Dynamic Behavior of a Harmonically Excited Electromechanical Drive With Elastic Couplings

1997 ◽  
Vol 119 (1) ◽  
pp. 21-30 ◽  
Author(s):  
V. Chaika ◽  
M. Mariunas
Keyword(s):  
Dynamic Behavior ◽  
Numerical Optimization ◽  
Vibration Analysis ◽  
Optimization Technique ◽  
Harmonic Excitation ◽  
Response Curves ◽  
Electromechanical Drive ◽  
Rotary Machines ◽  
Elastic Couplings ◽  
Parameter Values

Steady-state vibration of a lumped rotary system containing an electric drive is considered. The system is subjected to the harmonic excitation caused by the variation of voltage of the electric motor and the resisting torque of the operating machine. The influence of several types of elastic couplings on the dynamic behavior of an electromechanical drive is investigated. Numerical-analytical methods of nonlinear vibration analysis are applied. Frequency-response curves of rotary machines for different coupling cases are obtained. A numerical optimization technique for the estimation of the rational parameter values of the system is developed. Vibration controlling properties of standard and centrifugal couplings are compared.

Strongly Nonlinear Vibrations of a Hyperelastic Thin-walled Cylindrical Shell Based on the Modified Lindstedt–Poincaré Method

2019 ◽  
Vol 19 (12) ◽  
pp. 1950160 ◽  
Author(s):  
Jing Zhang ◽  
Jie Xu ◽  
Xuegang Yuan ◽  
Wenzheng Zhang ◽  
Datian Niu
Keyword(s):  
Cylindrical Shell ◽  
Nonlinear System ◽  
Differential Equations ◽  
Nonlinear Vibrations ◽  
Harmonic Excitation ◽  
System Of Differential Equations ◽  
Response Curves ◽  
Strongly Nonlinear ◽  
Hardening Behavior ◽  
Thin Walled

Some significant behaviors on strongly nonlinear vibrations are examined for a thin-walled cylindrical shell composed of the classical incompressible Mooney–Rivlin material and subjected to a single radial harmonic excitation at the inner surface. First, with the aid of Donnell’s nonlinear shallow-shell theory, Lagrange’s equations and the assumption of small strains, a nonlinear system of differential equations for the large deflection vibration of a thin-walled shell is obtained. Second, based on the condensation method, the nonlinear system of differential equations is reduced to a strongly nonlinear Duffing equation with a large parameter. Finally, by the appropriate parameter transformation and modified Lindstedt–Poincar[Formula: see text] method, the response curves for the amplitude-frequency and phase-frequency relations are presented. Numerical results demonstrate that the geometrically nonlinear characteristic of the shell undergoing large vibrations shows a hardening behavior, while the nonlinearity of the hyperelastic material should weak the hardening behavior to some extent.

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.

Vibration Isolation From Harmonic Disturbances Through Use of Internally Rotating Masses

2015 ◽  
Author(s):  
Eric Smith ◽  
Al Ferri
Keyword(s):  
Kinetic Energy ◽  
Vibration Isolation ◽  
Harmonic Excitation ◽  
Impulsive Loading ◽  
Qualitative Behavior ◽  
Single Degree Of Freedom ◽  
Transmitted Force ◽  
A Chain ◽  
Isolation Systems ◽  
Parameter Values

This paper considers the use of a chain of translating carts or housings having internally rotating eccentric masses in order to accomplish vibration isolation. First a single degree-of-freedom system is harmonically excited to uncover the qualitative behavior of each rotating mass. The simple model is then expanded into a chain of housings, containing rotating eccentric masses, which are interconnected with springs. The internal rotating eccentric masses are damped along their circular pathway by means of linear viscous damping. Due to the lack of elastic or gravitational constraint on the rotating eccentric masses, they provide a nonlinear inertial coupling to their housings. Previous research has shown that such systems are capable of reducing shock or impulsive loading by converting some of the translational kinetic energy into rotational kinetic energy of the internal masses. This paper examines the potential for vibration isolation of a chain of such systems subjected to persistent, harmonic excitation. It is seen that the dynamics of these systems is very complicated, but that trends are observed which have implications for practical isolation systems. Using simulation studies, tradeoffs are examined between displacement and transmitted force for a range of physical parameter values.

A Numerical Optimization Technique Applied to the Design of Two-Dimensional Cavitating Hydrofoil Sections

1996 ◽  
Vol 40 (01) ◽  
pp. 28-38
Author(s):  
Shigenori Mishima ◽  
Spyros A. Kinnas
Keyword(s):  
Numerical Optimization ◽  
Cavity Length ◽  
Optimization Technique ◽  
Cavitation Number ◽  
Quadratic Functions ◽  
Two Dimensional ◽  
Systematic Design ◽  
Hydrodynamic Analysis ◽  
Total Drag ◽  
Cavitating Hydrofoil

A numerical nonlinear optimization technique is applied to the systematic design of two-dimensional partially or supercavitating hydrofoil sections. The design objective is to minimize the hydrofoil drag for given lift and cavitation number. The hydrodynamic analysis of the cavitating hydrofoil is performed in nonlinear theory, via a low-order potential-based panel method. The effects of viscosity are taken into account via a uniform friction coefficient applied on the wetted foil surface. The total drag, lift, cavitation number, and other quantities involved in the imposed constraints, are expressed in terms of quadratic functions of the main parameters of the hydrofoil geometry, angle of attack, and the cavity length. The optimization is based on the method of multipliers by coupling the Lagrange multiplier terms and the penalty function terms. The robustness and convergence of the method are extensively investigated, and the results are compared with those from applying other design methods.

Efficient Structural Design Using a Numerical Optimization Technique

2019 ◽  
Author(s):  
Qian Wang ◽  
Lucas Schmotzer ◽  
Yongwook Kim
Keyword(s):  
Structural Design ◽  
Numerical Optimization ◽  
Optimization Technique ◽  
Optimization Method ◽  
Optimization Techniques ◽  
Convergence Criteria ◽  
Efficient Design ◽  
Concrete Building ◽  
Gradient Based ◽  
Structural Responses

<p>Structural designs of complex buildings and infrastructures have long been based on engineering experience and a trial-and-error approach. The structural performance is checked each time when a design is determined. An alternative strategy based on numerical optimization techniques can provide engineers an effective and efficient design approach. To achieve an optimal design, a finite element (FE) program is employed to calculate structural responses including forces and deformations. A gradient-based or gradient-free optimization method can be integrated with the FE program to guide the design iterations, until certain convergence criteria are met. Due to the iterative nature of the numerical optimization, a user programming is required to repeatedly access and modify input data and to collect output data of the FE program. In this study, an approximation method was developed so that the structural responses could be expressed as approximate functions, and that the accuracy of the functions could be adaptively improved. In the method, the FE program was not required to be directly looped in the optimization iterations. As a practical illustrative example, a 3D reinforced concrete building structure was optimized. The proposed method worked very well and optimal designs were found to reduce the torsional responses of the building.</p>

Large Amplitude Forced Vibration Analysis of Stiffened Plates under Harmonic Excitation

2012 ◽  
pp. 26-61
Author(s):  
Anirban Mitra ◽  
Prasanta Sahoo ◽  
Kashinath Saha
Keyword(s):  
Free Vibration ◽  
Forced Vibration ◽  
Large Amplitude ◽  
Vibration Analysis ◽  
Mathematical Formulation ◽  
Free Vibration Analysis ◽  
Harmonic Excitation ◽  
Stiffened Plates ◽  
Backbone Curve ◽  
Forced Vibration Analysis

Large amplitude forced vibration behaviour of stiffened plates under harmonic excitation is studied numerically incorporating the effect of geometric non-linearity. The forced vibration analysis is carried out in an indirect way in which the dynamic system is assumed to satisfy the force equilibrium condition at peak excitation amplitude. Large amplitude free vibration analysis of the same system is carried out separately to determine the backbone curves. The mathematical formulation is based on energy principles and the set of governing equations for both forced and free vibration problems derived using Hamilton’s principle. Appropriate sets of coordinate functions are formed by following the two dimensional Gram-Schmidt orthogonalization procedure to satisfy the corresponding boundary conditions of the plate. The problem is solved by employing an iterative direct substitution method with an appropriate relaxation technique and when the system becomes computationally stiff, Broyden’s method is used. The results are furnished as frequency response curves along with the backbone curve in the dimensionless amplitude-frequency plane. Three dimensional operational deflection shape (ODS) plots and contour plots are provided in a few cases.

A Non-Classical Analytical Approach for Vibration Analysis of Isotropic and Fgm Plate Containing a Star Shaped Crack

2020 ◽  
Vol 36 (4) ◽  
pp. 465-484
Author(s):  
Ankur Gupta ◽  
Shashank Soni ◽  
N. K. Jain
Keyword(s):  
Governing Equation ◽  
Vibration Analysis ◽  
Plate Theory ◽  
Couple Stress Theory ◽  
Modified Couple Stress Theory ◽  
Multiple Cracks ◽  
Arbitrary Orientation ◽  
Response Curves ◽  
Classical Plate Theory ◽  
Orientation Gradient

ABSTRACTA non-classical analytical model for vibration analysis of thin isotropic and FGM plate containing multiple part-through cracks (star shaped) of arbitrary orientation is proposed. A plate containing four concentric cracks of arbitrary orientation in the form of continuous line is considered for analysis. The proposed governing equation is derived based on classical plate theory and modified couple stress theory. Line spring model is modified to accommodate all the crack terms. The application of Berger’s formulation introduces nonlinearities in the governing equation and then the Galerkin’s method is applied for solving final governing equation. Results for fundamental frequencies for different values of crack length, crack orientation, gradient index and material length scale parameters are presented for two different boundary conditions. Furthermore, to study the phenomenon of bending hardening/softening in a cracked plate, the frequency response curves are plotted for the parameters stated above. Based on the outcomes of this study, it can be concluded that stiffness of the plate is severely affected by the presence of multiple cracks and the stiffness goes on decreasing with increase in number of cracks thereby affecting the fundamental frequency.

Sign in / Sign up

Export Citation Format

Share Document