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<p>Geometrical nonlinear oscillations of doubly curved sandwich shells under the action of axial harmonic excitation are analyzed. Outer thin layers of sandwich shell are manufactured from orthotropic composite material. Hexagonal honeycomb core of this structure is manufactured from orthotropic plastic by using additive technology. Honeycomb core is homogenized and transformed into orthotropic layer. Oscillations of every layer of sandwich structure are described by five generalized displacements (three displacements projections of the middle surfaces and two rotation angles of normal to the middle surfaces). The higher order shear deformation theory and geometrically nonlinear deformation theory are used to model thin-walled structure. The assumed mode method is used to derive the system of nonlinear ordinary differential equations of structure oscillations. Geometrically nonlinear structure oscillations in vicinity of principal parametric resonance and two internal resonances 1:1 and 1:2 are analyzed by asymptotic multiple scales method (MSM). Periodic oscillations of the structure, their stability and bifurcations are analyzed semi-analytically. As a result of semi-analytical analysis, two regions of trivial equilibrium instability in vicinity of one principal parametric resonance are obtained. Intricate resonant behavior of the structure periodic oscillations is discussed. Resonant periodic oscillations undergo the Neimark-Sacker bifurcations. As a result of these bifurcations, quasi-periodic motions originate.</p>

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Asymptotic analysis of resonant nonlinear oscillations of composite sandwich doubly curved shell with soft honeycomb core under axial harmonic excitation

  • 期刊论文

  • 发表日期：

    2026年2月21日

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  • K. Avramov,
  • B. Uspensky,
  • B. Liubarskyi

摘要

Geometrical nonlinear oscillations of doubly curved sandwich shells under the action of axial harmonic excitation are analyzed. Outer thin layers of sandwich shell are manufactured from orthotropic composite material. Hexagonal honeycomb core of this structure is manufactured from orthotropic plastic by using additive technology. Honeycomb core is homogenized and transformed into orthotropic layer. Oscillations of every layer of sandwich structure are described by five generalized displacements (three displacements projections of the middle surfaces and two rotation angles of normal to the middle surfaces). The higher order shear deformation theory and geometrically nonlinear deformation theory are used to model thin-walled structure. The assumed mode method is used to derive the system of nonlinear ordinary differential equations of structure oscillations. Geometrically nonlinear structure oscillations in vicinity of principal parametric resonance and two internal resonances 1:1 and 1:2 are analyzed by asymptotic multiple scales method (MSM). Periodic oscillations of the structure, their stability and bifurcations are analyzed semi-analytically. As a result of semi-analytical analysis, two regions of trivial equilibrium instability in vicinity of one principal parametric resonance are obtained. Intricate resonant behavior of the structure periodic oscillations is discussed. Resonant periodic oscillations undergo the Neimark-Sacker bifurcations. As a result of these bifurcations, quasi-periodic motions originate.