scholarly journals A Novel Elastic Metamaterial with Multiple Resonators for Vibration Suppression

2021 ◽  
Vol 2021 ◽  
pp. 1-16
Author(s):  
Saman Ahmadi Nooraldinvand ◽  
Hamid M. Sedighi ◽  
Amin Yaghootian
Keyword(s):  
Vibration Suppression ◽  
Equations Of Motion ◽  
Small Mass ◽  
The Other ◽  
Governing Equations ◽  
System Parameters ◽  
Rectangular Frame ◽  
Adams Software ◽  
Linear Spring ◽  
Base Structure

In this paper, two models of elastic metamaterial containing one and two resonators are proposed to obtain the bandgaps with the aim of providing broadband vibration suppression. The model with one DOF is built by assembling several unite cells in which each unite cell consists of a rectangular frame as the base structure and a rack-and-pinion mechanism that is joined to the frame with a linear spring on both sides. In the second model with two DOF, a small mass is added while its center is attached to the center of the pinion on one side and the other side is connected to the rectangular frame via a linear spring. In the first mechanism, the pinion is considered as the single resonator, and in the 2DOF model, on the other hand, the pinion and small mass acted as multiple resonators. By obtaining the governing equations of motion for a single cell in each model, the dynamic behavior of two metastructures is thoroughly investigated. Therefore, the equations of motion for the two models are written in matrix form, and then, the dispersion relations are presented to analyze the influences of system parameters on the bandgaps’ starting/ending frequencies. Finally, two models are successfully compared and then numerically simulated via MATLAB-SIMULINK and MSC-ADAMS software. With the aid of closed-form expressions for starting/ending frequencies, the correlation between the system parameters and bandgap intervals can be readily recognized.

Dynamic Modeling of a Piggybacked Cantilever Beam System

2014 ◽  
Author(s):  
Troy Lundstrom ◽  
Nader Jalili
Keyword(s):  
Vibration Suppression ◽  
Equations Of Motion ◽  
Continuous System ◽  
Element Model ◽  
System Response ◽  
Structure Response ◽  
Beam System ◽  
Geometric Boundary ◽  
Primary Base ◽  
Base Structure

Typically, active resonators for vibration suppression of flexible systems are uniaxial and can only affect structure response in the direction of the applied force. The application of piezoelectric bender actuators as active resonators may prove to be advantageous over typical, uniaxial actuators as they can dynamically apply both torque and translational force to the base structure attachment point; this minimizes the likelihood that the attachment location is the node of a mode (rotary or translational). In this paper, Hamilton’s Principle is used to develop the equations of motion for a continuous two-beam system composed of a cantilevered, primary base beam with a secondary piezoelectric bender mounted to its surface. A disturbance force is applied near the fixture location of the base beam and the system response is estimated using a sufficient quantity of assumed eigenfunctions that satisfy the geometric boundary conditions. A theoretical study is performed to compared the continuous system eigenfunctions to a finite element model (FEM) of the two-beam structure and the required number of eigenfunctions required to yield a convergent solution for an impulse excitation is explored. In addition, the frequency response function for the dynamic system is presented and compared to that of a FEM.

Vibration Suppression in a Pinned-Pinned Nonlinear Rod Using a Frictionless Slider

2012 ◽  
Author(s):  
Tingli Cai ◽  
Ranjan Mukherjee ◽  
Alejandro R. Diaz
Keyword(s):  
Feedback Loop ◽  
Vibration Suppression ◽  
Equilibrium Configuration ◽  
Equations Of Motion ◽  
Lyapunov Stability Theory ◽  
Governing Equations ◽  
Constraint Force ◽  
Negative Work ◽  
Slider Motion ◽  
Principle Of Virtual Displacements

We propose a new method for vibration suppression in a flexible structure using a frictionless sliding constraint. The constraint force applied by the slider is assumed known from measurements and the slider motion is prescribed to do negative work on the structure. The structure is modeled as a two-dimensional nonlinear rod with pinned-pinned boundary conditions and the slider is assumed to constrain the position of one point on the rod but not its slope. The problem is formulated using variable-length finite elements in the framework of Arbitrary Lagrange-Euler (ALE) description. The governing equations of motion are derived using the principle of virtual displacements and D’Alembert’s principle. Numerical simulation results are presented to demonstrate the effectiveness of the control strategy based on the idea of negative work. To meet the bandwidth requirement of the actuator, a nonlinear filter is placed in the feedback loop and asymptotic stability of the equilibrium configuration is established using Lyapunov stability theory.

Elastic System Moving on an Elastically Supported Beam

1984 ◽  
Vol 106 (2) ◽  
pp. 292-297 ◽  
Author(s):  
T. C. Huang ◽  
V. N. Shah
Keyword(s):  
Elastic System ◽  
Equations Of Motion ◽  
Variable Coefficients ◽  
Structural Members ◽  
Governing Equations ◽  
Linear Spring ◽  
Inertia Properties ◽  
Elastically Supported ◽  
Predictor Corrector ◽  
Unsprung Mass

The problem of a two-dimensional elastic system moving on a beam is considered. The moving elastic system or vehicle is represented by the structural members with distributed stiffness, damping, and inertia properties, and it is supported by the suspension units. Each suspension unit consists of a linear spring, a viscous damper, and an unsprung mass. The beam is supported at discrete points along its length, and/or by an elastic foundation. The deformations of the moving system and the beam are represented by their corresponding eigenfunction series. The resulting governing equations are represented by the coupled, ordinary differential equations with variable coefficients. The equations of motion for an elastic platform moving with constant velocity on a beam are derived and solved by the Hamming’s predictor-corrector method. Numerical examples are presented.

scholarly journals Theoretical Analysis and Optimization of a Gloved Hand-arm System

2021 ◽  
Author(s):  
Oreoluwa Alabi ◽  
Sunit Kumar Gupta ◽  
Oumar Barry
Keyword(s):  
Harmonic Balance ◽  
Equations Of Motion ◽  
Biomechanical Model ◽  
Lumped Parameter Model ◽  
Human Hand ◽  
Governing Equations ◽  
Lumped Parameter ◽  
Hand Tool ◽  
Modeling Techniques ◽  
Linear Spring

Abstract Studies have shown that isolators in the form of anti-vibration gloves effectively reduce the transmission of unwanted vibration from vibrating equipment to the human hand. However, as most of these studies are based on experimental or modeling techniques, the level of effectiveness and optimum glove properties for better performance remains unclear. To fill this gap, hand-arm system dynamics with and without gloves are studied analytically in this work. In the current work, we use a lumped parameter model of the hand-arm system, with hand-tool interaction modeled as a linear spring-damper system. The resulting governing equations of motion are solved analytically using the method of harmonic balance. Parametric analysisis performed on the biomechanical model of the hand-armsystem with and without a glove to identify key design pa-rameters. It is observed that the effect of glove parameters on its performance is not repetitive and changes in the studied different frequency ranges. This observation further motivates us to optimize the glove parameters to minimize the overall transmissibility in different frequency ranges.

Maneuver Control and Vibration Suppression of a Smart Flexible Satellite Using Robust Passivity Based Control

2012 ◽  
Vol 488-489 ◽  
pp. 1803-1807
Author(s):  
Mohammad Azadi
Keyword(s):  
Differential Equations ◽  
Ordinary Differential Equations ◽  
Vibration Suppression ◽  
Equations Of Motion ◽  
Governing Equations ◽  
Lagrange Method ◽  
Piezoelectric Layers ◽  
Simulation Results ◽  
Passivity Based Control ◽  
Flexible Appendages

In this paper a satellite with two flexible appendages and the piezoelectric layers which are attached to them and a central hub is considered. The piezoelectric layers are used as actuators. The governing equations of motion are derived based on Lagrange method. Using Rayleigh-Ritz technique ordinary differential equations of motion are obtained. A robust passivity based control is applied to the system to not only control the three axes maneuver of the satellite but also suppress the vibrations of the flexible appendages. Finally, the system is simulated and simulation results show the good performance of this controller.

Dynamic Modeling and Vibration Control of Electrorheological Mounts

2004 ◽  
Vol 126 (4) ◽  
pp. 537-541 ◽  
Author(s):  
Seung-Bok Choi ◽  
Sung-Ryong Hong
Keyword(s):  
Vibration Control ◽  
Frequency Domain ◽  
Dynamic Modeling ◽  
Static Load ◽  
Equations Of Motion ◽  
The Other ◽  
Flow Mode ◽  
Governing Equations ◽  
Field Dependent ◽  
Different Types

This paper presents two different types of electrorheological (ER) mounts that can support a static load of 200 kg. One is a flow mode type, and the other is a squeeze mode type. After analyzing the governing equations of motion, two ER mounts are designed and manufactured. The field-dependent displacement transmissibilities are evaluated in the frequency domain. In addition, vibration control responses of two ER mounts are experimentally investigated by implementing a skyhook controller.

Design of a slender turning cutting tool via a vibration absorber equipped with piezoelectric ceramic

2021 ◽  
pp. 107754632110144
Author(s):  
Yiqing Yang ◽  
Haoyang Gao ◽  
Qiang Liu
Keyword(s):  
Piezoelectric Ceramic ◽  
Cutting Tool ◽  
Vibration Suppression ◽  
Equations Of Motion ◽  
Electrical Energy ◽  
Diameter Ratio ◽  
Vibration Absorber ◽  
Machined Surface ◽  
Structural Part ◽  
Machined Surface Roughness

Turning cutting tool with large length–diameter ratio has been essential when machining structural part with deep cavity and in-depth hole features. However, chatter vibration is apt to occur with the increase of tool overhang. A slender turning cutting tool with a length–diameter ratio of 7 is developed by using a vibration absorber equipped with piezoelectric ceramic. The vibration absorber has dual functions of vibration transfer to the absorber mass and vibration conversion to the electrical energy via the piezoelectric effect. Equations of motion are established considering the dual damping from the piezoelectric ceramic and rubber gasket. The equivalent damping of piezoelectric ceramic is derived, and the geometries are optimized to achieve optimal vibration suppression. The modal analysis demonstrates that the cutting tool with the vibration absorber can reach 80.1% magnitude reduction. Machining tests are carried out in the end. The machining acceleration and machined surface roughness validate the vibration suppression of the VA, and the output voltage by the piezoelectric ceramic demonstrates the ability of vibration sensing.

Simulation of Engine Vibration on Nonlinear Hydraulic Engine Mounts

2005 ◽  
Author(s):  
A. R. Ohadi ◽  
G. Maghsoodi
Keyword(s):  
Equations Of Motion ◽  
Low Frequency ◽  
Governing Equations ◽  
Engine Mounts ◽  
Engine Vibration ◽  
Engine Mount ◽  
Rotational Motions ◽  
The Time Domain ◽  
Nonlinear Equations Of Motion ◽  
Four Cylinders

In this paper, vibration behavior of engine on nonlinear hydraulic engine mount including inertia track and decoupler is studied. In this regard, after introducing the nonlinear factors of this mount (i.e. inertia and decoupler resistances in turbulent region), the vibration governing equations of engine on one hydraulic engine mount are solved and the effect of nonlinearity is investigated. In order to have a comparison between rubber and hydraulic engine mounts, a 6 degree of freedom four cylinders V-shaped engine under inertia and balancing masses forces and torques is considered. By solving the time domain nonlinear equations of motion of engine on three inclined mounts, translational and rotational motions of engines body are obtained for different engine speeds. Transmitted base forces are also determined for both types of engine mount. Comparison of rubber and hydraulic mounts indicates the efficiency of hydraulic one in low frequency region.

Reduction of Noise Inside a Cavity by Piezoelectric Actuators

2003 ◽  
Vol 125 (1) ◽  
pp. 12-17 ◽  
Author(s):  
I. Hagiwara ◽  
D. W. Wang ◽  
Q. Z. Shi ◽  
R. S. Rao
Keyword(s):  
Sound Pressure ◽  
Control Mechanism ◽  
Equations Of Motion ◽  
Piezoelectric Actuators ◽  
Governing Equations ◽  
Control Laws ◽  
Modal Coupling ◽  
Modal Amplitude ◽  
Global And Local ◽  
Fully Coupled

A new analytical model is developed for the reduction of noise inside a cavity using distributed piezoelectric actuators. A modal coupling method is used to establish the governing equations of motion of the fully coupled acoustics-structure-piezoelectric patch system. Two performance functions relating “global” and “local” optimal control of sound pressure levels (SPL) respectively are applied to obtain the control laws. The discussions on associated control mechanism show that both the mechanisms of modal amplitude suppression and modal rearrangement may sometimes coexist in the implementation of optimal noise control.

Concise Equations for Rotor Dynamics Analysis

1995 ◽  
Author(s):  
W. J. Chen
Keyword(s):  
Equations Of Motion ◽  
Rotor Dynamics ◽  
Memory Storage ◽  
The Other ◽  
Dynamics Analysis ◽  
Real Domain ◽  
The Matrix ◽  
System Equations ◽  
Ordering Algorithms ◽  
Matrix Bandwidth

Abstract Concise equations for rotor dynamics analysis are presented. Two coordinate ordering methods are introduced in the element equations of motion. One is in the real domain and the other is in the complex domain. The two proposed ordering algorithms lead to more compact element matrices. A station numbering technique is also proposed for the system equations during the assembly process. This numbering technique can minimize the matrix bandwidth, the memory storage and can increase the computational efficiency.

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