TY - JOUR

T1 - Mechanical wave momentum from the first principles

AU - Slepyan, Leonid I.

N1 - Publisher Copyright:
© 2016 Elsevier B.V.

PY - 2017/1/1

Y1 - 2017/1/1

N2 - Axial momentum carried by waves in a uniform waveguide is considered based on the conservation laws and a kind of the causality principle. Specifically, we examine (without resorting to constitutive data) steady-state waves of an arbitrary shape, periodic waves which speed differs from the speed of its form and binary waves carrying self-equilibrated momentum. The approach allows us to represent momentum as a product of the wave mass and the wave speed. The propagating wave mass, positive or negative, is the excess of that in the wave over its initial value. This general representation is valid for mechanical waves of arbitrary nature and intensity. The finite-amplitude longitudinal and periodic transverse waves are examined in more detail. It is shown in particular, that the transverse excitation of a string or an elastic beam results in the binary wave. The closed-form expressions for the drift in these waves functionally reduce to the Stokes’ drift in surface water waves (a half the latter by the value). Besides, based on the general representation an energy–momentum relation is discussed and the physical meaning of the so-called “wave momentum” is clarified.

AB - Axial momentum carried by waves in a uniform waveguide is considered based on the conservation laws and a kind of the causality principle. Specifically, we examine (without resorting to constitutive data) steady-state waves of an arbitrary shape, periodic waves which speed differs from the speed of its form and binary waves carrying self-equilibrated momentum. The approach allows us to represent momentum as a product of the wave mass and the wave speed. The propagating wave mass, positive or negative, is the excess of that in the wave over its initial value. This general representation is valid for mechanical waves of arbitrary nature and intensity. The finite-amplitude longitudinal and periodic transverse waves are examined in more detail. It is shown in particular, that the transverse excitation of a string or an elastic beam results in the binary wave. The closed-form expressions for the drift in these waves functionally reduce to the Stokes’ drift in surface water waves (a half the latter by the value). Besides, based on the general representation an energy–momentum relation is discussed and the physical meaning of the so-called “wave momentum” is clarified.

KW - A. Dynamics

KW - B. Stress waves

KW - C. Asymptotic analysis

KW - Wave mass

UR - http://www.scopus.com/inward/record.url?scp=84994728006&partnerID=8YFLogxK

U2 - 10.1016/j.wavemoti.2016.11.005

DO - 10.1016/j.wavemoti.2016.11.005

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AN - SCOPUS:84994728006

SN - 0165-2125

VL - 68

SP - 283

EP - 290

JO - Wave Motion

JF - Wave Motion

ER -