Modal Interactions in Dynamical and Structural Systems

1989 ◽  
Vol 42 (11S) ◽  
pp. S175-S201 ◽  
Author(s):  
A. H. Nayfeh ◽  
B. Balachandran
Keyword(s):  
Dynamical Systems ◽  
Surface Waves ◽  
Nonlinear Response ◽  
Experimental Studies ◽  
Structural Systems ◽  
Qualitative Behavior ◽  
Modal Interactions ◽  
Chaotic Motions ◽  
Beam Structures ◽  
Quadratic Nonlinearities

We review theoretical and experimental studies of the influence of modal interactions on the nonlinear response of harmonically excited structural and dynamical systems. In particular, we discuss the response of pendulums, ships, rings, shells, arches, beam structures, surface waves, and the similarities in the qualitative behavior of these systems. The systems are characterized by quadratic nonlinearities which may lead to two-to-one and combination autoparametric resonances. These resonances give rise to a coupling between the modes involved in the resonance leading to nonlinear periodic, quasi-periodic, and chaotic motions.

scholarly journals Theoretical and Experimental Investigation of Two-to-One Internal Resonance in MEMS Arch Resonators

2018 ◽  
Vol 14 (1) ◽  
Author(s):  
Feras K. Alfosail ◽  
Amal Z. Hajjaj ◽  
Mohammad I. Younis
Keyword(s):  
Internal Resonance ◽  
Nonlinear Response ◽  
Multiple Scales ◽  
Hopf Bifurcations ◽  
Chaotic Motions ◽  
Different Types ◽  
Quadratic Nonlinearities ◽  
Multiple Scales Perturbation Method ◽  
Good Agreement ◽  
Perturbation Solutions

We investigate theoretically and experimentally the two-to-one internal resonance in micromachined arch beams, which are electrothermally tuned and electrostatically driven. By applying an electrothermal voltage across the arch, the ratio between its first two symmetric modes is tuned to two. We model the nonlinear response of the arch beam during the two-to-one internal resonance using the multiple scales perturbation method. The perturbation solution is expanded up to three orders considering the influence of the quadratic nonlinearities, cubic nonlinearities, and the two simultaneous excitations at higher AC voltages. The perturbation solutions are compared to those obtained from a multimode Galerkin procedure and to experimental data based on deliberately fabricated Silicon arch beam. Good agreement is found among the results. Results indicate that the system exhibits different types of bifurcations, such as saddle node and Hopf bifurcations, which can lead to quasi-periodic and potentially chaotic motions.

Nonresonant Modal Interactions

1995 ◽  
Author(s):  
Zaichun Feng
Keyword(s):  
Dynamical Systems ◽  
Nonlinear Systems ◽  
Mechanical System ◽  
Modal Interactions ◽  
Chaotic Motions ◽  
Work Mechanism ◽  
One To One ◽  
Energy Interchange

Abstract Modal interactions in nonlinear systems provide a means by which energy can be transferred between modes. This energy interchange may give rise to chaotic motions in dynamical systems. Extensive research has been focused on the resonant modal interactions when the frequencies of the interacting modes are commensurate such as one-to-one and one-to-two resonances. It is recently realized that modal interactions can also occur even if the frequencies of the interacting modes are non-commensurate. In this work, mechanism for these nonresonant modal interactions is identified and illustrated through a simple mechanical system.

Vibrations of Foundations Interacting With Subsoil Experimental Studies and BE Calculations

1991 ◽  
Author(s):  
L. Gaul
Keyword(s):  
Boundary Element Method ◽  
Dynamic Response ◽  
Surface Waves ◽  
Boundary Element ◽  
Constitutive Equations ◽  
Experimental Studies ◽  
Boundary Elements ◽  
Experimental Techniques ◽  
Embedded Structures ◽  
Element Method

Abstract Calculation of the dynamic response of sensitive structures like foundations for vibrating machinery requires to take the interaction with subsoil into account. Structures and soil are discretized by boundary elements and coupled by a substructure technique. Viscoelastic constitutive equations contain fractional time derivatives. Surface waves generated by machine foundations and diffracted by embedded structures and soil inhomogeneities are analyzed by conventional and optoelectronic experimental techniques and calculated by the boundary element method (BEM).

scholarly journals Robust H∞ Control of STMDs Used in Structural Systems by Hardware in the Loop Simulation Method

Actuators ◽  
2020 ◽  
Vol 9 (3) ◽  
pp. 55
Author(s):  
Huseyin Aggumus ◽  
Rahmi Guclu
Keyword(s):  
Natural Frequencies ◽  
Experimental Studies ◽  
Mr Damper ◽  
Simulation Method ◽  
Control Element ◽  
Structural Systems ◽  
Hardware In The Loop ◽  
Building Model ◽  
Mass Damper ◽  
Set Up

This paper investigated the performance of a semi-active tuned mass damper (STMD) on a multi-degree of freedom (MDOF) building model. A magnetorheological (MR) damper was used as a control element that provided semi-activity in the STMD. The Hardware in the Loop Simulation (HILS) method was applied to mitigate the difficulty and expense of experimental studies, as well as to obtain more realistic results from numerical simulations. In the implementation of this method for the STMD, the MR damper was set up experimentally, other parts of the system were modeled as computer simulations, and studies were carried out by operating these two parts simultaneously. System performance was investigated by excitation with two different acceleration inputs produced from the natural frequencies of the MDOF building. Additionally, a robust H ∞ controller was designed to determine the voltage transmitted to the MR damper. The results showed that the HILS method could be applied successfully to STMDs used in structural systems, and robust H ∞ controls improve system responses with semi-active control applications. Moreover, the control performance of the MR damper develops with an increase in the mass of the STMD.

Micromechanical Analysis of Nonlinear Response of Unidirectional Composites: A Fundamental Approach

2001 ◽  
Author(s):  
Virendra R. Jadhav ◽  
Srinivasan Sridharan
Keyword(s):  
Mechanical Model ◽  
Nonlinear Response ◽  
Experimental Studies ◽  
Matrix Cracking ◽  
Type Model ◽  
Unidirectional Composites ◽  
The Matrix ◽  
Experimental Response ◽  
Square Cells ◽  
Experimental Comparisons

Abstract Micromechanical models with different representative volume elements have been developed to study their ability to predict nonlinear response of unidirectional composites. A simple, square cells type micro-mechanical model similar to those widely used by other researchers is compared with a more advanced 3-phase finite element based micro-mechanical model. The models utilize the “bulk” properties of the matrix without attempting to “tune” the model to fit with experimental response of laminae. This is a more fundamental approach and constitutes a departure from current practice. The models account for shear softening, matrix cracking and the presence of residual stresses. A smeared cracking approach was used to characterize the micro-cracking in matrix. Experimental studies were performed on laminae, laminates and cylinders made from carbon epoxy composites. Experimental comparisons show that the more accurate micro-mechanical model with proper partial cracking options provides good bounds on experimental response with consistent accuracy. A square cells type model however is not consistent in its predictions, thus raising questions about its applicability in any general micro-mechanics based analysis.

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