Forced Vibration of a Clamped Rectangular Plate in Fluid Media

1955 ◽  
Vol 22 (4) ◽  
pp. 568-572
Author(s):  
Gordon C. K. Yeh ◽  
Johann Martinek
Keyword(s):  
Plane Wave ◽  
Rectangular Plate ◽  
Forced Vibration ◽  
High Frequency ◽  
Equations Of Motion ◽  
Shape Functions ◽  
Lagrange Equations ◽  
Fluid Media ◽  
Set Up ◽  
Plate Deflection

Abstract Forced vibration of a thin rectangular plate clamped in a rigid infinite baffle is analyzed. The plate is assumed to separate two different fluid media and the vibration is excited by a simple plane wave of high frequency (as compared with c / 2 π ab ) normally incident from one side of the plate. Using the characteristic shape functions, the Lagrange equations of motion of the plate are set up in generalized co-ordinates. The solutions of the equations render series expressions for the plate deflection and an energy-transmission coefficient. Certain numerical results are given.

Characteristics of the equations of motion of a reacting gas

1958 ◽  
Vol 4 (3) ◽  
pp. 276-282 ◽  
Author(s):  
L. J. F. Broer
Keyword(s):  
Heat Conduction ◽  
High Frequency ◽  
Sound Speed ◽  
Reaction Rate ◽  
Equations Of Motion ◽  
Sound Waves ◽  
Velocity Of Sound ◽  
Frequency Limit ◽  
Chemically Reacting ◽  
Set Up

The equations of motion for a chemically reacting gas in the absence of viscosity and heat conduction are set up. It is shown that the characteristic speed defined by this set of equations is the high-frequency limit of the phase velocity of sound waves as long as the reaction rate is finite. At infinite reaction rate (chemical equilibrium) the characteristics suddenly change to the lowfrequency sound speed. The nature of this transition is discussed in connection with a recent paper of Resler (1957).

Forced Vibration of Flexible Body Systems: A Dynamic Stiffness Method

1993 ◽  
Vol 115 (4) ◽  
pp. 468-476 ◽  
Author(s):  
T. S. Liu ◽  
J. C. Lin
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
Elastic Deformation ◽  
Forced Vibration ◽  
Dynamic Stiffness ◽  
Equations Of Motion ◽  
Flexible Body ◽  
Shape Functions ◽  
Stiffness Matrices ◽  
Dynamic Shape

Due to the development of high speed machinery, robots, and aerospace structures, the research of flexible body systems undergoing both gross motion and elastic deformation has seen increasing importance. The finite element method and modal analysis are often used in formulating equations of motion for dynamic analysis of the systems which entail time domain, forced vibration analysis. This study develops a new method based on dynamic stiffness to investigate forced vibration of flexible body systems. In contrast to the conventional finite element method, shape functions and stiffness matrices used in this study are derived from equations of motion for continuum beams. Hence, the resulting shape functions are named as dynamic shape functions. By applying the dynamic shape functions, the mass and stiffness matrices of a beam element are derived. The virtual work principle is employed to formulate equations of motion. Not only the coupling of gross motion and elastic deformation, but also the stiffening effect of axial forces is taken into account. Simulation results of a cantilever beam, a rotating beam, and a slider crank mechanism are compared with the literature to verify the proposed method.

scholarly journals Forced Vibration Analysis of Laminated Composite Plates under the Action of a Moving Vehicle

2021 ◽  
Vol 16 (59) ◽  
pp. 198-211
Author(s):  
Hossein Abbaszadeh Mobaraki ◽  
Ramazan-Ali Jafari-Talookolaei ◽  
Paolo S. Valvo ◽  
Reza Haghani Dogaheh
Keyword(s):  
Forced Vibration ◽  
Equations Of Motion ◽  
Shear Deformation Theory ◽  
Laminated Composite ◽  
Composite Plates ◽  
Laminated Composite Plates ◽  
Lagrange Equations ◽  
Element Analysis ◽  
Moving Vehicle ◽  
Coupled Equations

This paper provides a finite element analysis of laminated composite plates under the action of a moving vehicle. The vehicle is modeled as a rigid body with four suspension systems, each consisting of a spring-dashpot. Overall, the vehicle possesses three degrees of freedom: vertical, rolling, and pitching motions. The equations of motion of the plate are deduced based on first-order shear deformation theory. Using the Euler-Lagrange equations, the system of coupled equations of motion is extracted and solved by using the Newmark time discretization scheme. The algorithm is validated through the comparison of both the free and forced vibration results provided by the present model and exact or numerical results reported in the literature. The effects are investigated of several system parameters on the dynamic response.  

scholarly journals Couplinator: A simple computational tool for synthesis of multi-section coupled-line filter based on MPCM-TLM technique

2021 ◽  
pp. 1-10
Author(s):  
E. Faghand ◽  
S. Karimian ◽  
E. Mehrshahi ◽  
N. Karimian
Keyword(s):  
Comparative Analysis ◽  
Transmission Line ◽  
High Frequency ◽  
Computational Tool ◽  
Cad Tools ◽  
Coupled Line ◽  
High Frequency Structure Simulator ◽  
Transmission Line Method ◽  
Set Up ◽  
Planar Circuit

Abstract A new simple computational tool is proposed for the synthesis of multi-section coupled-line filters based on combined modified planar circuit method (MPCM) and transmission line method (TLM) analysis, referred to as MPCM-TLM. Due to its fundamentally simple architecture, the presented tool offers significantly faster optimization of coupled-line filters – for exactly the same initial simulation set-up – than other costly commercially-available tools, giving equally reliable results. Validity and accuracy of the proposed tool have been verified through the design of 3rd, 5th, and 7th order coupled-line filters and comparative analysis between results obtained from the proposed approach and the high-frequency structure simulator. A remarkable 99% time reduction in the analysis is recorded in the case of 7th order filter using the proposed tool, for almost identical results to HFSS. Therefore, it can be confidently claimed that the proposed technique can be used as a reliable alternative to existing complex, costly, processor-intensive CAD tools.

scholarly journals A least action principle for interceptive walking

2021 ◽  
Vol 11 (1) ◽  
Author(s):  
Soon Ho Kim ◽  
Jong Won Kim ◽  
Hyun Chae Chung ◽  
MooYoung Choi
Keyword(s):  
Social Systems ◽  
Equations Of Motion ◽  
Classical Mechanics ◽  
Action Principle ◽  
Lagrange Equations ◽  
Least Action Principle ◽  
Least Action ◽  
The Least Action Principle ◽  
Principle Of Least Action ◽  
Human Participants

AbstractThe principle of least effort has been widely used to explain phenomena related to human behavior ranging from topics in language to those in social systems. It has precedence in the principle of least action from the Lagrangian formulation of classical mechanics. In this study, we present a model for interceptive human walking based on the least action principle. Taking inspiration from Lagrangian mechanics, a Lagrangian is defined as effort minus security, with two different specific mathematical forms. The resulting Euler–Lagrange equations are then solved to obtain the equations of motion. The model is validated using experimental data from a virtual reality crossing simulation with human participants. We thus conclude that the least action principle provides a useful tool in the study of interceptive walking.

Analytical Solution for Rotational Rub-Impact Plate Under Thermal Shock

2016 ◽  
Vol 32 (3) ◽  
pp. 297-311
Author(s):  
T.-Y. Zhao ◽  
H.-Q. Yuan ◽  
B.-B. Li ◽  
Z.-J. Li ◽  
L.-M. Liu
Keyword(s):  
Thermal Shock ◽  
High Frequency ◽  
Equations Of Motion ◽  
Low Frequency ◽  
Cantilever Plate ◽  
Analysis Method ◽  
Multiple Frequency ◽  
Width Direction ◽  
Blade Tip ◽  
High Frequency Vibrations

AbstractThe analysis method is developed to obtain dynamic characteristics of the rotating cantilever plate with thermal shock and tip-rub. Based on the variational principle, equations of motion are derived considering the differences between rubbing forces in the width direction of the plate. The transverse deformation is decomposed into quasi-static deformation of the cantilever plate with thermal shock and dynamic deformation of the rubbing plate under thermal shock. Then deformations are obtained through the calculation of modal characteristics of rotating cantilever plate and temperature distribution function. Special attention is paid to the influence of tip-rub and thermal shock on the plate. The results show that tip-rub has the characteristics of multiple frequency vibrations, and high frequency vibrations are significant. On the contrary, thermal shock shows the low frequency vibrations. The thermal shock makes the rubbing plate gradually change into low frequency vibrations. Because rub-induced vibrations are more complicated than those caused by thermal shock, tip-rub is easier to result in the destruction of the blade. The increasing friction coefficient intensifies vibrations of the rubbing plate. Minimizing friction coefficients can be an effective way to reduce rub-induced damage through reducing the surface roughness between the blade tip and the inner surface of the casing.

Differential-Geometric Methods in Multibody Dynamics and Control

2005 ◽  
Author(s):  
P. Maißer
Keyword(s):  
Configuration Space ◽  
High Performance ◽  
Multibody System ◽  
Equations Of Motion ◽  
Geometric Approach ◽  
Motion Equations ◽  
Constrained Mechanical Systems ◽  
Dynamics And Control ◽  
Set Up ◽  
Lagrangian Motion

This paper presents a differential-geometric approach to the multibody system dynamics regarded as a point dynamics in a n-dimensional configuration space Rn. This configuration space becomes a Riemannian space Vn the metric of which is defined by the kinetic energy of the multibody system (MBS). Hence, all concepts and statements of the Riemannian geometry can be used to study the dynamics of MBS. One of the key points is to set up the non-linear Lagrangian motion equations of tree-like MBS as well as of constrained mechanical systems, the perturbed equations of motion, and the motion equations of hybrid MBS in a derivative-free manner. Based on this approach transformation properties can be investigated for application in real-time simulation, control theory, Hamilton mechanics, the construction of first integrals, stability etc. Finally, a general Lyapunov-stable force control law for underactuated systems is given that demonstrates the power of the approach in high-performance sports applications.

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