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Synthetic Scene Generation of the Stennis V and V Target Range for the Calibration of Remote Sensing Systems

The verification and validation (V&V) target range developed at Stennis Space Center is a useful test site for the calibration of remote sensing systems. In this paper, we present a simple algorithm for generating synthetic radiance scenes or digital models of this target range. The radiation propagation for the target in the solar reflective and thermal infrared spectral regions is modeled using the atmospheric radiative transfer code MODTRAN 4. The at-sensor, in-band radiance and spectral radiance for a given sensor at a given altitude is predicted. Software is developed to generate scenes with different spatial and spectral resolutions using the simulated at-sensor radiance values. The radiometric accuracy of the simulation is evaluated by comparing simulated with AVIRIS acquired radiance values. The results show that in general there is a good match between AVIRIS sensor measured and MODTRAN predicted radiance values for the target despite the fact that some anomalies exist. Synthetic scenes provide a cost-effective way for in-flight validation of the spatial and radiometric accuracy of the data. Other applications include mission planning, sensor simulation, and trade-off analysis in sensor design.

Cao, Chang-Yong↗

Robust Requirements Tracing via Internet Search Technology: Improving an IV and V Technique

There are three major objectives to this phase of the work. (1) Improvement of Information Retrieval (IR) methods for Independent Verification and Validation (IV&V) requirements tracing. Information Retrieval methods are typically developed for very large (order of millions - tens of millions and more documents) document collections and therefore, most successfully used methods somewhat sacrifice precision and recall in order to achieve efficiency. At the same time typical IR systems treat all user queries as independent of each other and assume that relevance of documents to queries is subjective for each user. The IV&V requirements tracing problem has a much smaller data set to operate on, even for large software development projects; the set of queries is predetermined by the high-level specification document and individual requirements considered as query input to IR methods are not necessarily independent from each other. Namely, knowledge about the links for one requirement may be helpful in determining the links of another requirement. Finally, while the final decision on the exact form of the traceability matrix still belongs to the IV&V analyst, his/her decisions are much less arbitrary than those of an Internet search engine user. All this suggests that the information available to us in the framework of the IV&V tracing problem can be successfully leveraged to enhance standard IR techniques, which in turn would lead to increased recall and precision. We developed several new methods during Phase II; (2) IV&V requirements tracing IR toolkit. Based on the methods developed in Phase I and their improvements developed in Phase II, we built a toolkit of IR methods for IV&V requirements tracing. The toolkit has been integrated, at the data level, with SAIC's SuperTracePlus (STP) tool; (3) Toolkit testing. We tested the methods included in the IV&V requirements tracing IR toolkit on a number of projects.

Hayes, Jane↗

Adaptations of guidance, navigation, and control verification and validation philosophies for small spacecraft

Decades of experience developing increasingly capable and more complex space-craft have resulted in a set of accepted practices and philosophies to verify and validate (V&V) guidance, navigation, and control (GN&C) subsystems. Until recently, small, low-cost spacecraft have had very simple or non-existent GN&C subsystems requiring minimal or no subsystem testing. As the next generation of small spacecraft take on more challenging GN&C requirements, the GN&C community is struggling with how to scale the subsystem V&V effort to produce spacecraft approaching the reliability of flagship-class missions while staying within the reduced resources of a small satellite project.For this paper, we will examine five aspects of GN&C V&V (requirements definition, software testing and analysis, hardware component testing, integrated vehicle testing, and in-flight V&V) and compare the V&V campaign of a flagship-class mission (Mars 2020) to that of two recent, successful CubeSat missions: ASTERIA and MarCO. Experiences from the development of these CubeSats yield valuable lessons learned and guidelines for future small spacecraft designers.

Chen, George T.↗

Formal Safety Certification of Aerospace Software

In principle, formal methods offer many advantages for aerospace software development: they can help to achieve ultra-high reliability, and they can be used to provide evidence of the reliability claims which can then be subjected to external scrutiny. However, despite years of research and many advances in the underlying formalisms of specification, semantics, and logic, formal methods are not much used in practice. In our opinion this is related to three major shortcomings. First, the application of formal methods is still expensive because they are labor- and knowledge-intensive. Second, they are difficult to scale up to complex systems because they are based on deep mathematical insights about the behavior of the systems (t.e., they rely on the "heroic proof"). Third, the proofs can be difficult to interpret, and typically stand in isolation from the original code. In this paper, we describe a tool for formally demonstrating safety-relevant aspects of aerospace software, which largely circumvents these problems. We focus on safely properties because it has been observed that safety violations such as out-of-bounds memory accesses or use of uninitialized variables constitute the majority of the errors found in the aerospace domain. In our approach, safety means that the program will not violate a set of rules that can range for the simple memory access rules to high-level flight rules. These different safety properties are formalized as different safety policies in Hoare logic, which are then used by a verification condition generator along with the code and logical annotations in order to derive formal safety conditions; these are then proven using an automated theorem prover. Our certification system is currently integrated into a model-based code generation toolset that generates the annotations together with the code. However, this automated formal certification technology is not exclusively constrained to our code generator and could, in principle, also be integrated with other code generators such as RealTime Workshop or even applied to legacy code. Our approach circumvents the historical problems with formal methods by increasing the degree of automation on all levels. The restriction to safety policies (as opposed to arbitrary functional behavior) results in simpler proof problems that can generally be solved by fully automatic theorem proves. An automated linking mechanism between the safety conditions and the code provides some of the traceability mandated by process standards such as DO-178B. An automated explanation mechanism uses semantic markup added by the verification condition generator to produce natural-language explanations of the safety conditions and thus supports their interpretation in relation to the code. It shows an automatically generated certification browser that lets users inspect the (generated) code along with the safety conditions (including textual explanations), and uses hyperlinks to automate tracing between the two levels. Here, the explanations reflect the logical structure of the safety obligation but the mechanism can in principle be customized using different sets of domain concepts. The interface also provides some limited control over the certification process itself. Our long-term goal is a seamless integration of certification, code generation, and manual coding that results in a "certified pipeline" in which specifications are automatically transformed into executable code, together with the supporting artifacts necessary for achieving and demonstrating the high level of assurance needed in the aerospace domain.

Denney, Ewen↗

Flight Testing ALHAT Precision Landing Technologies Integrated Onboard the Morpheus Rocket Vehicle

A suite of prototype sensors, software, and avionics developed within the NASA Autonomous precision Landing and Hazard Avoidance Technology (ALHAT) project were terrestrially demonstrated onboard the NASA Morpheus rocket-propelled Vertical Testbed (VTB) in 2014. The sensors included a LIDAR-based Hazard Detection System (HDS), a Navigation Doppler LIDAR (NDL) velocimeter, and a long-range Laser Altimeter (LAlt) that enable autonomous and safe precision landing of robotic or human vehicles on solid solar system bodies under varying terrain lighting conditions. The flight test campaign with the Morpheus vehicle involved a detailed integration and functional verification process, followed by tether testing and six successful free flights, including one night flight. The ALHAT sensor measurements were integrated into a common navigation solution through a specialized ALHAT Navigation filter that was employed in closed-loop flight testing within the Morpheus Guidance, Navigation and Control (GN&C) subsystem. Flight testing on Morpheus utilized ALHAT for safe landing site identification and ranking, followed by precise surface-relative navigation to the selected landing site. The successful autonomous, closed-loop flight demonstrations of the prototype ALHAT system have laid the foundation for the infusion of safe, precision landing capabilities into future planetary exploration missions.

Carson, John M. III↗

Design and Experimental Verification of Deployable/Inflatable Ultra-Lightweight Structures

Because launch cost of a space structural system is often proportional to the launch volume and mass and there is no significant gravity in space, NASA's space exploration programs and various science missions have stimulated extensive use of ultra-lightweight deployable/inflatable structures. These structures are named here as Highly Flexible Structures (HFSs) because they are designed to undergo large displacements, rotations, and/or buckling without plastic deformation under normal operation conditions. Except recent applications to space structural systems, HFSs have been used in many mechanical systems, civil structures, aerospace vehicles, home appliances, and medical devices to satisfy space limitations, provide special mechanisms, and/or reduce structural weight. The extensive use of HFSs in today's structural engineering reveals the need of a design and analysis software and a database system with design guidelines for practicing engineers to perform computer-aided design and rapid prototyping of HFSs. Also to prepare engineering students for future structural engineering requires a new and easy-to- understand method of presenting the complex mathematics of the modeling and analysis of HFSs. However, because of the high flexibility of HFSs, many unique challenging problems in the modeling, design and analysis of HFSs need to be studied. The current state of research on HFSs needs advances in the following areas: (1) modeling of large rotations using appropriate strain measures, (2) modeling of cross-section warpings of structures, (3) how to account for both large rotations and cross- section warpings in 2D (two-dimensional) and 1D structural theories, (4) modeling of thickness thinning of membranes due to inflation pressure, pretension, and temperature change, (5) prediction of inflated shapes and wrinkles of inflatable structures, (6) development of efficient numerical methods for nonlinear static and dynamic analyses, and (7) filling the gap between geometrically exact elastic analysis and elastoplastic analysis. The objectives of this research project were: (1) to study the modeling, design, and analysis of deployable/inflatable ultra-lightweight structures, (2) to perform numerical and experimental studies on the static and dynamic characteristics and deployability of HFSs, (3) to derive guidelines for designing HFSs, (4) to develop a MATLAB toolbox for the design, analysis, and dynamic animation of HFSs, and (5) to perform experiments and establish an adequate database of post-buckling characteristics of HFSs.

Pai, P. Frank↗

Adaptations of Guidance, Navigation and Control Verification and Validation Philosophies for Small Spacecraft

Decades of experience developing increasingly capable and more complex space-craft have resulted in a set of accepted practices and philosophies to verify and validate (V&V) guidance, navigation, and control (GN&C) subsystems. Until recently, small, low-cost spacecraft have had very simple or non-existent GN&C subsystems requiring minimal or no subsystem testing. As the next generation of small spacecraft take on more challenging GN&C requirements, the GN&C community is struggling with how to scale the subsystem V&V effort to produce spacecraft approaching the reliability of flagship-class missions while staying within the reduced resources of a small satellite project. For this paper, we will examine five aspects of GN&C V&V (requirements definition, software testing and analysis, hardware component testing, integrated vehicle testing, and in-flight V&V) and compare the V&V campaign of a flagship-class mission (Mars 2020) to that of two recent, successful CubeSat missions: ASTERIA and MarCO. Experiences from the development of these CubeSats yield valuable lessons learned and guidelines for future small spacecraft designers.

Pong, Christopher M.↗

DAKOTA (Design Analysis Kit for Optimization and Terascale) v.6.14

Sandia's Dakota software supports science and engineering transformation through advanced exploration of simulations. Specifically, Dakota manages and analyzes ensembles of simulations to provide broader and deeper perspective for analysts and decision makers. This enables them to: (1) enhance understanding of risk, (2) improve products, and (3) assess simulation credibility. In its simplest mode, Dakota can automate typical parameter variation studies through a generic interface to a computational model. Dakota also delivers advanced parametric analysis techniques enabling design exploration, optimization, model calibration, risk analysis, and quantification of margins and uncertainty with such models. It directly supports verification and validation activities. The algorithms implemented in Dakota aim to address challenges in performing these analyses with complex science and engineering models from desktop to high performance computers. Sandia National Laboratories is a multimission laboratory managed and operated by National Technology & Engineering Solutions of Sandia, LLC, a wholly owned subsidiary of Honeywell International Inc., for the U.S. Department of Energy’s National Nuclear Security Administration under contract DE-NA0003525 SAND2021-10468 O

Adams, BrianM.↗

DAKOTA (Design Analysis Kit for Optimization and Terascale) v.6.16

Sandia's Dakota software supports science and engineering transformation through advanced exploration of simulations. Specifically, Dakota manages and analyzes ensembles of simulations to provide broader and deeper perspective for analysts and decision makers. This enables them to: (1) enhance understanding of risk, (2) improve products, and (3) assess simulation credibility. In its simplest mode, Dakota can automate typical parameter variation studies through a generic interface to a computational model. Dakota also delivers advanced parametric analysis techniques enabling design exploration, optimization, model calibration, risk analysis, and quantification of margins and uncertainty with such models. It directly supports verification and validation activities. The algorithms implemented in Dakota aim to address challenges in performing these analyses with complex science and engineering models from desktop to high performance computers. Sandia National Laboratories is a multimission laboratory managed and operated by National Technology & Engineering Solutions of Sandia, LLC, a wholly owned subsidiary of Honeywell International Inc., for the U.S. Department of Energy’s National Nuclear Security Administration under contract DE-NA0003525 SAND2021-10468 O

Adams, BrianM.↗

Status Report on NEAMS System Analysis Module Development

Under the Reactor Product Line (RPL) of DOE-NE’s Nuclear Energy Advanced Modeling and Simulation (NEAMS) program, an advanced SFR System Analysis Module (SAM) is being developed at Argonne National Laboratory. The goal of the SAM development is to provide fast-running, improved-fidelity, whole-plant transient analyses capabilities. SAM utilizes an object-oriented application framework MOOSE), and its underlying meshing and finite-element library libMesh, as well as linear and non-linear solvers PETSc, to leverage modern advanced software environments and numerical methods. It also incorporates advances in physical and empirical models and seeks closure models based on information from high-fidelity simulations and experiments. This report provides an update on the SAM development, and summarizes the activities performed in FY15 and the first quarter of FY16. The tasks include: (1) implement the support of 2nd-order finite elements in SAM components for improved accuracy and computational efficiency; (2) improve the conjugate heat transfer modeling and develop pseudo 3-D full-core reactor heat transfer capabilities; (3) perform verification and validation tests as well as demonstration simulations; (4) develop the coupling requirements for SAS4A/SASSYS-1 and SAM integration.

21 SPECIFIC NUCLEAR REACTORS AND ASSOCIATED PLANTS↗

Ares I-X Range Safety Simulation Verification and Analysis IV and V

NASA s ARES I-X vehicle launched on a suborbital test flight from the Eastern Range in Florida on October 28, 2009. NASA generated a Range Safety (RS) flight data package to meet the RS trajectory data requirements defined in the Air Force Space Command Manual 91-710. Some products included in the flight data package were a nominal ascent trajectory, ascent flight envelope trajectories, and malfunction turn trajectories. These data are used by the Air Force s 45th Space Wing (45SW) to ensure Eastern Range public safety and to make flight termination decisions on launch day. Due to the criticality of the RS data in regards to public safety and mission success, an independent validation and verification (IV&V) effort was undertaken to accompany the data generation analyses to ensure utmost data quality and correct adherence to requirements. Multiple NASA centers and contractor organizations were assigned specific products to IV&V. The data generation and IV&V work was coordinated through the Launch Constellation Range Safety Panel s Trajectory Working Group, which included members from the prime and IV&V organizations as well as the 45SW. As a result of the IV&V efforts, the RS product package was delivered with confidence that two independent organizations using separate simulation software generated data to meet the range requirements and yielded similar results. This document captures ARES I-X RS product IV&V analysis, including the methodology used to verify inputs, simulation, and output data for an RS product. Additionally a discussion of lessons learned is presented to capture advantages and disadvantages to the IV&V processes used.

Tarpley, Ashley↗

Ares I-X Range Safety Analyses Overview

Ares I-X was the first test flight of NASA's Constellation Program's Ares I Crew Launch Vehicle designed to provide manned access to low Earth orbit. As a one-time test flight, the Air Force's 45th Space Wing required a series of Range Safety analysis data products to be developed for the specified launch date and mission trajectory prior to granting flight approval on the Eastern Range. The range safety data package is required to ensure that the public, launch area, and launch complex personnel and resources are provided with an acceptable level of safety and that all aspects of prelaunch and launch operations adhere to applicable public laws. The analysis data products, defined in the Air Force Space Command Manual 91-710, Volume 2, consisted of a nominal trajectory, three sigma trajectory envelopes, stage impact footprints, acoustic intensity contours, trajectory turn angles resulting from potential vehicle malfunctions (including flight software failures), characterization of potential debris, and debris impact footprints. These data products were developed under the auspices of the Constellation's Program Launch Constellation Range Safety Panel and its Range Safety Trajectory Working Group with the intent of beginning the framework for the operational vehicle data products and providing programmatic review and oversight. A multi-center NASA team in conjunction with the 45th Space Wing, collaborated within the Trajectory Working Group forum to define the data product development processes, performed the analyses necessary to generate the data products, and performed independent verification and validation of the data products. This paper outlines the Range Safety data requirements and provides an overview of the processes established to develop both the data products and the individual analyses used to develop the data products, and it summarizes the results of the analyses required for the Ares I-X launch.

Starr, Brett R.↗

Ares I-X Range Safety Flight Envelope Analysis

Ares I-X was the first test flight of NASA's Constellation Program's Ares I Crew Launch Vehicle designed to provide manned access to low Earth orbit. As a one-time test flight, the Air Force's 45th Space Wing required a series of Range Safety analysis data products to be developed for the specified launch date and mission trajectory prior to granting flight approval on the Eastern Range. The range safety data package is required to ensure that the public, launch area, and launch complex personnel and resources are provided with an acceptable level of safety and that all aspects of prelaunch and launch operations adhere to applicable public laws. The analysis data products, defined in the Air Force Space Command Manual 91-710, Volume 2, consisted of a nominal trajectory, three sigma trajectory envelopes, stage impact footprints, acoustic intensity contours, trajectory turn angles resulting from potential vehicle malfunctions (including flight software failures), characterization of potential debris, and debris impact footprints. These data products were developed under the auspices of the Constellation's Program Launch Constellation Range Safety Panel and its Range Safety Trajectory Working Group with the intent of beginning the framework for the operational vehicle data products and providing programmatic review and oversight. A multi-center NASA team in conjunction with the 45th Space Wing, collaborated within the Trajectory Working Group forum to define the data product development processes, performed the analyses necessary to generate the data products, and performed independent verification and validation of the data products. This paper outlines the Range Safety data requirements and provides an overview of the processes established to develop both the data products and the individual analyses used to develop the data products, and it summarizes the results of the analyses required for the Ares I-X launch.

Starr, Brett R.↗

Automated Verification of Spatial Resolution in Remotely Sensed Imagery

Image spatial resolution characteristics can vary widely among sources. In the case of aerial-based imaging systems, the image spatial resolution characteristics can even vary between acquisitions. In these systems, aircraft altitude, speed, and sensor look angle all affect image spatial resolution. Image spatial resolution needs to be verified with estimators that include the ground sample distance (GSD), the modulation transfer function (MTF), and the relative edge response (RER), all of which are key components of image quality, along with signal-to-noise ratio (SNR) and dynamic range. Knowledge of spatial resolution parameters is important to determine if features of interest are distinguishable in imagery or associated products, and to develop image restoration algorithms. An automated Spatial Resolution Verification Tool (SRVT) was developed to rapidly determine the spatial resolution characteristics of remotely sensed aerial and satellite imagery. Most current methods for assessing spatial resolution characteristics of imagery rely on pre-deployed engineered targets and are performed only at selected times within preselected scenes. The SRVT addresses these insufficiencies by finding uniform, high-contrast edges from urban scenes and then using these edges to determine standard estimators of spatial resolution, such as the MTF and the RER. The SRVT was developed using the MATLAB programming language and environment. This automated software algorithm assesses every image in an acquired data set, using edges found within each image, and in many cases eliminating the need for dedicated edge targets. The SRVT automatically identifies high-contrast, uniform edges and calculates the MTF and RER of each image, and when possible, within sections of an image, so that the variation of spatial resolution characteristics across the image can be analyzed. The automated algorithm is capable of quickly verifying the spatial resolution quality of all images within a data set, enabling the appropriate use of those images in a number of applications.

Davis, Bruce↗

Bridging the Gap Between Requirements and Simulink Model Analysis

Formal veri fication and simulation are powerful tools for the veri fication of requirements against complex systems. Requirements are developed in early stages of the software lifecycle and are typically expressed in natural language. There is a gap between such requirements and their software implementations. We present a framework that bridges this gap by supporting a tight integration and feedback loop between high-level requirements and their analysis against software artifacts. Our framework implements an analysis portal within the fret requirements elicitation tool, thus forming an end-to-end, open-source environment where requirements are written in an intuitive, structured natural language, and are veri fied automatically against Simulink models.

FRET↗

Advanced Simulation Capability for Environmental Management - Current Status and Phase II Demonstration Results - 13161

The U.S. Department of Energy (US DOE) Office of Environmental Management (EM), Office of Soil and Groundwater, is supporting development of the Advanced Simulation Capability for Environmental Management (ASCEM). ASCEM is a state-of-the-art scientific tool and approach for understanding and predicting contaminant fate and transport in natural and engineered systems. The modular and open source high-performance computing tool facilitates integrated approaches to modeling and site characterization that enable robust and standardized assessments of performance and risk for EM cleanup and closure activities. The ASCEM project continues to make significant progress in development of computer software capabilities with an emphasis on integration of capabilities in FY12. Capability development is occurring for both the Platform and Integrated Tool-sets and High-Performance Computing (HPC) Multi-process Simulator. The Platform capabilities provide the user interface and tools for end-to-end model development, starting with definition of the conceptual model, management of data for model input, model calibration and uncertainty analysis, and processing of model output, including visualization. The HPC capabilities target increased functionality of process model representations, tool-sets for interaction with Platform, and verification and model confidence testing. The Platform and HPC capabilities are being tested and evaluated for EM applications in a set of demonstrations as part of Site Applications Thrust Area activities. The Phase I demonstration focusing on individual capabilities of the initial tool-sets was completed in 2010. The Phase II demonstration completed in 2012 focused on showcasing integrated ASCEM capabilities. For Phase II, the Hanford Site deep vadose zone (BC Cribs) served as an application site for an end-to-end demonstration of capabilities, with emphasis on integration and linkages between the Platform and HPC components. Other demonstrations, addressing attenuation-based remedies at the Savannah River Site F Area and performance assessment for a representative waste tank, illustrate integration of linked ASCEM capabilities and initial integration efforts with tools from the Cementitious Barriers Partnership. (authors)

54 ENVIRONMENTAL SCIENCES↗

SU-F-BRA-07: Dosimetric Verification of the Valencia Skin Applicator Using Gafchromic EBT3 Film

Purpose: The Valencia applicators have recently been introduced for HDR treatment of small and shallow superficial skin lesions (< 20 mm diameter and 3-mm depth). Per AAPM TG 56, any HDR applicator internal dimensions must be verified prior to clinical use. However radiographic and tomographic imaging to validate the Valencia applicators is impractical due to the Tungsten alloy housing and flattening filter. In this study, we propose to use EBT3 film to indirectly confirm the physical integrity of the Valencia applicators. Methods: Treatment plans were created using the Oncentra MasterPlan TPS v4.5 for the H2 (20-mm dia.) and H3 (30-mm dia.) Valencia Applicators. A virtual CT phantom (2-mm slice thickness) was created with one source position in water. The published effective depth method was used for each applicator to delivery 500 cGy to a 3-mm depth using the TG-43 formalism. Film measurements (n=3) at 3-mm depth and vertical plane in solid water were performed for each applicator to verify the prescribed dose calculated by the TPS. Percent depth dose curves and off-axis profiles (phantom surface and 3-mm depth) were measured and compared to published data. Films were analyzed using an in-house written program and RIT113 v6 software. Film calibration was performed per TG-55 protocol using the Ir-192 source with NIST-traceable calibration. Results: The prescription absolute dose difference was 1% for the Valencia H2 applicator and 4% for the Valencia H3 applicator. The measured percent depth dose curves and off-axis dose profiles measured for the H2 and H2 Valencia applicators are in excellent agreement with the Granero et al. Monte Carlo results{sup 1}. Conclusion: Gafchromic EBT3 film can be used to indirectly verify the internal components of special HDR skin applicators constructed from high Z materials.{sup 1}Granero et al. “Design and evaluation of a HDR skin applicator with flattening filter”, Med. Phys. 35(2), 495–503, 2008.

60 APPLIED LIFE SCIENCES↗

A Coupled Fluid-Structure Interaction Analysis of Solid Rocket Motor with Flexible Inhibitors

A capability to couple NASA production CFD code, Loci/CHEM, with CFDRC's structural finite element code, CoBi, has been developed. This paper summarizes the efforts in applying the installed coupling software to demonstrate/investigate fluid-structure interaction (FSI) between pressure wave and flexible inhibitor inside reusable solid rocket motor (RSRM). First a unified governing equation for both fluid and structure is presented, then an Eulerian-Lagrangian framework is described to satisfy the interfacial continuity requirements. The features of fluid solver, Loci/CHEM and structural solver, CoBi, are discussed before the coupling methodology of the solvers is described. The simulation uses production level CFD LES turbulence model with a grid resolution of 80 million cells. The flexible inhibitor is modeled with full 3D shell elements. Verifications against analytical solutions of structural model under steady uniform pressure condition and under dynamic condition of modal analysis show excellent agreements in terms of displacement distribution and eigen modal frequencies. The preliminary coupled result shows that due to acoustic coupling, the dynamics of one of the more flexible inhibitors shift from its first modal frequency to the first acoustic frequency of the solid rocket motor.

Yang, H. Q.↗