Aerospace Systems Research Articles

The role of polymer gel electrolyte infiltration for enhancement of capacitance and cycle stability

With the increasing application of electronic materials in various fields such as flexible electronic textiles, wearable and portable gadgets, aerospace and aircraft systems etc., the demand for clean high-power energy storage devices is also increasing rapidly. To date, the application of market available supercapacitors has not met the energy expectations in the range of market leading Li-ion batteries (LIBs) due to their unreliable mechanical flexibility, electrolyte leakage, low voltage application, low capacity, low cycle stability and moderate rate-capability. Inappropriate utilization of the maximum porosity of the electrode material and inefficient activities of the electrode/electrolyte interface are major challenges for present supercapacitor development. In this work, for the first time, the role of polymer gel electrolyte infiltration to improve the electrochemical performance of a supercapacitor has been explicitly studied and investigated. It has been observed that 1-Ethyl-3- Methylimidazolium bis(trifluoromethylsulfonyl)imide [EMIM][TFSI] ionic liquid electrolyte embedded in Polypropylene Carbonate (PPC) and Polycarbonate (PC) polymer matrix polymer gel electrolyte (PGE) showed excellent supercapacitive performance at high voltage window 2.6 V by delivering maximum total capacitance of 5.81 F and maximum energy density 10.9 Wh kg-1 at 30 mA current (0.06 A g-1). Regular infiltration of the polymer gel electrolyte inside the electrode material is also observed during long cycle operation of 10,000 cycles. Infiltration of electrolyte ions into the pores of electrode materials plays a significant role in increasing capacitance and cycle Stability. These results highlight the potential of this novel high-voltage polymer gel electrolyte for future high-power energy storage device applications.

Understanding the Interplay of Battery and Flight Dynamics Using Coupled Battery and Flight Physics Simulations for Electric Aircraft

Electric aviation has been a major focus of research in recent years as the aviation industry has seen significant growth in electric aircraft development. Most of the current literature related to electric aircraft modeling focuses on aircraft design and optimization with less focus given to battery analysis. Many studies utilize battery simplifications such as linear voltage profiles1 or the use of equivalent circuit models2. Similarly, in the emerging field of electric vertical takeoff and landing (eVTOL) aircraft, battery analysis is often reduced to considering just weight and empirical power parameters, failing to capture physical and electrochemical battery behavior and its effect on battery performance characteristics3. These simplifications can often lead to inaccurate battery state estimations and performance prediction. Moreover, the battery packs used for both electric conventional take-off and landing (eCTOL) aircraft and eVTOLs see unique operating requirements that are often significantly more demanding than those seen in electric vehicles (EVs)4. This suggests the need to analyze aircraft battery pack performance limitations in greater detail. However, only a few such studies have been reported in the literature5-6.In this work, we perform coupled simulation studies of longitudinal flight dynamics and physics-based battery dynamics. For modeling battery dynamics, we use the well-known single particle model7. This coupling enables more reliable estimation of battery states and can better inform battery pack design for electric aircraft. The simulations are performed to understand the interplay between battery cell dynamics governed by its design parameters and parameters associated with fixed-wing flight dynamics, such as cruise altitude, flight path angle, and velocity. Additionally, the simulations show how varying these parameters and operating temperature effects the range and endurance of electric aircraft which can be used to determine the optimal aircraft operating parameters for a desired mission profile. Results from this simulation study are compared against an equivalent circuit battery model to highlight the importance of detailed battery analysis in electric aviation. This work will be extended to develop similar coupled physics-based battery models with the state-of-the-art aircraft configurations emerging in the eVTOL field.References M. Kaptsov and L. Rodrigues, Journal of Guidance, Control, and Dynamics, 41, 288 (2018).N. Biju and H. Fang, Applied Energy, 339, 120905 (2023).L. Kiesewetter, K. H. Shakib, P. Singh, M. Rahman, B. Khandelwal, S. Kumar and K. Shah, Progress in Aerospace Sciences, 142, 100949 (2023).X.-G. Yang, T. Liu, S. Ge, E. Rountree and C.-Y. Wang, Joule, 5, 1644 (2021).A. Ayyaswamy, B. S. Vishnugopi and P. P. Mukherjee, Joule, 7, 2016 (2023).M. Wang, S. Kolluri, K. Shah, V. R. Subramanian and M. Mesbahi, IEEE Transactions on Aerospace and Electronic Systems, 59, 1084 (2022).S. Santhanagopalan, Q. Guo, P. Ramadass and R. E. White, Journal of power sources, 156, 620 (2006).

Analysis of the tri-hybrid Maxwell nanofluid flow with temperature-dependent thermophysical characteristics on static and dynamic surfaces employing Levenberg-Marquardt artificial neural networks

Using the Levenberg-Marquardt Artificial Neural Network (LM-ANN) model, this study applies computational neuroscience to the analysis of flow, heat, and mass transport characteristics. The novel characteristics of MHD Maxwell tri-hybrid nanofluid passing through static and moving wedge with temperature-dependent thermophysical properties (thermal conductivity, viscosity, diffusivity, and electrical field) in permeable, radiative, and mixed convection processes are investigated in this paper. Nonlinear PDEs are transformed into nonlinear ODEs using similarity variables. A dataset for the LM-ANN is generated across various scenarios by varying parameters such as the temperature-dependent viscosity parameter ( 0.07 − 0.1 ) , variable diffusivity parameter ( 0.4 − 2.5 ) , thermal buoyancy parameter ( 0.1 − 0.5 ) , nonlinear thermal buoyancy parameter ( 0.2 − 0.5 ) , thermal radiation ( 1 − 1.5 ) , buoyancy ratio parameter ( 0.2 − 0.5 ) , chemical reaction parameter ( 1 − 3 ) , and Schmidt number ( 1 − 3 ) using the Bvp5c numerical algorithm. The testing, training, and validation procedure of LM-ANN is utilized to examine the estimated solutions of specific situations, and the proposed algorithm is then validated. After that, the proposed LM-ANN is validated using regression analysis, MSE, and histogram analysis. The prescribed approach impeccably mirrors the recommended and cited findings, evincing a precision level within the realm of 10−9. Results indicate that increasing the permeability parameter from 1 to 1.2 and the temperature-dependent thermal conductivity parameter from 0.4 to 2.5 enhances the Nusselt number. Additionally, increasing the chemical reaction parameter from 1 to 3 leads to an increase in the Sherwood number. The significance of this study lies in its potential applications in industries such as aerospace, chemical processing, and energy systems, where efficient heat and mass transfer processes are crucial. For instance, the findings can be applied to enhance cooling techniques in high-performance aerospace components, optimize reactor designs in chemical plants, and improve thermal management in power generation systems.

Rapid screening of creep resistance in additive manufactured Ti-6Al-4V alloy

In this study, rapid screening of creep resistance for additively manufactured (AM) materials is enabled using an accelerated creep test (ACT) called the dynamic negative stepped test (DNST). Additively manufactured components are on the rise in aerospace systems, particularly turbine engine parts. It can be challenging to identify the AM process parameters that correspond to high-temperature strength and creep resistance. Tests are needed that rapidly screen and qualify creep resistance. In DNST, the temperature is held constant, and the specimen is taken through a series of load holds from high to low. The DNST contains two distinct characteristics: (1) the hold duration for each step is “dynamically” controlled to ensure the minimum-creep-strain-rate is achieved at every step, and (2) the “descending” profile maximizes damage accumulation while remaining on the edge of instability. The DNST assesses a material's ability to resist creep damage accumulated across multiple deformation mechanisms. In this study, electron beam melted Ti–6Al–4V, built at six (6) directions: 0°, 30°, 45°, 60°, 90°, and V, is tested using a four-step DNST at 650 °C. Analysis of the minimum-creep-strain-rate (at each step), creep ductility, and rupture were performed. A strain energy density (SED) benchmark metric was established to rapidly screen and classify creep resistance using an “Ashby-like” plot that balanced energy dissipated and energy dissipation rate. The creep resistance was found to be ranked from V, 60, 45, 30, 90, and 0 in descending order. Microstructural and crystallographic characterization revealed grain refinement progressing from the strain-free to the high-strain regions, indicative of dynamic recrystallization (DRX). Further observations revealed that the material's energy capacity increased with the alignment of the grains' long axis and tensile direction.

Multistability of segmented rings by programming natural curvature

Multistable structures have widespread applications in the design of deployable aerospace systems, mechanical metamaterials, flexible electronics, and multimodal soft robotics due to their capability of shape reconfiguration between multiple stable states. Recently, the snap-folding of rings, often in the form of circles or polygons, has shown the capability of inducing diverse stable configurations. The natural curvature of the rod segment (curvature in its stress-free state) plays an important role in the elastic stability of these rings, determining the number and form of their stable configurations during folding. Here, we develop a general theoretical framework for the elastic stability analysis of segmented rings (e.g., polygons) based on an energy variational approach. Combining this framework with finite element simulations, we map out all planar stable configurations of various segmented rings and determine the natural curvature ranges of their multistable states. The theoretical and numerical results are validated through experiments, which demonstrate that a segmented ring with a rectangular cross-section can show up to six distinct planar stable states. The results also reveal that, by rationally designing the segment number and natural curvature of the segmented ring, its one- or multiloop configuration can store more strain energy than a circular ring of the same total length. We envision that the proposed strategy for achieving multistability in the current work will aid in the design of multifunctional, reconfigurable, and deployable structures.

Dual input single Output quadratic Boost converter for DC microgrid

DC-DC converters play a critical role in various applications, including DC microgrids, electrical vehicles, data centres and aerospace power systems. This article provides a description of a non-isolated Dual Input Single Output Quadratic Boost DC-DC Converter (DISOQBC) designed for DC microgrids. PV module and battery are low dc voltage power generators. DC microgrid requires high voltage for its operation effectively. By utilizing the proposed converter, the PV module and battery are integrated with separate sources. Achieving a high efficiency and voltage conversion ratio, the proposed converter is distinguished by low components used. The operation of the converter, component design, steady state analysis, and small-signal model has been reported. The proposed converter's benefits include the converter's ability to handle more than one source, deliver more gain than the conventional converter, simple control and reduced losses. The outcome of simulating the converter validates the proposed converter's theoretical operation. The laboratory prototype is ultimately employed to validate and verify the performance of the proposed DISOQBC.

Numerical simulation for MHD slip flow with heat transfer over a stretching bullet‐shaped object

AbstractThis paper investigates magnetohydrodynamic (MHD) boundary layer slip flow with heat transfer over a bullet shaped object. The study addresses a significant problem in fluid dynamics and heat transport with applications in various engineering and industrial domains, including aerospace, material processing, and energy systems. The governing equations are resolved using the bvp4c, an inbuilt MATLAB tool, and the arithmetic computation for the momentum and thermotic equations are executed. The results are exhibited graphically. Numerical outcomes are graphically depicted with the aid of velocity and temperature profiles for several model variables. The achieved results exhibit a promising agreement with the previously established findings available in the open literature. The heat transfer processes and fluid flow are remarkably influenced by means of the ratio of surface thickness and stretching potential. The results obtained designated that the Mixed convection parameter λ increases momentum BL thickness, whereas the temperature profile diminishes. Furthermore, momentum and temperature profile improve for surface thickness parameter . The current investigation highlights the potential utility of heat transport rate and friction factor in the industrial divisions for regulating cooling rates and enhancing the quality of end products.

Computational imaging-based single-lens imaging systems and performance evaluation.

The minimalist optical system has a simple structure, small size, and lightweight, but the low optical complexity will produce optical aberration. Addressing the significant aberration degradation in minimalist systems, we propose a high-quality computational optical framework. This framework integrates a global point spread function (PSF) change imaging model with a transformer-based U-Net deep learning algorithm to achieve high-quality imaging in minimalist systems. Additionally, we introduce an imaging performance evaluation method based on the modulation transfer degree of resolution (MTR). We addressed severe chromatic and spherical aberrations in single-lens systems, a typical example of minimalist optical systems, by simulating the degradation process and reconstructing the imaging effects. This approach demonstrated significant improvements, thus validating the feasibility of our method. Specifically, our technique calculated the MTR values in real images captured with the GCL010109 single lens at 0.8085, and with the GCL010110 single lens at 0.8055. Our method enhanced the imaging performance of minimalist systems by 4 times, upgrading minimalist system capabilities from poor to good lens grade. This work can provide reference for wavefront coding, matelens, diffraction optical systems, and other computational imaging work. It can also promote the application of miniaturization of medical, aerospace, and head-mounted optical systems.

Systems‐Theoretic Concept Design: An Intent Model for Early Concept Generation

AbstractThe complexity of engineered systems has grown leaps and bounds over the last forty years. One of the main challenges in modern engineering is managing this complexity, particularly as the pace of technological change continues to accelerate across industries. While most systems professionals agree, a viable early design concept is crucial to meeting stakeholders' needs and successfully scoping a development program, traditional early concept generation approaches focus on a design‐first approach, often glossing over an analysis of system intent and a synthesis of system goals and objectives. This tendency leads to an early focus on low‐level, highly‐granular design activities that focus on advanced technologies as design components instead of on the high‐level policy or desired emergence that the new system is being designed to achieve. To combat these shortcomings, this paper introduces a new framework for conceptualizing an early design for novel, complex systems in aerospace and defense that are employed as part of a portfolio‐of‐systems in an attempt to achieve a high‐level policy or portfolio‐level capability. It outlines an intent model for framing a new system's contribution to a portfolio‐level capability, and it posits a framework for delivering a new model for early design concepts while providing a foundation to extend system‐theoretic hazard and security analysis techniques to systematically analyze safety and security engineering challenges for the designs in the earliest possible phase of their lifecycle.

Reciprocating wear behavior of multi-directionally forged and aged Al-Cu-Li alloy

Al-Cu-Li alloys have drawn attention because of their decreased density, which is a result of the growing need for lightweight material systems in aerospace and aircraft applications. The alloy was subjected to multi-directional forging (MDF) and post-MDF artificial aging. Reciprocating sliding wear tests were conducted to investigate the effects of these processes on wear properties under different load conditions. After MDF, a decrease in wear resistance was noticed, on the other hand, 12 pass MDF treated samples showed improved wear resistance upon aging treatment. Wear scars and counter ball surfaces were examined using scanning electron microscope (SEM) to understand the wear mechanism and wear mode. The findings demonstrated that, at lower loads, adhesion and abrasion were the main wear processes; at greater loads, delamination, adhesion, and abrasion were clearly visible. The study revealed that the MDF and subsequent aging have a substantial effect on the wear behavior of Al-Cu-Li alloy and is an effective thermomechanical processing route to enhance wear resistance.

A Model for Cybersecurity Education through Challenge Events

AbstractThe INCOSE Vision 2035 sets an important Cybersecurity goal: “Cybersecurity will be as foundational a perspective in systems design as system performance and safety are today”. A critical enabler of achieving this vision is educating cyber informed engineers and professionals. Across industries, the demand for talented cybersecurity professionals is high, which means the personnel and students need inspirational education and training to fill these opportunities. This is particularly the case for complex systems in transportation, maritime, agriculture, aerospace, energy, and industries that rely on operational technology implemented with embedded systems. This broad category of sectors need talent and community to address cybersecurity concerns. Often these economic sectors have systems with long lifecycles, regulations, market forces, or other constraints that preclude security solutions envisioned for information technologies. To address the needs for cybersecurity personnel for these industries, a model for developing talent and building community is explained in general terms with specific examples as it relates to automotive, heavy duty, maritime, and agriculture. The model describes the CyberX Challenge, where X is an industry sector, such as the CyberAuto Challenge, CyberTruck Challenge, CyberBoat Challenge, and CyberTractor Challenge. These Challenge Events are described in detail with a focus on the characteristics of what makes those successful or difficult. The successful events have strong industry support, elite instructors, and motivated students. The model for the event is described in detail, with the intention that other industry verticals may inspire additional students and further build communities able to address cyberthreats to our modern way of life. This work directly contributes solutions to addressing the needed foundational concept of Security Education and Competency development as highlighted by the INCOSE FuSE working group.

Exploring transfer learning for improving ultrasonic guided wave-based damage localization

Designing maintenance strategies to reduce the failure risk of plated structures is paramount for increasing the safety level of aerospace, civil and mechanical systems. Although traditional time-scheduled maintenance policies are reliable, they come with costly operations and avoidable downtimes. Recently, more complex condition-based strategies have been studied in the literature. This class of maintenance actions rely on structural health monitoring (SHM) frameworks: a sensor network is installed on the structure diagnostic data are processed to monitor the health state of the structure. The high dimensionality of data and the limitations of model-based SHM algorithms have led researchers to investigate data-driven solutions for improving the reliability of condition-based strategies. So far, supervised machine learning strategies have mainly been considered. However, since the cost of generating labeled datasets usually turns out to be prohibitive, two alternative solutions have gained attention: unsupervised methods and transfer learning (TL). While the former approach has been proved to provide satisfactory damage detection performance, it requires external knowledge sources to also localize and quantify damage. Instead, transfer learning could be used for performing all the damage diagnosis tasks, without the need for coupling the data-driven method with complex algorithms to restore the information lost by using smaller datasets for training. TL allows adapting pre-trained ML tools to new situations, new tasks and new environments. Moreover, TL can be leveraged when few labeled data are available, or to adapt efficient tools that have already been trained on a slightly different task. In this work, TL and convolutional neural networks (CNNs) were leveraged for performing damage localization and quantification in metal and composite plated structures. That is, an in-house CNN-based framework for localizing and quantifying structural damage was considered, and the fine-tuning TL technique was employed to make the framework flexible enough to work in different domains.

A piezoelectric vibration sensor with excellent performance based on Bi12SiO20 crystal for high-temperature applications

High-temperature piezoelectric vibration sensors play a crucial role in the accurate monitoring of the dynamic mechanical conditions in aerospace, automotive, and energy generation systems. However, the use of conventional piezoelectric materials in high-temperature environments is restricted owing to their limited Curie temperatures. In this study, we grew a piezoelectric crystal Bi12SiO20 (BSO) with the crystal cut optimized for high longitudinal piezoelectric coefficient and low piezoelectric crosstalk behaviors. Subsequently, a compression-type piezoelectric vibration sensor utilizing the BSO bulk crystal was developed and fabricated for structural health monitoring under high temperatures. The impact of pre-tightening torques on the sensor performance was investigated. Moreover, the sensor performance was analyzed under temperatures up to 650 °C. The BSO-based sensor exhibited an average sensitivity of ∼3.89 pC/g between 25 and 650 °C under 160 Hz frequency, with a variation of 5.5%. Additionally, the BSO-based sensor demonstrated ultra-stable sensitivity at 600 °C, highlighting its strong sensing capabilities and reliability under high temperatures. Thus, the BSO-based vibration sensor is a promising option for structural health monitoring applications under high temperatures.

Preliminary design and performance evaluation of optical fiber-based load sensor for aerospace systems

Preliminary design and performance evaluation of optical fiber-based load sensor for aerospace systems

Systems Perspective Outcomes from Aerospace Failure Investigations

AbstractMany tools are available for managing complexity in the development of large aerospace systems. Complexity manifests in components, software and so many possible human interactions that all the operational states of the system are not predicted ahead of time. System behaviors are seemingly unexpected, unpredictable, and often unwanted. However, finding these failure modes before they happen can be done by techniques that are qualitative, quantitative, or mixed methods, used situationally, as needed for each particular circumstance. Through studies of failure investigations from NASA and the aerospace industry, recommendations coalesce on using a systems perspective to increase communication and reduce the risk of failure. Overall, a consistent outcome of these investigations is the suggestion to listen to as many value‐added perspectives as possible. Preventing failures in operation is managed by improving collaboration within and among teams, which is an effective way to reveal those perspectives, through both formal and informal communication techniques properly contextualized.

SINGLE-DEGREE-OF-FREEDOM VIBRATION ISOLATION SYSTEM WITH ONE ADDITIONAL SUPPORT

Vibration isolation is one of the most effective methods for reducing vibration levels of supporting structures when installing vibroactive equipment (active vibration isolation) or vibration levels of vibro-sensitive objects relative to foundation vibration levels (passive vibration isolation). Damping devices utilizing high-speed fluid flow through apertures have found wide applications in shock vibration isolation and vibration isolation systems in aerospace and defense sectors. Recent research has led to the development of viscous fluid dampers (VFDs) for use in civil engineering, particularly in earthquake-prone areas. Scientists conducted experiments aimed at determining the ability of viscous fluid dampers to reduce damages and displacements of structures without increasing stresses. Mathematical models have been developed and are applied in vibration isolation systems. When vibroactive equipment is installed on building and structure support systems, vibrations with sufficiently high vibration parameters may occur, potentially leading to loss of load-bearing capacity. In such cases, vibration isolation is considered one of the most effective methods for reducing these vibration levels. In this study, a calculation method has been developed, and calculation dependencies and algorithms for calculating vibration protection systems with nonlinear characteristics (additional support connections, viscous fluid damper) have been derived for both single-degree-of-freedom and two-degree-of-freedom systems. The research involved an analysis of normative and scientific-technical literature on the subject: types, structural solutions, calculation, and analysis of vibration protection systems. The main method selected was based on the use of transfer functions of linear systems (the non-traditional "normal form" method). Calculations were performed using computer mathematics systems- Matlab.

Development of a Feature Extraction Methodology for Prognostic Tasks of Aerospace Structures and Systems

Development of a Feature Extraction Methodology for Prognostic Tasks of Aerospace Structures and Systems

Robust Adaptive Control of Linear Parameter-Varying Systems with Unmatched Uncertainties

In control of aerospace systems with large operating envelopes, it is often necessary to adjust the desired dynamics according to operating conditions. This paper presents a robust adaptive control architecture for linear parameter-varying (LPV) systems that allows for the desired dynamics to be systematically scheduled, while being able to handle a broad class of uncertainties, both matched and unmatched, which can depend on both time and states. The proposed controller adopts an L1 adaptive control architecture for designing the adaptive control law and peak-to-peak gain (PPG) minimization for designing the robust control law to mitigate the effect of unmatched uncertainties. Leveraging the PPG bound of a LPV system, we derive transient and steady-state performance bounds in terms of the input and output signals of the actual closed-loop system with respect to a nominal system. The proposed control architecture is applied to control the longitudinal motion of an F-16 aircraft operating within a large envelope. Simulation results using both LPV and fully nonlinear models validate the efficacy of the proposed method.

Application of Lee–Tarver Model for Energetic Materials Safety Assessment Utilized in Aerospace Applications

Energetic materials, essential for rocket propulsion, play a crucial role in aerospace systems. These materials lack sufficient safety assessments and pose significant risks to life and infrastructure. The slow progress in this field is hindered by prohibitively high experimental costs and the inherently destructive nature of these experiments. This study aimed to evaluate modeling-based safety assessments, primarily utilizing the Lee–Tarver model. It specifically addressed the threat posed by shaped charges during transportation. Experimental analyses employed 50 mm JH-2 shaped charges, targeting RDX-based JH-2 formulation, since RDX is widely used in various rocket motor propellant formulations. TNT was also used to enhance the validation of the Lee–Tarver model findings. Various logistical configurations were explored, testing steel container walls ranging from 10 mm thickness to reinforced walls of 50 mm, 60 mm, and 65 mm steel. Comparative analysis with experiments reinforced the accuracy of the Lee–Tarver model’s numerical predictions. Both simulations and experiments affirmed that a 65 mm steel protection suffices for the safe transportation of RDX-based JH-2 formulations and TNT within a 10 mm storage box in logistical setups. Furthermore, this study emphasizes the Lee–Tarver model’s reliability for most energetic materials safety assessments, while acknowledging certain limitations.

Vibration control of thin shallow paraboloidal shells with light-activated shape memory polymers

With the applications of thin-walled paraboloidal shell structure in aviation, aerospace and communication systems, smart-structure based active vibration control becomes essential to improve the performance of thin-walled parabolic structures. Light-activated shape memory polymer (LaSMP) is a novel actuator material that exhibits dynamic Young's modulus and strain properties under ultraviolet (UV) light exposures, which can be used for non-contact vibration control. This study focuses on investigating the vibration control performance of a shallow parabolic thin shell, with simply supported boundary conditions, with laminated LaSMP patches. Based on the LaSMP strain model, the vibration control effect of LaSMP patch on the thin shell is discussed. A finite element model of the simply supported parabolic thin shell is developed to obtain the natural frequencies. The modal expansion method is employed to investigate the vibration control of the shallow parabolic thin shell laminated with LaSMPs, and independent modal responses are calculated. According to the different control mode, the effects of LaSMP actuators on vibration control of shallow paraboloid shell are studied in three cases with varying actuation position and coverage area of LaSMP actuators. The results indicate that LaSMP can control the vibration of the thin shell by reducing the vibration amplitude and the final vibration control effect is determined by the mode shape, the initial LaSMP strain, and the location and area covered by LaSMP actuators. By establishing the model between the LaSMP actuator force and the attenuations in modal amplitude, this study provides an analytical tool for the application of LaSMPs in vibration control of flexible structures.