Soft Interlayer With Near-Zero Stiffness Could Silence Rattling Pipelines

Deep-sea pipelines, subsea risers and high-pressure industrial tubing share an uncomfortable secret: they rattle. In pipe-in-pipe (PIP) assemblies, where one tube runs inside another to provide thermal insulation or mechanical protection, the gap between the two pipes is usually filled with foam, rubber or simple spacers. These fillers must do two jobs at once, carrying the weight of the inner pipe while cushioning it from the relentless vibration that travels along the outer wall. In practice, the two demands fight each other. A stiff filler carries load well but passes vibration straight through; a soft filler isolates vibration but collapses under weight. A team of Chinese researchers now reports a way out of that trade-off, using a carefully shaped thermoplastic polyurethane (TPU) interlayer engineered to behave as if its stiffness were almost zero.

The study, published in Advanced Composites and Hybrid Materials by Yuchen Gu, Zili Wang, Shuyou Zhang, Xiwen Gu, Liangyou Li, Jianrong Tan and Mengyu Fu, with affiliations at Zhejiang University and a Zhejiang-based equipment company, proposes an architected TPU interlayer for aluminium pipe-in-pipe systems. Rather than relying on the intrinsic softness of the polymer alone, the design exploits geometry. When the interlayer is compressed, its internal structure deforms in a way that keeps the resisting force nearly constant over a wide range of displacement. In the language of structural mechanics, the effective tangent stiffness, the rate at which force increases with displacement, drops close to zero across that plateau. This is the quasi-zero stiffness (QZS) regime, and it is the sweet spot where a structure can support a static load while offering almost no resistance to small dynamic disturbances superimposed on that load.

Quasi-zero stiffness is not a new idea in isolation theory. Classic QZS vibration isolators combine a positive-stiffness spring with a negative-stiffness mechanism, such as two oblique springs or buckled beams, so that the positive and negative contributions cancel near the equilibrium point. What makes the new work distinctive is that the cancellation is achieved entirely through the geometric deformation of a single moulded polymer component, with no separate mechanisms, springs or moving parts. That matters for PIP systems, where space between the pipes is tight, assembly must be simple, and any loose hardware inside the annulus would be a liability over decades of service.

To understand and predict the behaviour of the interlayer, the researchers built analytical models describing both its quasi-static force-displacement response and its dynamic displacement transmissibility, the ratio of the vibration amplitude transmitted to the inner pipe relative to the outer pipe. The analytical treatment, elaborated in the paper’s appendix, is notably careful. The authors derive the effective interlayer tangent stiffness from the elastic energy of the deformed structure, accounting for the relaxation of internal coordinates at fixed interface displacement. They then embed that stiffness in an idealized two-degree-of-freedom model, in which effective masses represent the outer and inner pipes, tangent stiffness terms represent the pipes and the interlayer coupling, and a viscous damping coefficient captures energy dissipation. From this model they obtain an explicit expression for the absolute displacement transmissibility as a function of frequency, mass and stiffness parameters.

The team was equally candid about the limits of the model. The appendix states that a small coupling stiffness is not, by itself, proof of quasi-zero stiffness in the assembled system, and that a candidate QZS interval on a compression curve alone does not establish that a vibration experiment operates at a stable QZS equilibrium. Stability, they note, depends on the complete tangent matrix and the admissible vibration modes, and damping of relative motion alone does not guarantee decay of every relevant mode. The two-coordinate idealization also breaks down near local resonances, where the eliminated internal degrees of freedom of the interlayer cease to follow equilibrium quasi-statically and their inertia produces frequency-dependent behaviour that a constant-stiffness model cannot represent. This kind of explicit boundary-drawing is rare in engineering papers and gives readers a precise map of where the predictions can be trusted.

With the analytical framework in place, the researchers turned to finite element simulations and physical experiments. Compression tests assessed the plateau force, the width of the quasi-zero stiffness plateau, and the specific energy absorption, a normalized measure of how much mechanical energy the structure can absorb per unit mass. Vibration experiments measured how much of the outer pipe’s motion reached the inner pipe through the interlayer. Parametric studies then swept through the material properties and the geometric parameters of the architecture, identified in the paper as parameters l1 through l6, h1 and h2, and r1, along with the number of circumferential and axial arrays of the repeating units. The results showed that these parameter variations could widen the QZS plateau by 200 to 300 percent relative to the baseline configuration, while also tuning the plateau force. A wider plateau means the isolator keeps its near-zero stiffness over a larger range of compression, which is crucial because the static load on the interlayer varies along a real pipeline and with installation conditions.

Three representative configurations were then fabricated and tested experimentally, allowing the team to check the predicted compression and vibration responses against reality. The comparison between numerical prediction and measurement revealed differences that the authors attribute to three familiar culprits: the actual viscoelastic behaviour of the TPU, which departs from the idealized constitutive assumptions; manufacturing variability in the printed or moulded architecture; and boundary conditions in the test setup that differ from the idealized constraints of the model. None of these discrepancies undermines the approach, but they underline a lesson that recurs throughout the architected materials literature: the gap between a simulation and a specimen is where most engineering risk lives, and honest quantification of that gap is more valuable than a perfect-looking curve.

The multifunctional promise of the design is what elevates it beyond a routine vibration study. Because the interlayer is a single TPU component, it simultaneously serves as the mechanical spacer that keeps the pipes concentric, the energy absorber that crushes progressively under impact or overload, and the vibration isolator that decouples the inner tube from disturbances on the outer wall. TPU itself brings practical advantages: it is tough, abrasion-resistant, chemically robust and thermoplastic, meaning it can be processed by additive manufacturing or moulding and potentially recycled. For aluminium PIP systems in offshore and subsea applications, where corrosion resistance and weight savings already motivate the use of aluminium, a polymer interlayer that adds isolation without adding hardware is an attractive package.

The analytical machinery developed in the paper also has implications beyond this specific geometry. By defining the effective interlayer tangent stiffness through a rigorous condensation of the full elastic energy, the authors provide a template for connecting quasi-static compression data to dynamic vibration models, a connection that is often made loosely or not at all. Their derivation shows that the derivative of the full compression force between plates does not generally equal the derivative of the interlayer restoring force, because pipe deformation and contact effects intervene. An explicit mapping between coordinates and forces is required before compression measurements can supply coupling parameters for a dynamic model. For engineers designing any layered or sandwiched structure, from automotive mounts to aerospace panels, that distinction is a useful corrective against the tempting shortcut of reading isolation performance directly off a load-deflection curve.

Looking forward, the study positions architected interlayers as a design space rather than a single product. The parametric results demonstrate that geometry is a genuine tuning knob: the same material can be reshaped to trade plateau force against plateau width, shifting the isolator’s operating window to match a particular pipe weight or excitation environment. The authors describe their work as a basis for further development of architected interlayers for tubular assemblies, and the open-access publication, funded by the National Natural Science Foundation of China and several regional Chinese research programs, makes the models and methods available to other groups. If subsequent work closes the remaining gap between idealized models and manufactured parts, pipelines of the future may carry their own silence inside the wall, one geometrically clever polymer layer at a time.

Subject of Research: Quasi-zero stiffness thermoplastic polyurethane interlayers for vibration-isolating aluminium pipe-in-pipe systems

Article Title: Quasi-zero stiffness TPU interlayer for aluminium–polymer pipe-in-pipe systems: design, modeling and multifunctional performance

Article References: Gu, Y., Wang, Z., Zhang, S., Gu, X., Li, L., Tan, J., & Fu, M. (2026). Quasi-zero stiffness TPU interlayer for aluminium–polymer pipe-in-pipe systems: design, modeling and multifunctional performance. Advanced Composites and Hybrid Materials. https://doi.org/10.1007/s42114-026-02123-9

Image Credits: AI Generated

DOI: 10.1007/s42114-026-02123-9

Keywords: quasi-zero stiffness, thermoplastic polyurethane, pipe-in-pipe systems, vibration isolation, architected materials, finite element analysis, energy absorption, aluminium structures, structural mechanics, soft materials, interlayer design, displacement transmissibility