Nonlinear Vibration Analysis of Delaminated Composite Plate Structures in Supersonic Flow

Mechanics Mechanical Engineering Materials Science Engineering Aerospace Engineering Physics
nonlinear vibration delaminated composite supersonic flow finite element analysis aeroelasticity

Background Introduction

In aerospace engineering, thin laminated composite structures (such as wings) are prone to vibration under high-speed airflow, which may lead to instability phenomena such as flutter or divergence, affecting the safety and performance of aircraft. Particularly, when delamination (i.e., adhesive failure between layers) exists in composite structures, their mechanical responses are significantly altered, further complicating the vibration problem. Therefore, studying the nonlinear vibration behavior of delaminated composite plates in supersonic flow has significant engineering implications.

However, existing research has primarily focused on the vibration analysis of intact structures, and the impact of delamination defects has not been fully explored. Additionally, traditional numerical simulation methods for fluid-solid interaction problems are often computationally expensive and lack dedicated finite element models for delaminated structures. To address these issues, this paper aims to develop a new finite element method for analyzing the nonlinear vibration behavior of delaminated composite plates in supersonic flow. Through stability analysis and nonlinear vibration simulations, the influence of delamination on the dynamic stability of structures is revealed.

Source of the Paper

This paper is authored by Bence Hauck and András Szekrényes, both affiliated with the Department of Applied Mechanics at the Budapest University of Technology and Economics, Hungary. The paper was accepted on February 18, 2025, and published in the journal Nonlinear Dynamics, with the DOI 10.1007/s11071-025-11031-4.

Research Process and Results

1. Development of the Finite Element Model

The core of this paper is the development of a new finite element model for simulating the nonlinear vibration behavior of delaminated composite plates in supersonic flow. The specific steps are as follows:
- Theoretical Foundation: The First-Order Shear Deformation Theory (FSDT) is adopted, combined with the Equivalent Single Layer (ESL) concept, to model the delaminated structure as two equivalent single layers (top and bottom).
- Nonlinear Strain Model: The von Kármán nonlinear strain is introduced to describe the nonlinear behavior of the structure, suitable for moderately nonlinear problems.
- Aerodynamic Pressure Model: The Piston Theory is used to describe the pressure exerted by supersonic flow on the plate, applicable for Mach numbers greater than 1.
- Finite Element Equations: The nonlinear finite element equations are derived using variational principles, and an improved Newmark direct time integration scheme is developed, incorporating an iterative predictor-corrector procedure to significantly reduce computational time and CPU requirements.

2. Model Validation

To validate the developed finite element model, the authors first applied it to intact structures and compared the results with known semi-analytical solutions. The results showed that the finite element model performs well in the vibration analysis of intact structures, confirming its reliability.

3. Linear Stability Analysis

By linearizing the nonlinear equations, the authors investigated the dynamic stability of delaminated composite plates in supersonic flow and introduced several dimensionless stability parameters, including average aerodynamic pressure, delamination size, delamination position, and delamination depth. The specific analyses are as follows:
- Effect of Delamination Size: By varying the delamination size, stability maps were generated for different boundary conditions. The results showed that delamination size significantly affects the stability of the structure, and in some cases, it can lead to a transition from divergence instability to flutter instability.
- Effect of Delamination Position: The influence of delamination position on stability was studied, revealing that changes in delamination position alter the critical aerodynamic pressure, with different trends observed under different boundary conditions.
- Effect of Delamination Depth: The impact of delamination depth on stability was analyzed, showing that delamination depth has a minor effect on stability under certain boundary conditions but a significant effect under others.

4. Nonlinear Vibration Analysis

Based on the results of the stability analysis, the authors selected specific cases to simulate the nonlinear vibration behavior of delaminated composite plates in supersonic flow. Using the improved Newmark time integration scheme, the displacement response of the plate was calculated, and phase plane diagrams were plotted. The results showed:
- In stable states, the structure returns to rest after a small perturbation.
- In flutter instability states, limit cycles emerge, and the shape and amplitude of the limit cycles are closely related to the delamination size and aerodynamic pressure.

Conclusions and Significance

This paper developed a new finite element model that successfully simulates the nonlinear vibration behavior of delaminated composite plates in supersonic flow. Through linear stability analysis and nonlinear vibration simulations, the influence of delamination size, position, and depth on the dynamic stability of the structure was revealed. The main significance of the research lies in:
- Engineering Application Value: Providing a theoretical basis for the safety assessment of composite structures with delamination defects, helping engineers determine whether delaminated structures can operate safely under specific conditions, thereby reducing material waste in the manufacturing process.
- Scientific Value: Proposing a finite element modeling method suitable for delaminated structures and developing an improved time integration scheme, offering new tools and methods for similar research.

Research Highlights

  • Innovative Finite Element Model: A finite element model for delaminated structures was developed by combining the First-Order Shear Deformation Theory and the Equivalent Single Layer concept.
  • Improved Time Integration Scheme: Computational costs were significantly reduced, and efficiency was improved through an iterative predictor-corrector procedure.
  • Comprehensive Stability Analysis: The effects of delamination size, position, and depth on the dynamic stability of composite plates were systematically studied for the first time, revealing the transition mechanism from divergence instability to flutter instability.

Future Outlook

The research methods in this paper can be further extended, for example:
- Investigating more complex delamination patterns, such as fully closed delaminations or multiple delaminated regions.
- Deriving aerodynamic damping and load stiffness matrices for subsonic flows.
- Improving the finite element model to handle plates with varying thickness, enabling more accurate simulation of real wing vibration behavior.

This paper provides important theoretical and methodological support for the nonlinear vibration analysis of delaminated composite plates in supersonic flow, with broad prospects for engineering applications.