh ◽  
Mehran Khaghani ◽  
Saeid Dousti

Ziegler’s pendulum is an appropriate model of a non-conservative dynamic system. By considering gravity effect, new equations of motion are extracted from Newton’s motion laws. The instability of equilibriums is determined by linear stability analysis. Chaotic behavior of the model is shown by numerical simulations. Sliding mode controller is used for eliminating chaos and for stabilizing the equilibriums.


1981 ◽  
Vol 103 (4) ◽  
pp. 805-810
Author(s):  
H. M. Chen ◽  
S. B. Malanoski

This paper presents a simplified analysis procedure to provide initial assessment and guidance on fan rotor dynamics including the foundation interaction. For purposes of early-design decision-making (or trouble-shooting), the interaction of a rotor-bearing dynamic system and a foundation-soil/piling dynamic system is viewed approximately for the vertical, horizontal, and rocking modes of vibration. The equations of motion are written in matrix form and include the pertinent parameters. A numerical example is presented to guide in the interpretation of the analysis; this example considers the unbalance response of the entire system as measured at the bearings.


1996 ◽  
Vol 118 (3) ◽  
pp. 499-507 ◽  
Author(s):  
Toshikazu Nakanishi ◽  
Xuegang Yin ◽  
A. A. Shabana

The mode shapes, frequencies, and modal mass and stiffness coefficients of multibody systems such as tracked vehicles can be determined using experimental identification techniques. In multibody simulations, however, knowledge of the modal parameters of the individual components is required, and consequently, a procedure for extracting the component modes from the mode shapes of the assembled system must be used if experimental modal analysis techniques are to be used with general purpose multibody computer codes. In this investigation, modal parameters (modal mass, modal stiffness, modal damping, and mode shapes), which are determined experimentally, are employed to simulate the nonlinear dynamic behavior of a multibody tracked vehicle which consists of interconnected rigid and flexible components. The equations of motion of the vehicle are formulated in terms of a set of modal and reference generalized coordinates, and the theoretical basis for extracting the component modal parameters of the chassis from the modal parameters of the assembled vehicle is described. In this investigation, the track of the vehicle is modeled as a closed kinematic chain that consists of rigid links connected by revolute joints, and the effect of the chassis flexibility on the motion singularities of the track is examined numerically. These singularities which are encountered as the result of the change in the track configuration are avoided by using a deformable secondary joint instead of using the loop-closure equations.


Author(s):  
Ismail Akharas ◽  
Michael P. Hennessey ◽  
Eric J. Tornoe

Abstract This paper introduces a novel method for playing dynamic animations of rigid body assemblies with internal motions in virtual reality (VR). Through previous research over a decade ago, an inexpensive, relatively straight-forward process has been developed that entailed using SolidWorks, MATLAB/Simulink, and movie player software to permit one to view 2D MP4 files, such as on a laptop, smart phone, etc. Inspired by the usefulness of these previous results, the approach presented here targets a VR environment, clearly representing a technological leap over viewing 2D MP4 files. It’s made possible by recent advances in VR & gaming software (e.g. Unity) along with some unique software interfacing, including use of CADLink, to permit importation of CAD files, such as from SolidWorks, into Unity. Those interested in VR visualization of their dynamic system can use the step-by-step process presented as a manual to guide them through the hardware and software setup and ultimately learn how to use SolidWorks, MATLAB/Simulink, and Unity interactively to visualize their simulations in VR. Another key point is that the analyst has considerable control and access over each step in the process, including the dynamic modeling, unlike that commonly found in large, structured dynamic simulation software packages. As an example to illustrate the process, a dynamic simulation of a classic pendulum/slider system was created using MATLAB/Simulink, which in effect numerically solves the ordinary differential equations of motion. The time-dependent displacement data for both the slider’s lateral movement and the pendulum’s angle, along with a time vector in incremental difference form, was saved as an Excel file. In turn, it was read by a C# script residing within Unity to permit an animation playback scenario of the SolidWorks CAD model of the entire pendulum/slider system (previously brought into Unity via CADLink with some reassembly), viewed more generally as an assembly with internal motions. Unity, a popular open-source piece of VR game development software used to produce both 2D and 3D video games and simulations, then serves as a platform to access the virtual world with the aid of an Oculus Rift (or Quest) VR headset and two hand controllers. In the end, the VR viewer can physically move around in the VR environment while at the same time view the playback motion of the pendulum/slider system from varying vantage points, just as one would expect in the real world. This work significantly advances the typical visualization experience with respect to dynamic system simulation & animation in addition to being widely applicable to generic mechanical assemblies.


1996 ◽  
Vol 118 (1) ◽  
pp. 107-114
Author(s):  
R. Ganesan

Parametric steady-state vibrations of an asymmetric rotor while passing through primary resonance and the associated stability behavior are analyzed. The undamped case is considered and the equations of motion are rewritten in a from suitable for applying the method of multiple scales. Sensitivity to the bearing as well as shaft asymmetries of the oscillations due to unbalance excitation is evaluated. Expressions for amplitude and frequency modulation functions are obtained and are specialized to yield the steady-state solutions near primary resonance. Frequency-amplitude relationships that result from combined parametric and mass unbalance excitations are derived. Stability regions in the parameter space are obtained based on the time evolution of the amplitude and phase of the steady-state motions. The effects of bearing asymmetry on the amplitude and phase of the resonant oscillations are brought out. The sensitivity of vibrational and stability characteristics to various rotor-dynamic system parameters is illustrated through a numerical investigation.


2015 ◽  
Vol 732 ◽  
pp. 247-252 ◽  
Author(s):  
Fillemon Nduvu Nangolo ◽  
František Klimenda

There are many ways to model and to analyze discrete event systems. In general these systems lead to a non-linear characteristic equation description in linear algebra. This paper presents an analytical method for solving the characteristic equation of higher order, which arise when solving ordinary differential equations of motion of rigid body systems with 2 ≤ p° ≤ 10 degrees of freedom. The objective of this work was to express the characteristic equation in the form of product quadratic polynomial, from which the modal components could be found. To validate the model, the modal parameters extraction technique – Ibrahim Time Domain (ITD) – was used to extract modal parameters from artificial data developed in MATLAB environment. The extracted modal components were compared to those obtained from the analytical model.


1978 ◽  
Vol 1 (2) ◽  
pp. 245-253
Author(s):  
Munawar Hussain

In this paper the classical theorem “a conservative holonomic dynamic system is invariantly connected with a certain differential form” is generalized to group variables. This general theorem is then used to reduce the order of a Hamiltonian system by the use of the integral of energy. Equations of motion of the reduced system so obtained are derived which are the so-called generalized Whittaker's equations. Finally an example is given as an application of the theory.


2012 ◽  
Vol 91 (105) ◽  
pp. 19-24
Author(s):  
Aleksandar Baksa

This article deals with a dynamic system whose motion is constrained by nonholonomic, reonomic, affine constraints. The article analyses the geometrical properties of the ?reactions" of nonholonomic constraints in Voronets?s equations of motion. The analysis shows their link with the torsion of the Ehresmann connection, which is defined by the nonholonomic constraints.


Author(s):  
Usik Lee ◽  
Sunghwan Kim ◽  
Jooyong Cho

This paper presents a feasibility study on a structural damage identification method (SDIM) developed herein for cylindrical shells. The SDIM is derived directly from the governing differential equations of motion of damaged cylindrical shells. A damage distribution function is used to represent the distribution and magnitudes of local damages within a cylindrical shell. In contrast with most of existing modal parameters-based SDIMs, which requires only model parameters measured in both intact and damaged states, the present SDIM utilizes the FRF-data in the damaged state instead of the modal parameters in the damaged state. By virtue of utilizing FRF-data, a sufficient number of equations can be derived by choosing as many sets of excitation frequency and FRF measurement point as needed. The feasibility of the present SDIM is numerically tested through some illustrative examples, taking into account the random noises in FRF-data.


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