The Effect of Wall Motions on the Governing Equations of Contained Fluids

1990 ◽  
Vol 57 (3) ◽  
pp. 783-785 ◽  
Author(s):  
Roger Ohayon ◽  
Carlos A. Felippa
Keyword(s):  
Wave Equation ◽  
Finite Elements ◽  
Governing Equation ◽  
Equations Of Motion ◽  
Governing Equations ◽  
Displacement Potential ◽  
Classical Wave ◽  
Classical Wave Equation ◽  
Acoustic Fluid

The equations of motion for an acoustic fluid enclosed in a moving or flexible container are studied. It is shown that the determination of the reference state must account for the surface-integrated effect of the wall motions. The governing equation of transient motions about this state in the displacement potential does not generally reduce to the classical wave equation unless special adjustments are made. The results are relevant to finite elements formulations based on the displacement potential.

Radiation and Response of Cylindrical Beams Excited by Sound

1972 ◽  
Vol 94 (1) ◽  
pp. 139-147 ◽  
Author(s):  
J. R. Bailey ◽  
F. J. Fahy
Keyword(s):  
Wave Equation ◽  
Pure Tone ◽  
Experimental Program ◽  
Acoustic Excitation ◽  
Resonant Response ◽  
Reverberation Chamber ◽  
At Resonance ◽  
Classical Wave ◽  
Theoretical Predictions ◽  
Classical Wave Equation

The sound radiated from an unbaffled cylindrical beam vibrating transversely at resonance is calculated by solution of the classical wave equation subject to the boundary conditions imposed by the motion of the beam. The interaction of sound and vibration is then demonstrated by using a theory based on the principle of reciprocity to predict the resonant response of a cylindrical beam to acoustic excitation. The results show that radiation and resonant response are highly frequency dependent. An experimental program is also reported. The power radiated from three cylindrical beams vibrating at resonance and the resonant response of the beams to pure-tone acoustic excitation are measured in a reverberation chamber. The experimental results agree well with the theoretical predictions.

Classical wave equation in fluid filament stretching

1988 ◽  
Vol 27 (5) ◽  
pp. 466-476 ◽  
Author(s):  
S. Kase ◽  
T. Nishimura
Keyword(s):  
Wave Equation ◽  
Filament Stretching ◽  
Classical Wave ◽  
Fluid Filament ◽  
Classical Wave Equation

scholarly journals The Determination of the Velocities after Impact for the Constrained Bar Problem

2009 ◽  
Vol 2009 ◽  
pp. 1-16
Author(s):  
André Fenili ◽  
Luiz Carlos Gadelha de Souza ◽  
Bernd Schäfer
Keyword(s):  
Mathematical Model ◽  
Numerical Integration ◽  
Equations Of Motion ◽  
Robotic Manipulators ◽  
Robotic Manipulator ◽  
Simple Mathematical Model ◽  
Governing Equations ◽  
Complex Problems ◽  
Constrained Equation

A simple mathematical model for a constrained robotic manipulator is investigated. Besides the fact that this model is relatively simple, all the features present in more complex problems are similar to the ones analyzed here. The fully plastic impact is considered in this paper. Expressions for the velocities of the colliding bodies after impact are developed. These expressions are important in the numerical integration of the governing equations of motion when one must exchange the set of unconstrained equations for the set of constrained equation. The theory presented in this work can be applied to problems in which robots have to follow some prescribed patterns or trajectories when in contact with the environment. It can also de applied to problems in which robotic manipulators must handle payloads.

Resonant oscillations of water waves I. Theory

1968 ◽  
Vol 306 (1484) ◽  
pp. 5-22 ◽  
Keyword(s):  
Resonant Frequency ◽  
Water Waves ◽  
Surface Profile ◽  
Sharp Change ◽  
Classical Wave ◽  
Small Parameters ◽  
Linearized Theory ◽  
Classical Wave Equation ◽  
Normal Laboratory

A theory is presented to describe the oscillations of a liquid in a tank near a resonant frequency, where linearized theory is invalid. It is shown that although the oscillations are described adequately by the classical wave equation, the boundary conditions cannot be properly satisfied unless the non-linear terms are included. The effects of dissipation and dispersion are also significant in the determination of the oscillations, even though the terms to which they give rise in the equations are multiplied by small parameters under normal laboratory conditions. When the former is dominant a weak bore is formed which travels to and fro in the tank and is continually reflected at either end. When dispersion is significant the surface profile can be likened to a series of cnoidal waves which also travel along the tank and suffer reflexion. Several novel features appear. The amplitude does not increase monotonically as the nominal resonant frequency is approached. There are several distinct frequencies at which there is a sharp change in amplitude and in the form of the profile. More than one stable oscillation is possible at some frequencies. Near a resonant frequency higher than the fundamental, subharmonic oscillations are possible over part of the range.

The Classical Connection

2017 ◽  
Author(s):  
John A. Adam
Keyword(s):  
Wave Equation ◽  
Inverse Scattering ◽  
Physical System ◽  
Equations Of Motion ◽  
Scattering Problem ◽  
Classical Mechanics ◽  
Inverse Scattering Problem ◽  
Alternative Approach ◽  
Classical Wave Equation ◽  
The Relationship

This chapter discusses the relationship between the elegance of the classical Lagrangian and Hamiltonian formulations of mechanics and optics. In physics, action is a mathematical functional which takes the trajectory, or path, of the system as its argument and has a real number as its result. Classical mechanics postulates that the path actually followed by a physical system is that for which the action is minimized, or, more generally, is stationary. The action is defined by an integral, and the classical equations of motion of a system can be derived by minimizing the value of that integral. The chapter first provides an overview of Lagrangians, action, and Hamiltonians in order to draw out an alternative approach to finding equations of motion. It then considers the classical wave equation and classical scattering and concludes with an analysis of the classical inverse scattering problem.

Harmonisation of Classical Wave Equation

2021 ◽  
Author(s):  
Alireza Jamali
Keyword(s):  
Wave Equation ◽  
Short Note ◽  
Scalar Fields ◽  
Nonlinear Pde ◽  
Classical Wave ◽  
Classical Wave Equation

In this short note we present a technique using which one attributes frequency and wavevector to (almost) arbitrary scalar fields. Our proposed definition is then applied to the classical wave equation to yield a novel nonlinear PDE.

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