Design and analysis of a novel negative stiffness mechanism using cosine semi-circular beam for low frequency vibration isolation

Abstract

This research article presents a Cosine Semi-Circular Beam (CSCB) inspired by the semi-circular arch with a cosine profile in lateral direction. The study investigates nonlinear stiffness of the CSCB to achieve low-frequency isolation. The isolator comprises two CSCBs coupled with four Semi-Circular Arch (SCA) elements to achieve the quasi-zero stiffness (QZS) property, which is crucial for vibration attenuation at low frequencies. The design of CSCB isolator is performed using finite element analysis and experimental procedures. Moreover, Symbolic Regression in julia programming language is employed to obtain the explicit equation for restoring force of the isolator. Static characteristics demonstrate the existence of QZS region in the force–displacement curve. Dynamic analysis is conducted by solving the equation of motion of the isolator using the Harmonic Balance Method (HBM) and the fourth order Runge–Kutta method (RK4). The dynamic response is scrutinised further for its chaotic behaviour using the displacement bifurcation diagram and the Lyapunov exponent across a range of excitation acceleration. Phase portraits at different frequencies illustrate the nonlinear response of the isolator changing from periodic to chaotic. The performance of the CSCB isolator at low frequencies is assessed through acceleration transmissibility, numerically, analytically and experimentally. Experimental findings from dynamic vibration test confirm the occurrence of sudden jump-down into the isolation region at 8Hz, while excitations above 9Hz can be effectively isolated. © 2026 Elsevier Ltd