A Novel Three-Dimensional Presentation of the Steady-State Response of a Simple Damped Linear Oscillator

1968 ◽  
Vol 35 (1) ◽  
pp. 181-182
Author(s):  
R. Butterfield
Keyword(s):  
Steady State ◽  
Three Dimensional ◽  
Linear Oscillator ◽  
Steady State Response ◽  
State Response ◽  
Three Dimensional Presentation

scholarly journals Dynamic Response of a Thick Piezoelectric Circular Cylindrical Panel: An Exact Solution

2014 ◽  
Vol 2014 ◽  
pp. 1-8 ◽  
Author(s):  
Atta Oveisi ◽  
Mohammad Gudarzi ◽  
Seyyed Mohammad Hasheminejad
Keyword(s):  
Steady State ◽  
Mathematical Formulation ◽  
Three Dimensional ◽  
Cylindrical Panel ◽  
Mode Shapes ◽  
Steady State Response ◽  
Two Dimensional ◽  
Finite Element Software ◽  
State Response ◽  
Thick Shells

One of the interesting fields that attracted many researchers in recent years is the smart structures. The piezomaterials, because of their ability in converting both mechanical stress and electricity to each other, are very applicable in this field. However, most of the works available used various inexact two-dimensional theories with certain types of simplification, which are inaccurate in some applications such as thick shells while, in some applications due to request of large displacement/stress, thick piezoelectric panel is needed and two-dimensional theories have not enough accuracy. This study investigates the dynamic steady state response and natural frequency of a piezoelectric circular cylindrical panel using exact three-dimensional solutions based on this decomposition technique. In addition, the formulation is written for both simply supported and clamped boundary conditions. Then the natural frequencies, mode shapes, and dynamic steady state response of the piezoelectric circular cylindrical panel in frequency domain are validated with commercial finite element software (ABAQUS) to show the validity of the mathematical formulation and the results will be compared, finally.

Reduced-Order Modeling for Stability and Steady-State Response Analysis of Asymmetric Rotor Using Three-Dimensional Finite Element Model

2019 ◽  
Vol 141 (10) ◽  
Author(s):  
Zhaoli Zheng ◽  
Yonghui Xie ◽  
Di Zhang
Keyword(s):  
Finite Element ◽  
Steady State ◽  
Three Dimensional ◽  
Element Model ◽  
Response Analysis ◽  
Steady State Response ◽  
Reduced Order ◽  
State Response ◽  
Asymmetric Rotor ◽  
Bearing System

A generalized and efficient technique of reduced-order model (ROM) is proposed in this paper for stability and steady-state response analysis of an asymmetric rotor based on three-dimensional (3D) finite element model. The equations of motion of the asymmetric rotor-bearing system are established in the rotating frame. Therefore, the periodic time-variant coefficients only exist at a tiny minority of degrees-of-freedom (DOFs) of bearings. During the model reduction process, the asymmetric rotor-bearing system is divided into rotor and bearings. Only the rotor was reduced. And the physical coordinates of bearings are kept in the reduced model during reduction. Then, the relationship between the rotor and bearings is established by inserting periodic time-variant stiffness and damping matrix of bearings into the reduced model of rotor. There is no reduction to the matrices of bearings, which guarantees the accuracy of the calculation. This technique combined with fixed-interface component mode synthesis (CMS) and free-interface CMS is compared with other existing modal reduction method on an off-center asymmetric rotor and shows good performance.

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