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- W97416413 abstract "We present a mathematical model exhibiting the empirically observed damping rates in elastic systems. The models studied are of the form (<inline-formula content-type=math/mathml> <mml:math xmlns:mml=http://www.w3.org/1998/Math/MathML alttext=upper A> <mml:semantics> <mml:mi>A</mml:mi> <mml:annotation encoding=application/x-tex>A</mml:annotation> </mml:semantics> </mml:math> </inline-formula> the relevant elasticity operator) <disp-formula content-type=math/mathml> [ <mml:math xmlns:mml=http://www.w3.org/1998/Math/MathML alttext=ModifyingAbove x With two-dots plus upper B ModifyingAbove x With dot plus upper A x equals 0> <mml:semantics> <mml:mrow> <mml:mrow class=MJX-TeXAtom-ORD> <mml:mover> <mml:mi>x</mml:mi> <mml:mo>¨<!-- ¨ --></mml:mo> </mml:mover> </mml:mrow> <mml:mo>+</mml:mo> <mml:mi>B</mml:mi> <mml:mrow class=MJX-TeXAtom-ORD> <mml:mover> <mml:mi>x</mml:mi> <mml:mo>˙<!-- ˙ --></mml:mo> </mml:mover> </mml:mrow> <mml:mo>+</mml:mo> <mml:mi>A</mml:mi> <mml:mi>x</mml:mi> <mml:mo>=</mml:mo> <mml:mn>0</mml:mn> </mml:mrow> <mml:annotation encoding=application/x-tex>ddot x + Bdot x + Ax = 0</mml:annotation> </mml:semantics> </mml:math> ] </disp-formula> with <inline-formula content-type=math/mathml> <mml:math xmlns:mml=http://www.w3.org/1998/Math/MathML alttext=upper B> <mml:semantics> <mml:mi>B</mml:mi> <mml:annotation encoding=application/x-tex>B</mml:annotation> </mml:semantics> </mml:math> </inline-formula> related in various ways to the positive square root, <inline-formula content-type=math/mathml> <mml:math xmlns:mml=http://www.w3.org/1998/Math/MathML alttext=upper A Superscript 1 slash 2> <mml:semantics> <mml:mrow class=MJX-TeXAtom-ORD> <mml:msup> <mml:mi>A</mml:mi> <mml:mrow class=MJX-TeXAtom-ORD> <mml:mn>1</mml:mn> <mml:mrow class=MJX-TeXAtom-ORD> <mml:mo>/</mml:mo> </mml:mrow> <mml:mn>2</mml:mn> </mml:mrow> </mml:msup> </mml:mrow> <mml:annotation encoding=application/x-tex>{A^{1/2}}</mml:annotation> </mml:semantics> </mml:math> </inline-formula>, of <inline-formula content-type=math/mathml> <mml:math xmlns:mml=http://www.w3.org/1998/Math/MathML alttext=upper A> <mml:semantics> <mml:mi>A</mml:mi> <mml:annotation encoding=application/x-tex>A</mml:annotation> </mml:semantics> </mml:math> </inline-formula>. Comparison with existing “ad hoc” models is made." @default.
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- W97416413 title "A mathematical model for linear elastic systems with structural damping" @default.
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