[Paper Review] Stress-optimized inertial amplified metastructure with opposite chirality for vibration attenuation

Rachele Zaccherini, Andrea Colombi+3 more|arXiv (Cornell University)|Nov 13, 2021

Acoustic Wave Phenomena Research4 citations

TL;DR

This paper proposes a stress-optimized, inertial-amplified mechanical metastructure with opposite chirality for low-frequency vibration attenuation. By coupling axial and torsional motions via arch-like ligaments connecting a hollow-square plate to a ring, the structure achieves a wide, tunable bandgap at low frequencies; experimental validation confirms a 95% reduction in vibration amplitude, and optimization minimizes bandgap frequency while limiting self-weight-induced stresses to prevent failure.

ABSTRACT

In this work, we investigate the dynamics and attenuation properties of a one-dimensional inertial amplified lattice with opposite chirality. The unit cell of the structure consists of a hollow-square plate connected to a ring through arch-like ligaments. The peculiar geometry and orientation of the links allow for coupling the axial and the torsional motion of the lattice, thus amplifying the inertia of the system. We develop both simplified analytical and numerical models of the building block to derive the complex dispersion relation of the infinite lattice. The structure supports a frequency-tailorable attenuation zone, whose lower bound is controlled by the second coupled axial-torsional mode. Laboratory measurements of the transmission spectrum on a 3D printed sample match very well with the analytical and numerical predictions, confirming the wide-band filtering properties of this lattice. We complete our investigation by developing and solving a constrained optimization model to obtain the optimized geometric parameters of the unit cell that minimize the bandgap opening frequency and, at the same time, fulfill structural requirements. In particular, the internal stresses induced by the self-weight of the structure are kept to a low by virtue of the employed design, with the aim to prevent plastic deformations and failure. The inertial amplification mechanism, proposed and investigated in this work, offers an efficient variant for the efficient design of materials and structures for vibration mitigation and shock protection.

Motivation & Objective

• To design a mechanical metastructure with low-frequency, wide bandgaps for effective vibration mitigation.
• To incorporate inertial amplification via axial-torsional coupling using arch-like ligaments with opposite chirality.
• To minimize the bandgap opening frequency while satisfying structural integrity constraints under self-weight loading.
• To ensure low internal stresses to prevent plastic deformation and enhance durability in load-bearing applications.
• To validate the theoretical and numerical models through experimental testing of a 3D-printed prototype.

Proposed method

• Developed a simplified analytical model to derive the complex dispersion relation of the infinite lattice based on coupled axial-torsional dynamics.
• Formulated a numerical model using finite element analysis to simulate wave propagation and bandgap characteristics.
• Designed a unit cell with a hollow-square plate connected to a ring via four arch-like ligaments oriented for opposite chirality to enable torsional-axial coupling.
• Conducted laboratory-scale experiments on a 2-unit-cell 3D-printed sample using selective laser sintering in Nylon 12 to measure transmission spectra.
• Formulated a constrained optimization model to minimize bandgap opening frequency, subject to maximum allowable von Mises stress from self-weight.
• Varied geometric parameters—especially ring external radius and ligament cross-section—while enforcing stress limits to ensure structural safety.

Experimental results

Research questions

• RQ1 How does the opposite chirality in arch-like ligaments affect the coupling between axial and torsional modes in a metastructure?
• RQ2 What is the impact of axial-torsional coupling on the bandgap frequency and width in an inertial-amplified system?
• RQ3 Can the bandgap opening frequency be minimized while maintaining low internal stresses due to self-weight?
• RQ4 To what extent do analytical and numerical predictions match experimental transmission spectra in a finite-sized sample?
• RQ5 Which geometric parameters most significantly influence the bandgap frequency and stress distribution?

Key findings

• The analytical and numerical dispersion curves reveal a wide bandgap whose lower bound is governed by the second coupled axial-torsional mode.
• Experimental transmission measurements on a 2-unit-cell 3D-printed prototype show a 95% reduction in vibration amplitude within the predicted bandgap, confirming strong filtering performance.
• The bandgap opening frequency decreases with increasing ring external radius and decreasing ligament cross-sectional area, as predicted by optimization.
• For a maximum allowable stress of 100 MPa (~43% of yield stress), the optimized bandgap opening frequency reaches 57.87 Hz, with a ring external radius of 10.00 cm and ligament thickness of 3.36 mm.
• The external radius of the ring and the ligament cross-section are the most influential geometric parameters in minimizing the bandgap frequency under stress constraints.
• The stress-constrained optimization successfully limits internal stresses to prevent plastic deformation, ensuring structural safety and durability in load-bearing applications.