Design and performance analysis of an H_∞-optimized hybrid lever-inertial amplified dynamic vibration absorber

Abstract This research proposes a novel hybrid lever-inertial amplified dynamic vibration absorber (LIADVA), which integrates lever and inertial amplification mechanisms within a grounded-type dynamic vibration absorber (DVA) framework. The proposed configuration significantly enhances vibration mitigation by amplifying effective inertia and improving energy dissipation, thereby overcoming the bandwidth and mass limitations of conventional passive DVAs. A single-degree-of-freedom (SDOF) system coupled with the LIADVA is modeled using Lagrange’s method, and closed-form analytical solutions are derived. Tuning parameters for frequency and damping, optimized via <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" overflow="scroll"> <mml:msub> <mml:mrow> <mml:mi mathvariant="normal">H</mml:mi> </mml:mrow> <mml:mrow> <mml:mi mathvariant="normal">∞</mml:mi> </mml:mrow> </mml:msub> </mml:math> criteria, are analytically derived using the two-fixed-point theory. Design parameter boundaries are systematically analyzed, and a pre-design estimation chart is introduced to support practical implementation. Results demonstrate that LIADVA effectively suppresses both system and absorber responses, achieving substantial peak amplitude reduction and broadening the vibration attenuation bandwidth. The absorber also exhibits strong robustness against parameter detuning, maintaining high performance without requiring large physical mass. Analytical results are validated through numerical simulations, confirming the accuracy and practical applicability of the proposed LIADVA tuning formulas. Compared to <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" overflow="scroll"> <mml:msub> <mml:mrow> <mml:mi mathvariant="normal">H</mml:mi> </mml:mrow> <mml:mrow> <mml:mi mathvariant="normal">∞</mml:mi> </mml:mrow> </mml:msub> </mml:math> -optimized lever-based, grounded, and conventional DVAs, LIADVA reduces absorber response by 36%–78% and expands the effective bandwidth by approximately 34%–130%, offering improved installation efficiency and enhanced feasibility for real-world engineering applications.