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A system whose energy is not conserved is called nonconservative. To investigate if there exists a con- served quantity that has the same dimension as energy and is positively definite, the author analyzed the bending vibration of an axially moving beam with geometric nonlinearity. Based on the governing equation, the energy was proven to be not conserved in the case where the beam has two simply supported or fixed ends. A definitely positive quantity with the energy dimension was defined. The quantity was verified to remain a constant during the motion. The investigation indicates that an energy-like conserved quantity may exist in a nonlinear nonconservative continuous system.
A behavior whose body is not conserved is called nonconservative. the governing equation, the energy was proven to be not conserved in the case where the beam has two simply supported or fixed ends. A definitely positive quantity with the energy dimension was defined. The quantity was verified to remain a constant during the motion. The investigation indicates that an energy-like conserved quantity may exist in a nonlinear nonconservative continuous system.