Transfer Function of a Class of Nonlinear Multidegree of Freedom Oscillators

1987 ◽  
Vol 54 (1) ◽  
pp. 215-225 ◽  
Author(s):  
L. E. Galhoud ◽  
S. F. Masri ◽  
J. C. Anderson
Keyword(s):  
Exact Solution ◽  
Mechanical Model ◽  
Geometric Nonlinearity ◽  
Experimental Studies ◽  
Harmonic Excitation ◽  
System Response ◽  
Distributed Parameter ◽  
Experimental Measurements ◽  
Practical Engineering ◽  
Two Degree Of Freedom

Analytical and experimental studies were made of the dynamic response of a multidegree-of-freedom system with a geometric nonlinearity, which is encountered in many practical engineering applications. An exact solution was derived for the steady-state motion of a viscously damped two-degree-of-freedom oscillator with an unsymmetric geomtric nonlinearity, under the action of harmonic excitation. Experimental measurements of a distributed-parameter mechanical model under harmonic excitation verified the analytical findings. The effect of various dimensionless parameters on the system response was determined.

Dynamic Response of a Beam With a Geometric Nonlinearity

1981 ◽  
Vol 48 (2) ◽  
pp. 404-410 ◽  
Author(s):  
S. F. Masri ◽  
Y. A. Mariamy ◽  
J. C. Anderson
Keyword(s):  
Dynamic Response ◽  
Mechanical Model ◽  
Geometric Nonlinearity ◽  
Experimental Studies ◽  
Harmonic Excitation ◽  
Random Excitation ◽  
System Response ◽  
Experimental Measurements ◽  
Euler Beam ◽  
Practical Engineering

Analytical and experimental studies were made of the dynamic response of a system with a geometric nonlinearity, which is encountered in many practical engineering applications. An exact solution was derived for the steady-state motion of a viscously damped Bernoulli-Euler beam with an unsymmetric geometric nonlinearity, under the action of harmonic excitation. Experimental measurements of a mechanical model under harmonic as well as random excitation verified the analytical findings. The effect of various dimensionless parameters on the system response was determined.

Analytical and Experimental Studies of a Dynamic System With a Gap

1978 ◽  
Vol 100 (3) ◽  
pp. 480-486 ◽  
Author(s):  
S. F. Masri
Keyword(s):  
Experimental Study ◽  
Dynamic System ◽  
Mechanical Model ◽  
Experimental Studies ◽  
Harmonic Excitation ◽  
Resonance Phenomenon ◽  
Mechanical Equipment ◽  
Experimental Measurements ◽  
System Parameters ◽  
Closed Form Analytical Solution

An analytical and experimental study is made of the forced vibration of a dynamic system with a motion-limiting stop, which is encountered in many practical cases involving mechanical equipment. An exact closed-form analytical solution is derived for the steady-state motion of the system when it is subjected to harmonic excitation. Experimental measurements with a mechanical model verify the analytical findings. The effects of various system parameters on the response are determined. Some interesting features of the motion are observed and compared to the jump resonance phenomenon exhibited by the solution of Duffing’s equation.

NONLINEAR INTERACTIONS BETWEEN TWO WIDELY SPACED MODES — EXTERNAL EXCITATION

1993 ◽  
Vol 03 (02) ◽  
pp. 417-427 ◽  
Author(s):  
S.A. NAYFEH ◽  
A.H. NAYFEH
Keyword(s):  
Natural Frequency ◽  
High Frequency ◽  
Analytical Study ◽  
Experimental Studies ◽  
Low Frequency ◽  
Harmonic Excitation ◽  
Frequency Mode ◽  
Large Contribution ◽  
High Frequency Mode ◽  
Two Degree Of Freedom

Recent experimental studies indicate that energy can be transferred from high- to low-frequency modes in structures with weak nonlinearity. In each of these experiments, a high-frequency mode was driven near its natural frequency but the response included a large contribution due to the first mode of the structure. In this paper, an analytical study of the response of a two-degree-of-freedom nonlinear system with widely spaced modes to a simple-harmonic excitation near the natural frequency of its high-frequency mode is presented. This system serves as a paradigm for the interaction of high- and low-frequency modes.

Nonlinear Vibrations of Viscoelastic Plane Truss Under Harmonic Excitation

2014 ◽  
Vol 14 (04) ◽  
pp. 1450009 ◽  
Author(s):  
Andrew Yee Tak Leung ◽  
Hong Xiang Yang ◽  
Ping Zhu
Keyword(s):  
Steady State ◽  
Fractional Derivatives ◽  
Harmonic Excitation ◽  
Homotopy Continuation ◽  
Response Curves ◽  
System A ◽  
Structural Responses ◽  
Voigt Model ◽  
Two Degree Of Freedom ◽  
Steady State Solutions

This paper is concerned with the steady state bifurcations of a harmonically excited two-member plane truss system. A two-degree-of-freedom Duffing system having nonlinear fractional derivatives is derived to govern the dynamic behaviors of the truss system. Viscoelastic properties are described by the fractional Kelvin–Voigt model based on the Caputo definition. The combined method of harmonic balance and polynomial homotopy continuation is adopted to obtain steady state solutions analytically. A parametric study is conducted with the help of amplitude-response curves. Despite its seeming simplicity, the mechanical system exhibits a wide variety of structural responses. The primary and sub-harmonic resonances and chaos are found in specific regions of system parameters. The dynamic snap-through phenomena are observed when the forcing amplitude exceeds some critical values. Moreover, it has been shown that, suppression of undesirable responses can be achieved via changing of viscosity of the system.

On the Free Vibration of Mono-Coupled Periodic Distributed Parameter Systems

1993 ◽  
Author(s):  
Gerhard G. G. Lueschen ◽  
Lawrence A. Bergman
Keyword(s):  
Exact Solution ◽  
Free Vibration ◽  
Periodic Structure ◽  
Classical Result ◽  
Discrete Systems ◽  
Distributed Parameter Systems ◽  
Distributed Parameter ◽  
New Approach

Abstract A new approach to the exact solution is given for the free vibration of a periodic structure comprised of a multiplicity of identical linear distributed parameter substructures, closely coupled through identical linear springs. The method used is an extension of a classical result for periodic discrete systems.

The Two-Degree-of-Freedom Tuned-Mass Damper for Suppression of Single-Mode Vibration Under Random and Harmonic Excitation

2005 ◽  
Vol 128 (1) ◽  
pp. 56-65 ◽  
Author(s):  
Lei Zuo ◽  
Samir A. Nayfeh
Keyword(s):  
Vibration Suppression ◽  
Single Mode ◽  
Tuned Mass Damper ◽  
Harmonic Excitation ◽  
Degree Of Freedom ◽  
Primary System ◽  
H Infinity ◽  
Mass Damper ◽  
Mode Vibration ◽  
Two Degree Of Freedom

Whenever a tuned-mass damper is attached to a primary system, motion of the absorber body in more than one degree of freedom (DOF) relative to the primary system can be used to attenuate vibration of the primary system. In this paper, we propose that more than one mode of vibration of an absorber body relative to a primary system be tuned to suppress single-mode vibration of a primary system. We cast the problem of optimization of the multi-degree-of-freedom connection between the absorber body and primary structure as a decentralized control problem and develop optimization algorithms based on the H2 and H-infinity norms to minimize the response to random and harmonic excitations, respectively. We find that a two-DOF absorber can attain better performance than the optimal SDOF absorber, even for the case where the rotary inertia of the absorber tends to zero. With properly chosen connection locations, the two-DOF absorber achieves better vibration suppression than two separate absorbers of optimized mass distribution. A two-DOF absorber with a negative damper in one of its two connections to the primary system yields significantly better performance than absorbers with only positive dampers.

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.

Transfer Function Analysis of Non-Uniformly Distributed Parameter Systems

1993 ◽  
Author(s):  
Bingen Yang ◽  
Houfei Fang
Keyword(s):  
Distributed Systems ◽  
Transfer Function ◽  
State Space ◽  
Fundamental Matrix ◽  
Function Analysis ◽  
Distributed Parameter Systems ◽  
System Response ◽  
Distributed Parameter ◽  
Transfer Function Analysis ◽  
Function Formulation

Abstract This paper studies a transfer function formulation for general one-dimensional, non-uniformly distributed systems subject to arbitrary boundary conditions and external disturbances. The purpose is to provide an useful alternative for modeling and analysis of distributed parameter systems. In the development, the system equations of the non-uniform system are cast into a state space form in the Laplace transform domain. The system response and distributed transfer functions are derived in term of the fundamental matrix of the state space equation. Two approximate methods for evaluating the fundamental matrix are proposed. With the transfer function formulation, various dynamics and control problems for the non-uniformly distributed system can be conveniently addressed. The transfer function analysis is also applied to constrained/combined non-uniformly distributed systems.

Transfer Function Modeling of Distributed Piezoelectric Vibration Energy Harvesters

2009 ◽  
Author(s):  
Chin An Tan ◽  
Heather L. Lai
Keyword(s):  
Transfer Function ◽  
Transfer Functions ◽  
Vibration Energy ◽  
System Response ◽  
Distributed Parameter ◽  
Domain Modeling ◽  
Vibration Energy Harvesting ◽  
Energy Harvesters ◽  
Adjoint Systems ◽  
The Stability

Extensive research has been conducted on vibration energy harvesting utilizing a distributed piezoelectric beam structure. A fundamental issue in the design of these harvesters is the understanding of the response of the beam to arbitrary external excitations (boundary excitations in most models). The modal analysis method has been the primary tool for evaluating the system response. However, a change in the model boundary conditions requires a reevaluation of the eigenfunctions in the series and information of higher-order dynamics may be lost in the truncation. In this paper, a frequency domain modeling approach based in the system transfer functions is proposed. The transfer function of a distributed parameter system contains all of the information required to predict the system spectrum, the system response under any initial and external disturbances, and the stability of the system response. The methodology proposed in this paper is valid for both self-adjoint and non-self-adjoint systems, and is useful for numerical computer coding and energy harvester design investigations. Examples will be discussed to demonstrate the effectiveness of this approach for designs of vibration energy harvesters.

scholarly journals The Dynamic Response of Tuned Impact Absorbers for Rotating Flexible Structures

2005 ◽  
Vol 1 (1) ◽  
pp. 13-24 ◽  
Author(s):  
Steven W. Shaw ◽  
Christophe Pierre
Keyword(s):  
Dynamic Response ◽  
Flexible Structures ◽  
Experimental Studies ◽  
Analytical Investigation ◽  
Design Parameters ◽  
System Response ◽  
Rotor Speed ◽  
Flexible System ◽  
Restoring Forces ◽  
And Performance

This paper describes an analytical investigation of the dynamic response and performance of impact vibration absorbers fitted to flexible structures that are attached to a rotating hub. This work was motivated by experimental studies at NASA, which demonstrated the effectiveness of these types of absorbers for reducing resonant transverse vibrations in periodically excited rotating plates. Here we show how an idealized model can be used to describe the essential dynamics of these systems, and used to predict absorber performance. The absorbers use centrifugally induced restoring forces so that their nonimpacting dynamics are tuned to a given order of rotation, whereas their large amplitude dynamics involve impacts with the primary flexible system. The linearized, nonimpacting dynamics are first explored in detail, and it is shown that the response of the system has some rather unique features as the hub rotor speed is varied. A class of symmetric impacting motions is also analyzed and used to predict the effectiveness of the absorber when operating in its impacting mode. It is observed that two different types of grazing bifurcations take place as the rotor speed is varied through resonance, and their influence on absorber performance is described. The analytical results for the symmetric impacting motions are also used to generate curves that show how important absorber design parameters—including mass, coefficient of restitution, and tuning—affect the system response. These results provide a method for quickly evaluating and comparing proposed absorber designs.

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