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- W4312682083 abstract "The Navier equation Eq. ( 1.4.13 ) is a coupled system of differential equations about three displacement components, i.e. $$u_{x}$$ , $$u_{y}$$ and $$u_{z}$$ . It is very difficult to solve Navier equation directly. For the convenience of solving Navier equation, the scalar potential $$varphi left( {{varvec{x}},t} right)$$ and the vector potential $${varvec{psi}}left( {{varvec{x}},t} right)$$ are introduced and the displacement field is thus expressed as $${varvec{u}}left( {{varvec{x}},t} right) = nabla varphi left( {{varvec{x}},t} right) + nabla times {varvec{psi}}left( {{varvec{x}},t} right) = {varvec{u}}^{left( 1 right)} left( {{varvec{x}},t} right) + {varvec{u}}^{left( 2 right)} left( {{varvec{x}},t} right)$$ [4]. According to the decomposition theorem of vector field, any single-value and finite vector field can be decomposed into a field without divergence plus a field without curl. There must be a scalar potential function $$varphi left( {{varvec{x}},t} right)$$ existing for the field without curl, which can be expressed as $$nabla varphi left( {x,t} right)$$ ." @default.
- W4312682083 created "2023-01-05" @default.
- W4312682083 creator A5035591319 @default.
- W4312682083 date "2022-01-01" @default.
- W4312682083 modified "2023-09-30" @default.
- W4312682083 title "Elastic Waves in an Infinite Medium" @default.
- W4312682083 doi "https://doi.org/10.1007/978-981-19-5662-1_2" @default.
- W4312682083 hasPublicationYear "2022" @default.
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