Advancing seismic isolation efficiency of rolling rod base isolators using nonlinear inertial amplifiers

Abstract Nonlinear inertial amplifier rolling rod isolators (NIARRI) are introduced in this paper to overcome the existing drawbacks of the conventional base isolators. The Euler-Lagrange equation is employed to derive the governing equations of motion. $$H_{2}$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:msub> <mml:mi>H</mml:mi> <mml:mn>2</mml:mn> </mml:msub> </mml:math> and $$H_{\infty }$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:msub> <mml:mi>H</mml:mi> <mml:mi>∞</mml:mi> </mml:msub> </mml:math> optimisation techniques are employed to derive the closed-form expressions for optimal frequency and damping ratio of the NIARRI. An analysis of the eigenvalues and the eigenvectors demonstrates that the inertial amplifier has two competing design priorities depending on the chosen optimisation case. The $$H_2$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:msub> <mml:mi>H</mml:mi> <mml:mn>2</mml:mn> </mml:msub> </mml:math> case demands that the angle of the inertial amplifier be minimised while the $$H_\infty $$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:msub> <mml:mi>H</mml:mi> <mml:mi>∞</mml:mi> </mml:msub> </mml:math> demands that the angle be maximised instead. The transfer matrix formation and harmonic balance method are employed to obtain frequency domain responses, while the Newmark-beta method is employed to obtain time domain responses. According to the frequency domain analysis, the dynamic response reduction capacity of NIARRI is 43.68% superior to conventional BI, while time domain analysis shows 25.21% superior vibration reduction than conventional BI. In addition to reducing structural vibrations, the NIARRI system significantly limits isolator displacements, thereby lowering stroke demands. Across various excitations, the NIARRI achieves peak isolator displacement reductions of 84.8%, confirming its effectiveness in enhancing both performance and reliability of seismic isolation systems.