In this paper, we will compute the transfer matrices to find the eigenfrequenciesfor the vibrations of the general non-collinear Euler-Bernoulli or Timoshenko beamstructure with dissipative joints. We will allow the s...In this paper, we will compute the transfer matrices to find the eigenfrequenciesfor the vibrations of the general non-collinear Euler-Bernoulli or Timoshenko beamstructure with dissipative joints. We will allow the structure to be three dimensional,and thus we must consider all types of vibrations simulaneously, including longitudinaland torsional vibrations. The general structure considered will consist of any number ofbeams joined end to end to form a chain. Many, different kinds of dampers areallowed, even within the same structure. We also will allow different materials withinthe structure as well as different beam widths. We then will show. that asymptotic estimates can be used to find the eigenfrequencies approximately.展开更多
This paper discusses the influence of environmental factors and of normal material aging on the eigenfrequencies of concrete bridges based on monitoring data registered during 4 years of a specific bridge. It is a new...This paper discusses the influence of environmental factors and of normal material aging on the eigenfrequencies of concrete bridges based on monitoring data registered during 4 years of a specific bridge. It is a new composite steel-concrete bridge built in 2006 in Luxembourg. The measurements are analyzed and compared to literature data. The final objective is the use of real monitored eigenfrequencies for structural health monitoring and damage detection based on identification of stiffness losses in practical applications. Therefore, it is very important to identify and compensate for outdoor influences namely temperature, excitation force level and normal aging effects, like creep and shrinkage of concrete and their impact on material properties. The present paper aims at describing these effects in order to separate them from damage effects. It is shown that temperature change rates and temperature gradients within the bridge have an influence on the eigenfrequencies. Hence the key idea for assessment from the full database is to select only measurements with small temperature differences and slow temperature change rates.展开更多
The eigenvalue problems of the buckling loads and natural frequencies of a braced beam on an elastic foundation are investigated. sented. The eigenvalues vary with the different The exact solutions for the eigenvalues...The eigenvalue problems of the buckling loads and natural frequencies of a braced beam on an elastic foundation are investigated. sented. The eigenvalues vary with the different The exact solutions for the eigenvalues are preparameters and are especially sensitive to the brace location. As the beam of a continuous system has infinite eigenvalues and these eigenvalues are influenced differently by a brace, the eigenvalues show rich variation patterns. Because these eigenvalues physically correspond to the structure buckling loads and natural frequencies, the study on the eigenvalues variation patterns can offer a design guidance of using a lateral brace of translation spring to strengthen the structure.展开更多
In an operation mode of atomic force micro- scopy that uses a higher eigenmode to determine the physical properties of material surface, the ratio between the eigenfrequency of a higher flexural eigenmode and that of ...In an operation mode of atomic force micro- scopy that uses a higher eigenmode to determine the physical properties of material surface, the ratio between the eigenfrequency of a higher flexural eigenmode and that of the first flexural eigenmode was identified as an important parameter that affects the sensitivity and accessibility. Structure features such as cut-out are often used to tune the ratio of eigenfrequencies and to enhance the performance. However, there lacks a systematic and automatic method for tailoring the ratio. In order to deal with this issue, a shape and topology optimization problem is formulated, where the ratio between two eigenfrequen- cies is defined as a constraint and the area of the cantilever is maximized. The optimization problem is solved via the level set based method.展开更多
A smooth bidirectional evolutionary structural optimization(SBESO),as a bidirectional version of SESO is proposed to solve the topological optimization of vibrating continuum structures for natural frequencies and dyn...A smooth bidirectional evolutionary structural optimization(SBESO),as a bidirectional version of SESO is proposed to solve the topological optimization of vibrating continuum structures for natural frequencies and dynamic compliance under the transient load.A weighted function is introduced to regulate the mass and stiffness matrix of an element,which has the inefficient element gradually removed from the design domain as if it were undergoing damage.Aiming at maximizing the natural frequency of a structure,the frequency optimization formulation is proposed using the SBESO technique.The effects of various weight functions including constant,linear and sine functions on structural optimization are compared.With the equivalent static load(ESL)method,the dynamic stiffness optimization of a structure is formulated by the SBESO technique.Numerical examples show that compared with the classic BESO method,the SBESO method can efficiently suppress the excessive element deletion by adjusting the element deletion rate and weight function.It is also found that the proposed SBESO technique can obtain an efficient configuration and smooth boundary and demonstrate the advantages over the classic BESO technique.展开更多
The approximate eigenfrequencies for the in-plane vibrations of a cable structure consisting of inclined cables, together with point masses at various points were computed. It was discovered that the classical transfe...The approximate eigenfrequencies for the in-plane vibrations of a cable structure consisting of inclined cables, together with point masses at various points were computed. It was discovered that the classical transfer matrix method was inadequate for this task, and hence the larger exterior matrices were used to determine the eigenfrequency equation. Then predictions of the dynamics of the general cable structure based on the asymptotic estimates of the exterior matrices were made.展开更多
In this paper, how to compute the eigenfrequencies of the structures composed of a series of inclined cables is shown. The physics of an inclined cable can be complicated, so solving the differential equations even ap...In this paper, how to compute the eigenfrequencies of the structures composed of a series of inclined cables is shown. The physics of an inclined cable can be complicated, so solving the differential equations even approximately is difficult. However, rather than solving the system of 4 first-order equations governing the dynamics of each cable, the governing equations are instead converted to a set of equations that the exterior matrix satisfies. Therefore, the exterior matrix method （EMM） is used without solving the original governing equations. Even though this produces a system of 6 first-order equations, the simple asymptotic techniques to find the first three terms of the perturbative solution can be used. The solutions can then be assembled to produce a 6 x 6 exterior matrix for a cable section. The matrices for each cable in the structure are multiplied together, along with the exterior matrices for each joint. The roots of the product give us the eigenfrequencies of the system.展开更多
One of the more severe fluctuating pressure environments encountered in supersonic or hypersonic flows is the shock wave oscillation driven by interaction of a shock wave with boundary layer. The high intensity oscill...One of the more severe fluctuating pressure environments encountered in supersonic or hypersonic flows is the shock wave oscillation driven by interaction of a shock wave with boundary layer. The high intensity oscillating shock wave may induce structure resonance of a high speed vehicle. The research for the shock oscillation used to adopt empirical or semiempirical methods because the phenomenon is very complex. In this paper a theoretical solution on shock oscillating frequency due to turbulent shear layer fluctuations has been obtained from basic conservation equations. Moreover, we have attained the regularity of the frequency of oscillating shock varying with incoming flow Much numbers M and turning angle . The calculating results indicate excellent agreement with measurements. This paper has supplied a valuable analytical method to study aeroelastic problems produced by shock wave oscillation.展开更多
Researchers are paying increasing attention to the development of low-cost and microcontroller-based accelerometers,in order to make structural health monitoring feasible for conventional bridges with limited monitori...Researchers are paying increasing attention to the development of low-cost and microcontroller-based accelerometers,in order to make structural health monitoring feasible for conventional bridges with limited monitoring budget.Parallel with the low-cost sensor development,the use of the embedded accelerometers of smartphones for eigenfrequency analysis of bridges is becoming popular in the civil engineering literature.This paper,for the first time in the literature,studies these two promising technologies by comparing the noise density and eigenfrequency analysis of a self-developed,validated and calibrated low-cost Internet of things based accelerometer LARA(low cost adaptable reliable accelerometer)with those of a state of the art smartphone(iPhone XR).The eigenfrequency analysis of a footbridge in San Sebastian,Spain,showed that the embedded accelerometer of the iPhone XR can measure the natural frequencies of the under study bridge.展开更多
Lightweight structures are widely used across different industry sectors.However,they get easily excited by external influences,such as vibrations.Undesired high vibration amplitudes can be avoided by shifting the str...Lightweight structures are widely used across different industry sectors.However,they get easily excited by external influences,such as vibrations.Undesired high vibration amplitudes can be avoided by shifting the structural eigenfrequencies,which can be achieved adapting the structural design considering optimisation procedures and structures primarily inspired by diatoms.This procedures has been applied to the development process of a girder structure installed in a synchrotron radiation facility to support heavy magnets and other components.The objective was to design a 2.9 m long girder structure with high eigenfrequencies,a high stiffness and a low mass.Based on a topology optimisation result,a parametric beam–shell model including biologically inspired structures(e.g.,Voronoi combs,ribs,and soft and organic-looking transitions)was built up.The subsequent cross-sectional optimisation using evolutionary strategic optimisation revealed an optimum girder structure,which was successfully manufactured using the casting technology.Eigenfrequency measurements validated the numerical models.Future changes in the specifications can be implemented in the bio-inspired development process to obtain adapted girder structures.展开更多
This paper concentrates on investigating the mechanical stability of a Beam Position Monitor (BMP)support prototype of the Shanghai Synchrotron Radiation Facility(SSRF)project.Both finite element analysis and vibratio...This paper concentrates on investigating the mechanical stability of a Beam Position Monitor (BMP)support prototype of the Shanghai Synchrotron Radiation Facility(SSRF)project.Both finite element analysis and vibration measurements have been performed.Inconsistent results between the simulations and experiments motivate us to study three connections between the support and the ground:ground bolt(used in the initial design),part grout and full grout(proposed in the later research).After changing the connection, the first eigenfrequency is increased from 20.2Hz to 50.2Hz,and the ratio of the integrated RMS displacement (4—50Hz)is decreased from 4.36 to 1.23 in the lateral direction.The mechanical stability is improved greatly.展开更多
Maximizing the fundamental eigenfrequency is an efficient means for vibrating structures to avoid resonance and noises.In this study,we develop an isogeometric analysis(IGA)-based level set model for the fonnulation a...Maximizing the fundamental eigenfrequency is an efficient means for vibrating structures to avoid resonance and noises.In this study,we develop an isogeometric analysis(IGA)-based level set model for the fonnulation and solution of topology optimization in cases with maximum eigenfrequency.The proposed method is based on a combination of level set method and IGA technique,which uses the non-uniform rational B-spline(NURBS),description of geometry,to perfonn analysis.The same NURBS is used for geometry representation,but also for IGA-based dynamic analysis and parameterization of the level set surface,that is,the level set function.The method is applied to topology optimization problems of maximizing the fundamental eigenfrequency for a given amount of material.A modal track method,that monitors a single target eigenmode is employed to prevent the exchange of eigenmode order number in eigenfrequency optimization.The validity and efficiency of the proposed method are illustrated by benchmark examples.展开更多
Acoustic characteristics of a thrust chamber with quarter-wave resonators are numerically studied based on the unsteady Reynolds-averaged Navier-Stokes(URANS) method. Organized pressure disturbance model and constant-...Acoustic characteristics of a thrust chamber with quarter-wave resonators are numerically studied based on the unsteady Reynolds-averaged Navier-Stokes(URANS) method. Organized pressure disturbance model and constant-volume bomb model are applied as artificial disturbances to excite pressure oscillations in the chamber. Eigenfrequencies and amplitudes of acoustic modes of the chamber are obtained by fast fourier transform(FFT) analysis, while damping characteristics are evaluated by the half-power bandwidth method. Predicted damping capacities of the chamber with and without quarter-wave resonators agree well with experimental results. Pressure oscillations can be controlled by a quarter-wave resonator mainly through reducing the amplitude of target acoustic mode, rather than increasing damping capacity of the chamber. Major damping mechanism of the resonator is cutting down pressure peak of target acoustic mode and raising up its pressure trough(CPRT);therefore the amplitude of target acoustic mode is reduced significantly. Moreover, acoustic energy can be dissipated by vortex at the orifice and by viscosity on the surface of a resonator, which increase damping capacity of the chamber slightly. Under the condition with multi-modes pressure oscillations, a resonator can still suppress pressure oscillations of target acoustic mode through CPRT.However, it may enhance pressure oscillations of other modes due to redistribution of oscillation energy among all acoustic modes.展开更多
The mechanical stability, a key problem for the 3rd synchrotron light source, is essential for the electron beam performance. This paper analyzes the influences of the first eigenfrequency and Q value on the mechanica...The mechanical stability, a key problem for the 3rd synchrotron light source, is essential for the electron beam performance. This paper analyzes the influences of the first eigenfrequency and Q value on the mechanical stability. Then the research on the improvement of the mechanical stability for the magnet girder assemblies (MGAs) and the dipole concrete assemblies (DCAs), both of which are the main parts of the Shanghai Synchrotron Radiation Faculty (SSRF), is performed. The measurement result shows that the mechanical stability is improved obviously for the MGAs by using the auxiliary supports and for the DCAs by using polymer-modification concrete instead of common concrete. The paper can give some guidance to the mechanical design of the 3rd generation light sources.展开更多
The modulus of viscoelastic materials varies with excitation frequency.However,during modal analysis of frequency dependent materials,a material evaluation frequency is necessary because stiffness cannot be modified d...The modulus of viscoelastic materials varies with excitation frequency.However,during modal analysis of frequency dependent materials,a material evaluation frequency is necessary because stiffness cannot be modified during eigenfrequency procedure.As a result,only those vibration modes are accurate,of which eigenfrequency is close to the material evaluation frequency.In order to obtain vibration modes of solid rocket motor(SRM) using material modulus based on frequency which is the same as the eigenfrequency,an iterative approach was proposed.Results of the iterative technique show that frequency modes obtained from the method are in complete agreement with the eigenfrequency and material evaluation frequency.展开更多
文摘In this paper, we will compute the transfer matrices to find the eigenfrequenciesfor the vibrations of the general non-collinear Euler-Bernoulli or Timoshenko beamstructure with dissipative joints. We will allow the structure to be three dimensional,and thus we must consider all types of vibrations simulaneously, including longitudinaland torsional vibrations. The general structure considered will consist of any number ofbeams joined end to end to form a chain. Many, different kinds of dampers areallowed, even within the same structure. We also will allow different materials withinthe structure as well as different beam widths. We then will show. that asymptotic estimates can be used to find the eigenfrequencies approximately.
文摘This paper discusses the influence of environmental factors and of normal material aging on the eigenfrequencies of concrete bridges based on monitoring data registered during 4 years of a specific bridge. It is a new composite steel-concrete bridge built in 2006 in Luxembourg. The measurements are analyzed and compared to literature data. The final objective is the use of real monitored eigenfrequencies for structural health monitoring and damage detection based on identification of stiffness losses in practical applications. Therefore, it is very important to identify and compensate for outdoor influences namely temperature, excitation force level and normal aging effects, like creep and shrinkage of concrete and their impact on material properties. The present paper aims at describing these effects in order to separate them from damage effects. It is shown that temperature change rates and temperature gradients within the bridge have an influence on the eigenfrequencies. Hence the key idea for assessment from the full database is to select only measurements with small temperature differences and slow temperature change rates.
基金supported by the National Natural Science Foundation of China(NSFC, Grant Nos. 10721202 and 11023001)supported by Chinese Academy of Sciences(Grant No. KJX2-EW-L03)
文摘The eigenvalue problems of the buckling loads and natural frequencies of a braced beam on an elastic foundation are investigated. sented. The eigenvalues vary with the different The exact solutions for the eigenvalues are preparameters and are especially sensitive to the brace location. As the beam of a continuous system has infinite eigenvalues and these eigenvalues are influenced differently by a brace, the eigenvalues show rich variation patterns. Because these eigenvalues physically correspond to the structure buckling loads and natural frequencies, the study on the eigenvalues variation patterns can offer a design guidance of using a lateral brace of translation spring to strengthen the structure.
文摘In an operation mode of atomic force micro- scopy that uses a higher eigenmode to determine the physical properties of material surface, the ratio between the eigenfrequency of a higher flexural eigenmode and that of the first flexural eigenmode was identified as an important parameter that affects the sensitivity and accessibility. Structure features such as cut-out are often used to tune the ratio of eigenfrequencies and to enhance the performance. However, there lacks a systematic and automatic method for tailoring the ratio. In order to deal with this issue, a shape and topology optimization problem is formulated, where the ratio between two eigenfrequen- cies is defined as a constraint and the area of the cantilever is maximized. The optimization problem is solved via the level set based method.
基金supported by the National Natural Science Foundation of China (Grant No.51505096)the Natural Science Foundation of Heilongjiang Province (Grant No.LH2020E064).
文摘A smooth bidirectional evolutionary structural optimization(SBESO),as a bidirectional version of SESO is proposed to solve the topological optimization of vibrating continuum structures for natural frequencies and dynamic compliance under the transient load.A weighted function is introduced to regulate the mass and stiffness matrix of an element,which has the inefficient element gradually removed from the design domain as if it were undergoing damage.Aiming at maximizing the natural frequency of a structure,the frequency optimization formulation is proposed using the SBESO technique.The effects of various weight functions including constant,linear and sine functions on structural optimization are compared.With the equivalent static load(ESL)method,the dynamic stiffness optimization of a structure is formulated by the SBESO technique.Numerical examples show that compared with the classic BESO method,the SBESO method can efficiently suppress the excessive element deletion by adjusting the element deletion rate and weight function.It is also found that the proposed SBESO technique can obtain an efficient configuration and smooth boundary and demonstrate the advantages over the classic BESO technique.
文摘The approximate eigenfrequencies for the in-plane vibrations of a cable structure consisting of inclined cables, together with point masses at various points were computed. It was discovered that the classical transfer matrix method was inadequate for this task, and hence the larger exterior matrices were used to determine the eigenfrequency equation. Then predictions of the dynamics of the general cable structure based on the asymptotic estimates of the exterior matrices were made.
文摘In this paper, how to compute the eigenfrequencies of the structures composed of a series of inclined cables is shown. The physics of an inclined cable can be complicated, so solving the differential equations even approximately is difficult. However, rather than solving the system of 4 first-order equations governing the dynamics of each cable, the governing equations are instead converted to a set of equations that the exterior matrix satisfies. Therefore, the exterior matrix method （EMM） is used without solving the original governing equations. Even though this produces a system of 6 first-order equations, the simple asymptotic techniques to find the first three terms of the perturbative solution can be used. The solutions can then be assembled to produce a 6 x 6 exterior matrix for a cable section. The matrices for each cable in the structure are multiplied together, along with the exterior matrices for each joint. The roots of the product give us the eigenfrequencies of the system.
基金The Project Supported by the National Natural Science Foundation of China
文摘One of the more severe fluctuating pressure environments encountered in supersonic or hypersonic flows is the shock wave oscillation driven by interaction of a shock wave with boundary layer. The high intensity oscillating shock wave may induce structure resonance of a high speed vehicle. The research for the shock oscillation used to adopt empirical or semiempirical methods because the phenomenon is very complex. In this paper a theoretical solution on shock oscillating frequency due to turbulent shear layer fluctuations has been obtained from basic conservation equations. Moreover, we have attained the regularity of the frequency of oscillating shock varying with incoming flow Much numbers M and turning angle . The calculating results indicate excellent agreement with measurements. This paper has supplied a valuable analytical method to study aeroelastic problems produced by shock wave oscillation.
基金supported by the projects PID2021-126405OB-C31,funded by FEDER funds—A Way to Make Europe and Spanish Ministry of Economy and Competitiveness MICIN/AEI/10.13039/501100011033/the National Natural Science Foundation of China(Grant Nos.52278313,52411540031)the Project to Attract Foreign Experts(No.G2023133018L),the Top Discipline Plan of Shanghai Universities—Class I.
文摘Researchers are paying increasing attention to the development of low-cost and microcontroller-based accelerometers,in order to make structural health monitoring feasible for conventional bridges with limited monitoring budget.Parallel with the low-cost sensor development,the use of the embedded accelerometers of smartphones for eigenfrequency analysis of bridges is becoming popular in the civil engineering literature.This paper,for the first time in the literature,studies these two promising technologies by comparing the noise density and eigenfrequency analysis of a self-developed,validated and calibrated low-cost Internet of things based accelerometer LARA(low cost adaptable reliable accelerometer)with those of a state of the art smartphone(iPhone XR).The eigenfrequency analysis of a footbridge in San Sebastian,Spain,showed that the embedded accelerometer of the iPhone XR can measure the natural frequencies of the under study bridge.
基金This study was financially supported by the Innovationsfonds from the Alfred Wegener Institute,Helmholtz Centre for Polar andMarine Research(AWI)and by the Deutsches Elektronen-Synchrotron(DESY),a research centre of the Helmholtz Association,christian.hamm@awi.de。
文摘Lightweight structures are widely used across different industry sectors.However,they get easily excited by external influences,such as vibrations.Undesired high vibration amplitudes can be avoided by shifting the structural eigenfrequencies,which can be achieved adapting the structural design considering optimisation procedures and structures primarily inspired by diatoms.This procedures has been applied to the development process of a girder structure installed in a synchrotron radiation facility to support heavy magnets and other components.The objective was to design a 2.9 m long girder structure with high eigenfrequencies,a high stiffness and a low mass.Based on a topology optimisation result,a parametric beam–shell model including biologically inspired structures(e.g.,Voronoi combs,ribs,and soft and organic-looking transitions)was built up.The subsequent cross-sectional optimisation using evolutionary strategic optimisation revealed an optimum girder structure,which was successfully manufactured using the casting technology.Eigenfrequency measurements validated the numerical models.Future changes in the specifications can be implemented in the bio-inspired development process to obtain adapted girder structures.
文摘This paper concentrates on investigating the mechanical stability of a Beam Position Monitor (BMP)support prototype of the Shanghai Synchrotron Radiation Facility(SSRF)project.Both finite element analysis and vibration measurements have been performed.Inconsistent results between the simulations and experiments motivate us to study three connections between the support and the ground:ground bolt(used in the initial design),part grout and full grout(proposed in the later research).After changing the connection, the first eigenfrequency is increased from 20.2Hz to 50.2Hz,and the ratio of the integrated RMS displacement (4—50Hz)is decreased from 4.36 to 1.23 in the lateral direction.The mechanical stability is improved greatly.
基金the National Natural Science Foundation of China(Grant No.51675197).
文摘Maximizing the fundamental eigenfrequency is an efficient means for vibrating structures to avoid resonance and noises.In this study,we develop an isogeometric analysis(IGA)-based level set model for the fonnulation and solution of topology optimization in cases with maximum eigenfrequency.The proposed method is based on a combination of level set method and IGA technique,which uses the non-uniform rational B-spline(NURBS),description of geometry,to perfonn analysis.The same NURBS is used for geometry representation,but also for IGA-based dynamic analysis and parameterization of the level set surface,that is,the level set function.The method is applied to topology optimization problems of maximizing the fundamental eigenfrequency for a given amount of material.A modal track method,that monitors a single target eigenmode is employed to prevent the exchange of eigenmode order number in eigenfrequency optimization.The validity and efficiency of the proposed method are illustrated by benchmark examples.
基金supported by the National Natural Science Foundation of China (Grant No. 91841303)。
文摘Acoustic characteristics of a thrust chamber with quarter-wave resonators are numerically studied based on the unsteady Reynolds-averaged Navier-Stokes(URANS) method. Organized pressure disturbance model and constant-volume bomb model are applied as artificial disturbances to excite pressure oscillations in the chamber. Eigenfrequencies and amplitudes of acoustic modes of the chamber are obtained by fast fourier transform(FFT) analysis, while damping characteristics are evaluated by the half-power bandwidth method. Predicted damping capacities of the chamber with and without quarter-wave resonators agree well with experimental results. Pressure oscillations can be controlled by a quarter-wave resonator mainly through reducing the amplitude of target acoustic mode, rather than increasing damping capacity of the chamber. Major damping mechanism of the resonator is cutting down pressure peak of target acoustic mode and raising up its pressure trough(CPRT);therefore the amplitude of target acoustic mode is reduced significantly. Moreover, acoustic energy can be dissipated by vortex at the orifice and by viscosity on the surface of a resonator, which increase damping capacity of the chamber slightly. Under the condition with multi-modes pressure oscillations, a resonator can still suppress pressure oscillations of target acoustic mode through CPRT.However, it may enhance pressure oscillations of other modes due to redistribution of oscillation energy among all acoustic modes.
基金supported by the National Natural Science Foundation of China (Grant No. 10805072)
文摘The mechanical stability, a key problem for the 3rd synchrotron light source, is essential for the electron beam performance. This paper analyzes the influences of the first eigenfrequency and Q value on the mechanical stability. Then the research on the improvement of the mechanical stability for the magnet girder assemblies (MGAs) and the dipole concrete assemblies (DCAs), both of which are the main parts of the Shanghai Synchrotron Radiation Faculty (SSRF), is performed. The measurement result shows that the mechanical stability is improved obviously for the MGAs by using the auxiliary supports and for the DCAs by using polymer-modification concrete instead of common concrete. The paper can give some guidance to the mechanical design of the 3rd generation light sources.
文摘The modulus of viscoelastic materials varies with excitation frequency.However,during modal analysis of frequency dependent materials,a material evaluation frequency is necessary because stiffness cannot be modified during eigenfrequency procedure.As a result,only those vibration modes are accurate,of which eigenfrequency is close to the material evaluation frequency.In order to obtain vibration modes of solid rocket motor(SRM) using material modulus based on frequency which is the same as the eigenfrequency,an iterative approach was proposed.Results of the iterative technique show that frequency modes obtained from the method are in complete agreement with the eigenfrequency and material evaluation frequency.
