42results about How to "Make up for and perfect limitations" patented technology

The invention discloses a metal fatigue crack full-life estimation method based on a damage mechanics non-probabilistic interval analysis model. The method comprises the following steps: firstly, selecting a damage evolution equation from a damage mechanics model to establish a finite element analysis formation which structurally comprises damage information, and inquiring a fatigue test manual to fit to obtain a parameter in the damage evolution equation; then, combining with a damage mechanics finite element method with an interval finite element method to regard an initial damage degree and a damage parameter as interval uncertainty variables to represent fatigue life dispersivity; further, establishing the finite element analysis model of the structure, giving an initial critical element damage degree increment, constantly carrying out iteration increase on the damage degrees of all elements, judging that the element is damaged through the damage degree of each element, and endowing with intensity and rigidity attributes; and finally, when crack expansion achieves critical crack length, judging that the structure is damaged, and calculating to obtain a fatigue life range via a damage evolution equation variant and an interval vertex propagation analysis method. By use of the metal fatigue crack full-life estimation method, the life of the fatigue crack can be more elaborately estimated.

The invention discloses a continuum structure non-probability topologicaloptimization method based on bounded uncertainty. The method comprises the following steps: first establishingoptimization feature distance d which is a non-probability reliability index based on a non-probabilistic set-based reliability model in consideration of uncertainty effects of load, material characteristics, a design permissible value and other parameters under a finite sample conditionaccording to stress characteristics of the continuum structure; and the establishing a topologicaloptimization model based on a moving asymptotesoptimization algorithm; and acquiring the most configuration of the continuum structure under a given external storage and boundary condition through repeated iteration by taking the reliability as the constraint, the weight-losing as an optimization target and the relative density of a unit as the design variable. By use of the non-probability topologicaloptimization method disclosed by the invention, the comprehensive influence of the uncertainty to the structure configuration is reasonably represented in the process of performing the topologicaloptimization design, the effective weight-losing can be realized, and the design takes account of the security and the economy by itself.

The invention discloses a composite material laminate non-probability reliability double-level optimization method. The method comprises: firstly, according to load-carrying characteristics of a composite material laminate, considering nondeterminacy effect of an intensity parameter of the composite material under condition of limited samples, based on a non-probability reliability theory, establishing a composite material laminate non-probability reliability evaluation model; in optimization of a first ply, using a simulated annealing method to optimize the composite material laminate, with thickness as a variable, and intensity reliability and rigid reliability as constraint; in optimization of a second ply, considering process constraint using stacking sequence as a variable, and optimizing with maximum intensity as target, through establishing a stacking scheme library which satisfies process requirements, using a genetic algorithm to optimize the stacking sequence of the laminate. The method ensures the composite material laminate has relatively high reliability and relatively low weight under nondeterminacy conditions, and meanwhile the method satisfies engineering actual technology level, and gives consideration to safety and economical efficiency.

The invention discloses a beam structure non-probabilistic reliability solving method capable of considering multi-failure modes. The correlation of two failure models including strength and rigidity is considered; firstly, existing multisource uncertain factors in material characteristics, environment external loading and the like are fully considered, interval mathematics and fuzzy mathematics are adopted to carry out quantization on the multisource uncertain factors and develop propagation analysis; then, the multisource uncertain factors are introduced into a general reliability solving theory, the non-probabilistic reliability solving method is developed, and on the basis of the method, the strength and rigidity reliability degree analysis of a beam structure can be independently carried out; and finally, the correlation of two failure models is comprehensively considered, a correlation constitutive relation equation is established, and the reasonable representation of the correlation among failure modes is realized. The method gives the comprehensive influence on structural strength reliability by different failure modes, can realize the comprehensive optimization design of the structural strength, and guarantees that the design gives consideration to safety and economy.

The invention discloses a time-variant reliability design method for a rectangular plate structure with initial defects. The method comprises the steps of firstly, according to stress characteristics of the defected plate structure, considering indeterministic effects of parameters such as a load, material characteristics, a design permissible value and the like under a finite sample condition, and establishing a non probability interval process model of crack expansion length of the rectangular plate structure; secondly, based on a classic Paris damage evolution formula and a first passage theory, constructing a time-variant reliability measurement model of the structure with the initial defects; and finally, by taking the reliability as a constraint condition, the weight reduction as an optimization target and the plate thickness as a design variable, performing repeated iterations to obtain an optimal design scheme of the structure within a set service time. According to the method, the comprehensive influence of indeterminacy on power safety of the structure with the initial defects within a set life cycle is reasonably characterized in an optimization design process, and the weight can be effectively reduced, thereby ensuring the safety and economy of the design.

The invention discloses a mixed fatigue reliability optimization method aiming at a composite material laminated plate. The mixed fatigue reliability optimization method comprises the steps of firstly taking a full consideration to existing multisource uncertain factors such as material intensity and useful load based on a small sample non-probabilistic method, integrating irregular sample data by applying a gray theory, exploring potential regularity of the irregular sample data and giving out a reasonable quantized result; then establishing a residual intensity model under the action of a fatigue load, introducing an uncertain parameter into a model and developing a non-probabilistic reliability solving method; then taking an overall consideration to a mixing form of a random variable and an interval variable, solving a mixing reliability index by utilizing an established non-probabilistic reliability solving method and combining with the probability reliability solving method; and finally carrying out composite material laminated plate thickness optimization design by regarding the mixing reliability index as constraint. Based on the mixed fatigue reliability optimization method aiming at the composite material laminated plate, intensity optimization design of large-scale structures in the presence of poor information and less data can be realized, and the design per se which considers both security and economy is ensured.

The invention discloses a static and dynamic hybrid uncertainty-oriented non-probabilistic reliability optimization design method for a ready-built structure. According to the method, multisource uncertainty conditions in an actual engineering structure are comprehensively considered, a quantitative index for effectively assessing the safety performance of the structure in a full-life period by static and dynamic hybrid uncertainty parameters is established, and the non-probabilistic reliability optimization of the ready-built structure is finished by taking the quantitative index as a design constraint condition. The method comprises the steps of firstly, reasonably representing an intrinsic law of static and dynamic hybrid uncertainty by utilizing an interval number and an interval process; secondly, constructing a dynamic function based on a response process of the ready-built structure in combination with an interval mathematic operation rule, and defining and analyzing a digital characteristic of the function by virtue of a discretization means; thirdly, defining and giving out an explicit expression of a hybrid reliability index of the structure by utilizing a first-passage theory; and finally, establishing a hybrid reliability-based non-probabilistic reliability optimization model of the ready-built structure, and performing quick iteration and robust solving of an optimization process in combination with an intelligent ant colony algorithm.

The invention discloses an existing structure static equivalent reliability evaluation method based on an interval set envelope function. The method comprises the steps that the envelope function is introduced into the reliability problem of a dynamic structure, a failure domain of the multi-parameter structure uncertainty changing along with time is approximately constructed through an envelope surface, a dynamic problem is transformed into a static problem, and effective evaluation on the structural security situation is achieved through reliability degree index calculation. According to the method, a partial differential equation is defined according to the character that the envelope surface in the internal set envelope function is tangent to a failure boundary hypersurface continuously changing along with time, and a risk moment corresponding to an extension point is solved; a limited dimensional static failure domain equivalent to an original dynamic problem at a limited risk moment is obtained by building a multi-dimensional hypercube model containing the correlation; the static equivalent reliability degree calculation process of an existing structure is finally achieved on the basis of a volume ratio idea, and the traditional time-varying reliability calculation scale is greatly reduced while the precision is guaranteed.

The invention discloses a non-probability dynamic reliability assessment method of a composite laminated structure facing whole life cycle. The method gives comprehensive consideration on a dynamic fluctuation effect of composite laminated structure load and accumulated degradation of material properties, and establishes a non-probability interval process model of the structure dynamic characteristics based on a finite element concept and an interval mathematic method, and then combining with a first passage theory and a failure determination criterion of a light laminated structure, non-probability dynamic reliability indexes of the structure are defined, and an efficient and steady solution strategy is explored. In a process of calculating reliability degree calculation, the method reasonably represents comprehensive influence of nondeterminacy on dynamic safety of the structure in the whole life cycle, and the method provides necessary data reference for ensuring refined design on the structure.

The invention discloses an estimation method for a sound vibration fatigue life containing an uncertain metal structure.According to the method, firstly, a finite element analytical model of a metal structure is established, the uncertain effect of material and structure characteristic parameters under finite sample conditions is considered, and a systematic transfer function is obtained based on the frequency response analytical theory; secondly, according to the characteristics of random noise loads, a mean square root response and stress power spectral density function (PSD) of displacement and stress of all key nodes is obtained through an SRSS method for typical broadband steady ergodic random noise loads; thirdly, in combination with a Dirlik model, an interval uncertain propagation second-order Taylor series expansion method and an analytical method for vibration fatigue within a frequency domain, the relation between a rain flow amplitude probability density function and the power spectral density function is set up; finally, the Miner linear accumulative damage theory is used for obtaining an interval range of the sound vibration fatigue life containing the uncertain metal structure.Dispersity of the structure and material parameters is taken into full consideration during calculation of the structural life excited by typical random noise, and therefore the obtained fatigue life is more reasonable.

The invention provides a method for synthesizing for non-probability time-varying reliability of a link mechanism containing a hinge gap. Firstly, according to the rod length and initial position of the link mechanism and specific characteristics of the hinge gap, a mathematic expression of a mechanism motion error function is obtained in combination with a vector method; secondly, rod length and hinge uncertainty information is introduced into an interval process model for establishing mechanism motion errors, and the time-varying uncertainty characteristic quantity of a mechanism motion precision limit state function is quickly calculated; thirdly, based on the first crossing theory and the dispersed strategy, index definition and solution of crossing failure possibility in any micro cyclic loading increment segment are completed, and then a time-varying reliability model is constructed; finally, the non-probability time-varying reliability index of motion precision serves as a target, non-probability reliability of mechanism existence conditions serves as a constraint condition, and synthesis of the non-probability time-varying reliability of the link mechanism containing the hinge gap is completed. In the process of mechanism synthesis, synthetic effects of uncertainty on the mechanism in a motion period are reasonably represented, and the time-varying reliability of the mechanism can be effectively improved.

The invention discloses a grey confidence interval-based reliability analysis method for a structure stress-intensity interference model set. For the problem that a conventional probability thought cannot provide effective estimation of a structure stress and intensity mean value due to finite sample information of structure stress and intensity parameters and difficult determination of statistic characteristics, the method comprises the steps of first defining grey distance measure of an inter-finite-sample topological relation and a distance relation, and performing grey generation of the grey distance measure to obtain an estimated value of the structure stress and intensity mean value; defining and solving a grey density index to obtain a confidence interval of the stress and intensity mean value under the condition of meeting the requirement of a certain grey confidence degree; and finally, introducing a structure reliability theory in a non-probability set theory framework to derive a two-dimensional reliability measure index for structure stress-intensity interference models, thereby realizing reasonable mapping of structure reliability analysis and confidence degree evaluation from samples, wherein the two-dimensional reliability measure index is of confidence degree significance.

The invention discloses a first passage theory-based method for analyzing non-probability power reliability of a vibrating active control system. According to the method, the influences, caused by interval uncertainty of materials, on well-posedness of the active control system is comprehensively considered. The method comprises the following steps: deriving a power response expression of the active control system on the basis of a one-order state-space equation and a state feedback control theory; constructing a non-probability interval process model of controlled structure power response on the basis of an interval mathematic thought and a time varying uncertainty propagation analysis method; and defining a non-probability power reliability index of the vibrating active control system by utilizing a first passage theory and a structure control rate failure criterion, and exploring an efficient and steady solving method. When the method is used for carrying out reliability calculation, the comprehensive influences, caused by material dispersity, on controlled structure power response is embodied, so that necessary and feasible theoretical reference is provided for the fine design of controllers.

The invention discloses an in-service structure optimal maintenance design method based on convex model time-variation reliability. The method comprehensively considers the influence of uncertainty under the time effect to the in-service structural mechanic behavior. At first, time-variation uncertainty parameters are characterized by defining the convex model process, and the explicit expression of the limit state function characteristic quantities is deduced; based on the spanning theory of vibration mechanics and the structure non-probabilistic reliability model, the time-variation reliability index of the in-service structure based on the convex model is defined; furthermore, by taking the relationship between the maintenance cost and the service life of the structure into account, an in-service structure reliability design model is built based on the optimal maintenance decision; and by taking the reliability as the optimization target and maintenance time as the design variable, and repeating iterations through an intelligent optimization algorithm, the optimal maintenance and reinforcement design scheme for the drafted service period structure can be finally obtained.

The invention discloses a fatigue system reliability analysis method of a composite material laminated structure. According to the method, under the action of a fatigue load and a given constraint condition, multiple failure modes of the structure and correlation of the failure modes are fully considered, so that system reliability analysis is carried out. The method comprises the following steps:firstly, calculating the failure probability of each failure element in different failure modes by combining a two-dimensional Hashin criterion according to specific characteristics of laminated plate structure materials, loads and the like, and considering that a layer with the maximum failure probability is damaged; secondly, according to the built one-way laminated plate degradation model, degrading material attributes in the fatigue loading process, subjecting the degraded model to reanalysis, calculating the failure probability of each failure element, and determining a main failure path; and finally, checking the residual strength of the structure after cyclic loading is finished, establishing a fatigue system reliability index on the basis, and providing guidance and reference forsubsequent analysis and optimization.

The invention discloses a non-probabilistic time-variant reliability solution method of a composite laminated plate. The method comprises the steps: firstly, introducing a damage driving force and damage evolution concept based on a damage mechanic analysis theory, and establishing a structural damage evolution equation; secondly, comprehensively considering uncertainty of a variable, giving a reasonable quantification result of the variable by a non-probabilistic interval statistical method, introducing the interval variable into the equation, and constructing a damage evolution equation including the interval variable; and finally, performing non-probabilistic time-variant reliability analysis on a composite laminated plate structure according to a non-probabilistic reliability analysis method and a first-passage theory. Based on the fact, the method can provide theoretical bases for strength optimization design of large structures and the like under the conditions of poor information and less data and ensures that the design gives consideration to safety and economy.

The invention discloses a vibration analysis method for an orthotropic opposite-side simply-supported rectangular thin plate. The method is based on a free vibration equation of an orthotropic rectangular thin plate, and comprises the following steps: firstly, establishing a vibration mode differential equation to complete the construction of a Hamiltonian regular equation; Secondly, according toan octane geometry method, using a separation variable method to perform solving, deriving expressions of characteristic values corresponding to the characteristic equation, and analyzing the value taking conditions of the two groups of characteristic values; constructing a general solution form of a vibration mode function containing an undetermined constant, deducing an intrinsic value and an intrinsic vector expression of the intrinsic value in combination with an edge-to-edge simple support boundary condition, and proving the octyl orthogonality and completeness of an intrinsic vector system; Unfolding an octangular eigenvector to obtain an expression of a state vector, thereby obtaining a general solution of the vibration mode function; And finally, aiming at six common boundary conditions of the opposite edge simple support, corresponding frequency equations are derived respectively, so that accurate solution of the free vibration frequency is realized, and a foundation can be laid for carrying out dynamic analysis and related application of the free vibration frequency.

The invention discloses a double-chain quantum genetic algorithm for structural optimization design. The design result obtained through the method better meets the actual requirement, and the engineering applicability is higher. Firstly, selection of an initial scheme of structure optimization is improved on the basis of a superposition state thought in quantum computing, and dependence of a traditional method on an initial value is avoided. A quantum genetic algorithm mechanism is introduced in the structure optimization process (size / topology), the search range of a solution space is expanded, and therefore the optimal configuration more suitable for actual engineering requirements is obtained. The method has the advantages that a new thought of a double-chain quantum genetic algorithm is introduced into structural optimization design; on one hand, the dependence of a traditional gradient optimization method on an initial value is overcome, on the other hand, the search range of theunderstanding space is expanded, compared with a common evolutionary algorithm, the method is not prone to falling into local optimum, higher global optimization capacity is achieved, and a new tool and means are provided for the structure optimization design problem in the field of aircraft design.

The invention discloses a quasi-static and non-linear kinetic analysis method for the uncertainty of a viscoelastic dielectric elastomer based on an interval method. In the method, a viscoelastic kinetic model of the dielectric elastomer is provided, uncertainty of material parameters, external load and voltage is considered, and creep analysis, relaxation analysis and kinetic response analysis are carried out on the dielectric elastomer with interval uncertainty parameters by introducing an interval perturbation method and a first-order Taylor expansion method. The effectiveness of the interval method provided by the invention is verified by a Monte Carlo simulation method, and the uncertainty prediction method can be used in the design of an active control system taking a dielectric elastomer as a driver or a sensor in the future.

The invention discloses a time-variant reliability design method for a rectangular plate structure with initial defects. The method comprises the steps of firstly, according to stress characteristics of the defected plate structure, considering indeterministic effects of parameters such as a load, material characteristics, a design permissible value and the like under a finite sample condition, and establishing a non probability interval process model of crack expansion length of the rectangular plate structure; secondly, based on a classic Paris damage evolution formula and a first passage theory, constructing a time-variant reliability measurement model of the structure with the initial defects; and finally, by taking the reliability as a constraint condition, the weight reduction as an optimization target and the plate thickness as a design variable, performing repeated iterations to obtain an optimal design scheme of the structure within a set service time. According to the method, the comprehensive influence of indeterminacy on power safety of the structure with the initial defects within a set life cycle is reasonably characterized in an optimization design process, and the weight can be effectively reduced, thereby ensuring the safety and economy of the design.

The invention discloses a method for evaluating the static force displacement boundary of a structure containing convex polyhedron uncertainty parameters based on linear programming. This method considers the uncertain parameters of the convex polyhedron. First, the convex polyhedron model of the static response problem of the uncertain structure is established. Through vector and matrix transformation and operation, the convex polyhedron model of the static response problem of the uncertain structure is completed to the The transformation of the standard form of the linear programming problem; furthermore, a series of linear programming sub-problems are formed by combining the vertex matrices of the structural stiffness convex polyhedron and the vertex vectors of the external load convex polyhedron; finally, based on the linear programming theory, a To solve a series of linear programming sub-problems feasible domain vertex values, use the vector transformation formula to express the maximum value and minimum value of a series of vertex values ​​as the upper bound and lower bound of the static displacement boundary, thus realizing the precise static displacement boundary Evaluate.

The invention provides a method for synthesizing for non-probability time-varying reliability of a link mechanism containing a hinge gap. Firstly, according to the rod length and initial position of the link mechanism and specific characteristics of the hinge gap, a mathematic expression of a mechanism motion error function is obtained in combination with a vector method; secondly, rod length and hinge uncertainty information is introduced into an interval process model for establishing mechanism motion errors, and the time-varying uncertainty characteristic quantity of a mechanism motion precision limit state function is quickly calculated; thirdly, based on the first crossing theory and the dispersed strategy, index definition and solution of crossing failure possibility in any micro cyclic loading increment segment are completed, and then a time-varying reliability model is constructed; finally, the non-probability time-varying reliability index of motion precision serves as a target, non-probability reliability of mechanism existence conditions serves as a constraint condition, and synthesis of the non-probability time-varying reliability of the link mechanism containing the hinge gap is completed. In the process of mechanism synthesis, synthetic effects of uncertainty on the mechanism in a motion period are reasonably represented, and the time-varying reliability of the mechanism can be effectively improved.

The invention discloses a beam structure non-probabilistic reliability solving method capable of considering multi-failure modes. The correlation of two failure models including strength and rigidity is considered; firstly, existing multisource uncertain factors in material characteristics, environment external loading and the like are fully considered, interval mathematics and fuzzy mathematics are adopted to carry out quantization on the multisource uncertain factors and develop propagation analysis; then, the multisource uncertain factors are introduced into a general reliability solving theory, the non-probabilistic reliability solving method is developed, and on the basis of the method, the strength and rigidity reliability degree analysis of a beam structure can be independently carried out; and finally, the correlation of two failure models is comprehensively considered, a correlation constitutive relation equation is established, and the reasonable representation of the correlation among failure modes is realized. The method gives the comprehensive influence on structural strength reliability by different failure modes, can realize the comprehensive optimization design of the structural strength, and guarantees that the design gives consideration to safety and economy.

A method for evaluating a static displacement boundary of a structure with convex polyhedron uncertainty parameters based on linear programming is disclosed. The method comprises that: considering theuncertainty parameters of the convex polyhedron, the convex polyhedron model of the static response of the uncertainty structure is established. The standard form of the linear programming problem istransformed from the convex polyhedron model of the static response of the uncertainty structure by vector and matrix transformation and operation. Furthermore, a series of linear programming subproblems are formed by combining the vertex matrices of stiffness convex polyhedron and the vertex vectors of external load convex polyhedron. Finally, based on the linear programming theory, the vertex values of feasible region of a series of linear programming subproblems are solved, and the maximum and minimum values of a series of vertex values are expressed as the upper and lower bounds of staticdisplacement boundary respectively by using vector transformation formula, thus the accurate evaluation of static displacement boundary is realized.

The invention discloses an active control method of structural vibration based on non-probability interval confidence reliability, wherein an automatically adjustable active vibration control system is designed, aiming at the uncertainty of structural parameters, in the original open-loop control system Based on the improvement, based on the calculation method of the dual reliability index of reliability and confidence, on the basis of the original basis, the research on the vibration suppression algorithm is carried out under the premise of the uncertainty of the structural parameters, and the confidence index is introduced to make the designed The self-adjusting active vibration control system can improve the reliability of the structure. The feasibility of the automatically adjustable active vibration control system proposed by the present invention is verified by using a continuous model and a discrete model, and this control method can be used in the design of active control systems of uncertain structures in the future.

The invention discloses a structural vibration active control method based on non-probability interval confidence reliability, and designs an active vibration control system capable of being automatically adjusted, and the system is improved on the basis of an original open-loop control system according to the uncertainty of structural parameters; according to the double-reliability-index calculation method based on reliability and confidence, vibration suppression algorithm research is conducted on the premise that structural parameters are uncertain on the original basis, and the confidenceindex is introduced, so that the designed active vibration control system capable of being automatically adjusted can improve the reliability of the structure. The feasibility of the active vibrationcontrol system capable of being automatically adjusted is verified through a continuous model and a discrete model, and the control method can be used for designing the active control system of an uncertain structure in the future.

The invention discloses a continuum structure non-probability topologicaloptimization method based on bounded uncertainty. The method comprises the following steps: first establishingoptimization feature distance d which is a non-probability reliability index based on a non-probabilistic set-based reliability model in consideration of uncertainty effects of load, material characteristics, a design permissible value and other parameters under a finite sample conditionaccording to stress characteristics of the continuum structure; and the establishing a topologicaloptimization model based on a moving asymptotesoptimization algorithm; and acquiring the most configuration of the continuum structure under a given external storage and boundary condition through repeated iteration by taking the reliability as the constraint, the weight-losing as an optimization target and the relative density of a unit as the design variable. By use of the non-probability topologicaloptimization method disclosed by the invention, the comprehensive influence of the uncertainty to the structure configuration is reasonably represented in the process of performing the topologicaloptimization design, the effective weight-losing can be realized, and the design takes account of the security and the economy by itself.

The invention discloses an existing structure static equivalent reliability evaluation method based on an interval set envelope function. The method comprises the steps that the envelope function is introduced into the reliability problem of a dynamic structure, a failure domain of the multi-parameter structure uncertainty changing along with time is approximately constructed through an envelope surface, a dynamic problem is transformed into a static problem, and effective evaluation on the structural security situation is achieved through reliability degree index calculation. According to the method, a partial differential equation is defined according to the character that the envelope surface in the internal set envelope function is tangent to a failure boundary hypersurface continuously changing along with time, and a risk moment corresponding to an extension point is solved; a limited dimensional static failure domain equivalent to an original dynamic problem at a limited risk moment is obtained by building a multi-dimensional hypercube model containing the correlation; the static equivalent reliability degree calculation process of an existing structure is finally achieved on the basis of a volume ratio idea, and the traditional time-varying reliability calculation scale is greatly reduced while the precision is guaranteed.

The invention discloses a method for analyzing the vibration of an orthotropic simply supported rectangular thin plate with opposite sides. This method is based on the free vibration equation of an orthotropic rectangular thin plate. Firstly, the mode differential equation is established, and the Hamiltonian canonical equation is constructed. Secondly, according to the symplectic geometry method, the separation of variables method is used to solve the problem, and the corresponding The expressions of the eigenvalues ​​of the two groups of eigenvalues ​​were analyzed; the general solution form of the mode shape function with undetermined constants was constructed, and the expressions of the eigenvalues ​​and their eigenvectors were derived by combining the simply supported boundary conditions on opposite sides , and proved the symplectic orthogonality and completeness of the eigenvector system; using the symplectic eigenvector expansion, the expression of the state vector was obtained, and then the general solution of the mode shape function was obtained; finally, for the six common Boundary conditions, the corresponding frequency equations were derived respectively, so as to realize the accurate solution of the free vibration frequency, which can lay the foundation for the development of its dynamic analysis and related applications.

The invention discloses an estimation method for a sound vibration fatigue life containing an uncertain metal structure.According to the method, firstly, a finite element analytical model of a metal structure is established, the uncertain effect of material and structure characteristic parameters under finite sample conditions is considered, and a systematic transfer function is obtained based on the frequency response analytical theory; secondly, according to the characteristics of random noise loads, a mean square root response and stress power spectral density function (PSD) of displacement and stress of all key nodes is obtained through an SRSS method for typical broadband steady ergodic random noise loads; thirdly, in combination with a Dirlik model, an interval uncertain propagation second-order Taylor series expansion method and an analytical method for vibration fatigue within a frequency domain, the relation between a rain flow amplitude probability density function and the power spectral density function is set up; finally, the Miner linear accumulative damage theory is used for obtaining an interval range of the sound vibration fatigue life containing the uncertain metal structure.Dispersity of the structure and material parameters is taken into full consideration during calculation of the structural life excited by typical random noise, and therefore the obtained fatigue life is more reasonable.