TWI384207B - Method of modal analysis by free vibration response only (mafvro) and system thereof - Google Patents
Method of modal analysis by free vibration response only (mafvro) and system thereof Download PDFInfo
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Description
本發明係關於一種僅自由振動響應之模態分析方法〔method of modal analysis by free vibration response only，MAFVRO〕及其系統，其特別是關於時間域〔time domain〕或頻率域〔frequency domain〕僅自由振動響應之模態分析方法及其系統。The present invention relates to a method of modal analysis by free vibration response only (MAFVRO) and a system thereof, which are particularly free with respect to a time domain or a frequency domain. Modal analysis method and system for vibration response.
現今解決振動問題最直接有效的方法係瞭解結構物的動態特性，而透過模態分析方式將可獲得結構物之自然頻率〔natural frequency〕及模態振型〔mode shape〕，其稱為模態參數〔modal parameters〕。任意結構系統具有固定之材料及形狀尺寸，以及既有之邊界條件，則其模態參數為唯一的、不變的，亦可視為系統之特性。The most direct and effective way to solve the vibration problem today is to understand the dynamic characteristics of the structure, and the modal analysis method can obtain the natural frequency and the mode shape of the structure, which is called the mode. Parameter [modal parameters]. Any structural system with a fixed material and shape size, as well as existing boundary conditions, its modal parameters are unique, constant, and can also be considered as a system characteristic.
一般而言，獲得模態參數方法可透過理論模態分析〔theoretical modal analysis，TMA〕及實驗模態分析〔experimental modal analysis，EMA〕。其中理論模態分析係必須求得系統之質量、勁度矩陣，方能由特徵值問題求得結構系統之正交模態〔normal modes〕。若考慮系統為一般化之非比例阻尼，則可得系統之複數模態〔complex modes〕。就實務而言，阻尼比並不能由理論分析求得，故需藉助實驗得之。In general, the method of obtaining modal parameters can be achieved through theoretical modal analysis (TMA) and experimental modal analysis (EMA). The theoretical modal analysis system must obtain the quality and stiffness matrix of the system, and then the normal modes of the structural system can be obtained from the eigenvalue problem. If the system is considered to be generalized non-proportional damping, then the complex modes of the system are available. As far as practice is concerned, the damping ratio cannot be obtained by theoretical analysis, so it is necessary to obtain experimental results.
傳統實驗模態分析具有其潛在限制及缺點如下：1、結構必須處於靜止狀態：運轉之機器必須為穩定干擾源，若待測物為土木結構如橋樑，常受風力、車輛行經等之干擾，因此不易進行傳統模態測試。The traditional experimental modal analysis has its potential limitations and shortcomings as follows: 1. The structure must be in a static state: the running machine must be a stable interference source. If the object to be tested is a civil structure such as a bridge, it is often interfered by wind power, vehicle travel, etc. Therefore, traditional modal testing is not easy.
2、必須能以可控制之激振源：如使用衝擊錘〔input hammer〕或激振器〔shaker〕，即系統輸入必須為已知，且接收訊號之儀器會限制輸入之大小範圍。2, must be able to control the source of vibration: If you use an impact hammer or shaker, the system input must be known, and the instrument receiving the signal will limit the size range of the input.
3、必須藉由輸入與輸出間的頻率響應函數〔Frequency Response Function，FRF〕求得模態參數，但在操作與作動狀態下的結構，輸入為未知數，因此傳統的實驗模態分析無法量測作動中的待測物。3. The modal parameters must be obtained by the frequency response function (FRF) between the input and the output. However, in the structure of the operation and actuation, the input is unknown, so the traditional experimental modal analysis cannot be measured. The object to be tested in action.
4、求得系統模態參數之過程繁瑣：藉由模態參數擷取方法〔modal parameter extraction method〕或以曲線嵌合法〔curve－fitting〕求得系統模態參數，該方法相當繁瑣，且常需要套裝軟體，其對工程應用之設備需求高，因而具有提高設備成本的限制。4. The process of obtaining the modal parameters of the system is cumbersome: the modal parameter extraction method or the curve modal method is used to obtain the system modal parameters, which is quite cumbersome and often A software package is required, which has a high demand for equipment for engineering applications and thus has a limitation on increasing equipment costs.
有鑑於此，本發明為了解決上述需求，特別是對於傳統EMA之限制，有必要開發新的振動分析與量测系統，藉由此分析系統突破，進一步取得結構的模態參數，以便在未來可進一步發展模型驗證及結構響應預測分析等應用。In view of the above, in order to solve the above-mentioned needs, especially for the limitation of the conventional EMA, it is necessary to develop a new vibration analysis and measurement system, thereby analyzing the system breakthrough and further obtaining the modal parameters of the structure so as to be available in the future. Further develop applications such as model validation and structural response prediction analysis.
本發明之主要目的係提供一種僅自由振動響應之模態分析方法及其系統，其選擇時間域或頻率域分析方法，利用自由振動響應估算系統模態參數，其達成解決傳統EMA限制之目的。The main object of the present invention is to provide a modal analysis method and system for free vibration response only, which selects a time domain or frequency domain analysis method, and estimates a system modal parameter using a free vibration response, which achieves the purpose of solving the conventional EMA limitation.
為了達成上述目的，本發明之僅自由振動響應之模態分析系統包含一理論自由振動響應分析流程單元、一實驗模態分析流程單元、一自由振動響應模態分析實驗流程單元及一自由振動響應模態分析流程單元。該理論自由振動響應分析流程單元用以提供 數個理論模態參數及數個理論系統自由振動響應。該實驗模態分析流程單元用以提供數個實驗衝擊振動響應及數個實驗模態參數。該自由振動響應模態分析實驗流程單元係自該實驗模態分析流程單元之實驗衝擊振動響應擷取數個實驗系統自由振動響應，並提供至該自由振動響應模態分析流程單元。該自由振動響應模態分析流程單元利用該理論系統自由振動響應或該實驗系統自由振動響應估算數個系統模態參數。In order to achieve the above object, the modal analysis system of the free vibration response of the present invention comprises a theoretical free vibration response analysis flow unit, an experimental modal analysis flow unit, a free vibration response modal analysis experimental flow unit and a free vibration response. Modal analysis process unit. The theoretical free vibration response analysis process unit is provided Several theoretical modal parameters and several theoretical systems free vibration response. The experimental modal analysis process unit is used to provide several experimental shock vibration responses and several experimental modal parameters. The free vibration response modal analysis experimental flow unit extracts a plurality of experimental system free vibration responses from the experimental shock vibration response of the experimental modal analysis flow unit, and provides the free vibration response modal analysis flow unit. The free vibration response modal analysis flow unit estimates a number of system modal parameters using the theoretical system free vibration response or the experimental system free vibration response.
本發明僅自由振動響應之模態分析系統之該理論系統自由振動響應及實驗系統自由振動響應包含位移自由振動響應、速度自由振動響應及加速度自由振動響應。The theoretical system free vibration response and the experimental system free vibration response of the modal analysis system of the free vibration response of the present invention include a displacement free vibration response, a velocity free vibration response, and an acceleration free vibration response.
本發明僅自由振動響應之模態分析系統之該系統模態參數包含自然頻率、模態振型向量及阻尼比。The system modal parameters of the modal analysis system of the free vibration response of the present invention include a natural frequency, a mode shape vector, and a damping ratio.
本發明之僅自由振動響應之模態分析方法包含步驟：輸入系統自由振動響應；定義自由振動響應模態分析參數；選擇時間域響應分析模式或頻率域響應分析模式，並依該自由振動響應模態分析參數取得時間域系統自由響應矩陣或頻率域系統自由響應矩陣；選擇比例阻尼自由振動響應模態分析方法或一般阻尼自由振動響應模態分析方法估算系統模態參數。The modal analysis method of the free vibration response of the present invention comprises the steps of: inputting a system free vibration response; defining a free vibration response modal analysis parameter; selecting a time domain response analysis mode or a frequency domain response analysis mode, and according to the free vibration response mode The state analysis parameters obtain the time domain system free response matrix or the frequency domain system free response matrix; the proportional damping free vibration response modal analysis method or the general damping free vibration response modal analysis method is used to estimate the system modal parameters.
本發明僅自由振動響應之模態分析方法之該系統自由振動響應包含理論系統自由振動響應及實驗系統自由振動響應。The system free vibration response of the modal analysis method of the free vibration response of the present invention includes the theoretical system free vibration response and the experimental system free vibration response.
本發明僅自由振動響應之模態分析方法之該理論系統自由振動響應及實驗系統自由振動響應包含位移自由振動響應、速度自 由振動響應及加速度自由振動響應。The free vibration response of the theoretical system and the free vibration response of the experimental system include the displacement free vibration response and the speed from the modal analysis method of the free vibration response of the present invention. Responsive by vibration response and acceleration free vibration.
本發明僅自由振動響應之模態分析方法之該系統模態參數包含自然頻率、模態振型向量及阻尼比。The modal parameter of the modal analysis method of the free vibration response of the present invention includes the natural frequency, the mode shape vector and the damping ratio.
為了充分瞭解本發明，於下文將例舉較佳實施例並配合所附圖式作詳細說明，且其並非用以限定本發明。In order to fully understand the present invention, the preferred embodiments of the present invention are described in detail below and are not intended to limit the invention.
本發明較佳實施例之僅自由振動響應之模態分析方法及其系統用以輸出系統模態參數，其可做為諸多後續應用，例如：模型驗証〔model verification〕、響應預測〔response prediction〕及非破壞試驗〔non－destructive testing〕，關於前述後續應用之技術部分，於此不予詳細贅述。The modal analysis method and system for free vibration response of the preferred embodiment of the present invention are used to output system modal parameters, which can be used for many subsequent applications, such as model verification and response prediction. And the non-destructive testing, the technical part of the aforementioned subsequent application, will not be described in detail herein.
第1A圖揭示本發明較佳實施例之僅自由振動響應之模態分析系統執行時間域自由振動響應模態分析方法之示意圖。第1B圖揭示本發明較佳實施例之僅自由振動響應之模態分析系統執行頻率域自由振動響應模態分析方法之示意圖。FIG. 1A is a schematic diagram showing a time domain free vibration response modal analysis method for a modal analysis system of a free vibration response according to a preferred embodiment of the present invention. FIG. 1B is a schematic diagram showing a method of performing a frequency domain free vibration response modal analysis of a modal analysis system with only free vibration response according to a preferred embodiment of the present invention.
請參照第1A及1B圖所示，本發明較佳實施例僅自由振動響應之模態分析系統僅需輸入系統自由振動響應即可進行估算，以便獲得系統模態參數。該系統自由振動響應包含時間域位移自由振動響應X(t) 及時間域加速度自由振動響應A(t) ，如第1A圖所示；該系統自由振動響應亦包含頻率域位移自由振動響應X(f) 及頻率域加速度自由振動響應A(f) ，如第1B圖所示。該系統模態參數包含自然頻率f r 、模態振型向量φ r 及阻尼比ξ r 。Referring to Figures 1A and 1B, in the preferred embodiment of the present invention, only the free vibration response modal analysis system can be estimated by inputting the system free vibration response to obtain system modal parameters. The free vibration response of the system includes time domain displacement free vibration response X(t) and time domain acceleration free vibration response A(t) , as shown in Fig. 1A; the system free vibration response also includes frequency domain displacement free vibration response X ( f) and the frequency domain acceleration free vibration response A(f) , as shown in Figure 1B. The modal parameters of the system include the natural frequency f r , the mode shape vector φ r and the damping ratio ξ r .
第2圖揭示本發明較佳實施例之僅自由振動響應之模態分析系統之流程方塊圖。請參照第2圖所示，本發明之僅自由振動響 應之模態分析系統包含一理論自由振動響應分析流程單元1、一實驗模態分析流程單元2、一自由振動響應模態分析實驗流程單元3及一自由振動響應模態分析流程單元4。該理論自由振動響應分析流程單元1用以提供數個理論模態參數及數個理論系統自由振動響應。該實驗模態分析流程單元2用以提供數個實驗衝擊振動響應及數個實驗模態參數。該自由振動響應模態分析實驗流程單元3係自該實驗模態分析流程單元2之實驗衝擊振動響應擷取數個實驗系統自由振動響應，並提供至該自由振動響應模態分析流程單元4。該自由振動響應模態分析流程單元4利用該理論系統自由振動響應或該實驗系統自由振動響應估算數個系統模態參數。Figure 2 is a block diagram showing the flow of a modal analysis system with only free vibration response in accordance with a preferred embodiment of the present invention. Please refer to FIG. 2, the only free vibration of the present invention The modal analysis system includes a theoretical free vibration response analysis flow unit 1, an experimental modal analysis flow unit 2, a free vibration response modal analysis experimental flow unit 3, and a free vibration response modal analysis flow unit 4. The theoretical free vibration response analysis process unit 1 is used to provide a plurality of theoretical modal parameters and a plurality of theoretical system free vibration responses. The experimental modal analysis process unit 2 is used to provide several experimental shock vibration responses and several experimental modal parameters. The free vibration response modal analysis experimental flow unit 3 extracts several experimental system free vibration responses from the experimental shock vibration response of the experimental modal analysis flow unit 2, and provides the free vibration response modal analysis flow unit 4. The free vibration response modal analysis flow unit 4 estimates a number of system modal parameters using the theoretical system free vibration response or the experimental system free vibration response.
第3圖揭示僅自由振動響應之模態分析系統執行理論自由振動響應分析之流程圖。理論自由振動響應分析係利用振動學的論點為基礎，由已知的系統參數進而推導出自由振動響應。請參照第3圖所示，執行理論自由振動響應分析之流程如下：首先，設定理論分析程式之系統矩陣：[M][C][K]矩陣；定義系統之自由度；設定暫態分析所需要的參數：時間點數N 1 與取樣頻寬ｆ s ；設定系統之初始條件：初始位移{x 0 }與初始速度{v 0 }；選擇理論自由振動響應分析預測的阻尼類型：理論比例阻尼分析模式或是理論一般化阻尼分析模式；進行模態分析：無論選擇的自由振動響應分析預測的阻尼類型是選擇比例阻尼分析模式或是一般化阻尼分析模式，都可進行模態態分析，以獲得系統之理論模態參數，其包含自然頻率f r 、模態振型{}、阻尼比ξr ； 進行暫態分析：藉由暫態分析可獲得理論之系統自由振動響應，包含位移{x (t )}或是加速度{(t )}；將雜訊程度加入於振動響應中：以MATLAB軟體內建之隨機(random)函數產生隨機數值加入於暫態響應資料中，以模擬雜訊響應；最後，將自由振動響應〔位移{x (t )}或是加速度{(t )}〕輸出，以供後續MAFVRO驗證分析所用。Figure 3 reveals a flow chart for performing a theoretical free vibration response analysis of a modal analysis system with only free vibration response. The theoretical free vibration response analysis is based on the arguments of vibration and the free vibration response is derived from known system parameters. Please refer to Figure 3, the flow of performing theoretical free vibration response analysis is as follows: First, set the system matrix of the theoretical analysis program: [M][C][K] matrix; define the degree of freedom of the system; set the transient analysis Required parameters: time point N 1 and sampling bandwidth f s ; set initial conditions of the system: initial displacement { x 0 } and initial velocity { v 0 }; select the theoretical free vibration response analysis predicted damping type: theoretical proportional damping Analytical mode or theoretical generalized damping analysis mode; modal analysis: whether the selected damping type of the free vibration response analysis is selected by the proportional damping analysis mode or the generalized damping analysis mode, the modal state analysis can be performed to Obtain the theoretical modal parameters of the system, including the natural frequency f r , the mode shape { }, damping ratio ξ r ; Transient analysis: theoretical transient vibration response of the system can be obtained by transient analysis, including displacement { x ( t )} or acceleration { ( t )}; Add the degree of noise to the vibration response: use the random function built in MATLAB software to generate random values to be added to the transient response data to simulate the noise response; finally, the free vibration response [ Displacement { x ( t )} or acceleration { ( t )}] output for subsequent MAFVRO verification analysis.
第4圖揭示本發明較佳實施例之之僅自由振動響應之模態分析系統執行實驗模態分析之流程圖。實驗模態分析係物體在靜止的狀態下，並在已知外力的情形下所做的實驗。請參照第4圖所示，執行實驗模態分析之流程如下：首先架設儀器，並設定實驗儀器擷取數據之參數，其包含時間點數N t 與取樣頻寬f s ；衝擊測試實驗；量測實驗所獲得之衝擊振動響應〔位移{x (t )}或加速度{(t )}〕，將該數據輸出至自由振動響應模態分析實驗流程，以擷取自由振動響應，並提供至自由振動響應模態分析流程，以進行MAFVRO分析所用；實驗模態分析所獲得之衝擊振動響應包含時間或頻率響應函數。將該時間或頻率響應函數透過後處理軟體進行曲線嵌合，以獲得實驗之系統模態參數(、{}、)，並將該系統模態參數輸出，以供後續進行模態參數比較時使用。Figure 4 is a flow chart showing the execution of an experimental modal analysis of a modal analysis system with only free vibration response in accordance with a preferred embodiment of the present invention. Experimental modal analysis is an experiment in which an object is in a stationary state and is known to have an external force. Please refer to Figure 4, the process of performing the experimental modal analysis is as follows: first set up the instrument, and set the parameters of the experimental instrument to retrieve the data, including the time point N t and the sampling bandwidth f s ; impact test experiment; The impact vibration response obtained by the test [displacement { x ( t )} or acceleration { ( t )}], output the data to the free vibration response modal analysis experimental process to extract the free vibration response and provide it to the free vibration response modal analysis process for MAFVRO analysis; experimental modal analysis obtained The shock vibration response includes a time or frequency response function. The time or frequency response function is subjected to curve fitting through the post-processing software to obtain experimental system modal parameters ( , { }, ), and output the system modal parameters for subsequent comparison of modal parameters.
第5圖揭示本發明較佳實施例之僅自由振動響應之模態分析系統執行自由振動響應模態分析實驗之流程圖。MAFVRO實驗係系統在作業的情形中，其系統所受的外力也在未知的情況下，利 用感測元件如位移計或加速度計量測該系統之響應。請參照第5圖所示，MAFVRO實驗之流程如下：首先架設儀器，並設定實驗儀器擷取數據之參數，其包含時間點數N 1 與取樣頻寬f s ；進行實驗；擷取實驗所獲得之自由振動響應〔位移{x (t )}或加速度{(t )}〕，其可由MAFVRO實驗求得系統之自由振動響應或可由實驗模態分析中的衝擊振動響應中擷取系統之自由振動響應；將自由振動響應輸出至自由振動響應模態分析流程，以供後續MAFVRO驗證分析之用。Figure 5 is a flow chart showing the execution of a free vibration response modal analysis experiment of a modal analysis system with only free vibration response in accordance with a preferred embodiment of the present invention. In the case of the MAFVRO experimental system, the external force received by the system is also unknown, and the response of the system is measured by a sensing element such as a displacement meter or an acceleration. Please refer to Figure 5, the flow of the MAFVRO experiment is as follows: first set up the instrument, and set the parameters of the experimental instrument to retrieve the data, including the time point N 1 and the sampling bandwidth f s ; carry out the experiment; Free vibration response [displacement { x ( t )} or acceleration { ( t )}], which can obtain the free vibration response of the system by the MAFVRO experiment or the free vibration response of the system by the shock vibration response in the experimental modal analysis; output the free vibration response to the free vibration response modal analysis process For subsequent MAFVRO verification analysis.
請再參照第2至5圖所示，本發明之僅自由振動響應之模態分析方法利用該理論自由振動響應分析流程單元1、實驗模態分析流程單元2、自由振動響應模態分析實驗流程單元3執行輸入系統自由振動響應。第2圖之區域A顯示該自由振動響應模態分析流程單元4讀取該理論自由振動響應分析流程單元1之自由振動響應；第2圖之區域B顯示該自由振動響應模態分析流程單元4讀取該實驗模態分析流程單元2及自由振動響應模態分析實驗流程單元3之自由振動響應。Referring to Figures 2 to 5 again, the modal analysis method of the free vibration response of the present invention utilizes the theoretical free vibration response analysis flow unit 1, the experimental modal analysis flow unit 2, and the free vibration response modal analysis experimental flow. Unit 3 performs an input system free vibration response. The area A of Fig. 2 shows that the free vibration response modal analysis flow unit 4 reads the free vibration response of the theoretical free vibration response analysis flow unit 1; the area B of Fig. 2 shows the free vibration response modal analysis flow unit 4 The free vibration response of the experimental modal analysis flow unit 2 and the free vibration response modal analysis experimental flow unit 3 is read.
第6圖揭示本發明較佳實施例之僅自由振動響應之模態分析系統執行自由振動響應模態分析方法之流程圖。將對已取得的自由振動響應做進一步的分析，以估算系統之模態參數。請參照第6圖所示，MAFVRO驗證分析之流程如下：首先讀取系統之自由振動響應〔位移{x (t )}或加速度{(t )}〕，其可自理論自由振動響應分析推導求得，或可經由實驗得到自由振動響 應；定義MAFVRO程式分析之參數值，其包含時間域響應資料之分析時間起始點k 、供時間域響應分析使用之資料點數N k 、頻率域響應資料之取樣起始點p 及供頻率域響應分析使用之資料點數N p ；選擇時間域響應分析模式或是頻率域響應分析模式；若選擇時間域響應分析模式時，選擇感測器的型式〔包含位移計及加速度計〕，依據理論響應分析所得到之自由振動響應的型式或實驗所採用的感測器決定感測器的型式，若選用位移計時，提供4種微分方法〔一階後差分法、二階後差分法、一階中央差分法、二階中央差分法〕皆可求得速度及加速度之時間域自由振動響應，若選用加速度計時，提供3種積分方法〔中點法則、梯形法則、辛普森法則〕皆可求得位移及速度之時間域自由振動響應，再依參數值k 、N k 、p 及N p 獲得位移、速度及加速度之時間域自由振動響應矩陣，若選擇頻率域響應分析模式時，選擇感測器的型式〔包含位移計及加速度計〕，依據理論響應分析所得到之自由振動響應的型式或實驗所採用的感測器決定感測器的型式，若選用位移計時，提供二階中央差分法可求得速度及加速度之時間域自由振動響應，若選用加速度計時，提供辛普森法則可求得位移及速度之時間域自由振動響應，再將位移、速度及加速度之時間域自由振動響應轉換成頻率域自由振動響應，再依參數值k 、N k 、p 及N p 獲得位移、速度及加速度之頻率域自由振動響應矩陣；選擇比例阻尼自由振動響應模態分析方法或一般阻尼自由振動響應模態分析方法估算系統模態參數，其包含自然頻率、模態 振型向量{}及阻尼比。Figure 6 is a flow chart showing a method for performing a free vibration response modal analysis of a modal analysis system with only a free vibration response according to a preferred embodiment of the present invention. The free vibration response obtained will be further analyzed to estimate the modal parameters of the system. Please refer to Figure 6, the process of MAFVRO verification analysis is as follows: First read the free vibration response of the system [displacement { x ( t )} or acceleration { ( t )}], which can be derived from the theoretical free vibration response analysis, or can obtain the free vibration response through experiments; define the parameter value of the MAFVRO program analysis, which includes the analysis time starting point k of the time domain response data, for The time domain response analysis uses the data points N k , the sampling start point p of the frequency domain response data, and the data points N p used for the frequency domain response analysis; the time domain response analysis mode or the frequency domain response analysis mode is selected; If the time domain response analysis mode is selected, the type of the sensor (including the displacement meter and the accelerometer) is selected, and the type of the free vibration response obtained by the theoretical response analysis or the sensor used in the experiment determines the type of the sensor. If the displacement timing is selected, four differential methods (first-order post-difference method, second-order post-difference method, first-order central difference method, and second-order central difference method) are provided to obtain the time-domain free vibration response of velocity and acceleration. Acceleration timing, providing three kinds of integral methods (midpoint rule, trapezoidal rule, Simpson's law) can obtain the time domain free vibration of displacement and velocity Dynamic response, and then obtain the time domain free vibration response matrix of displacement, velocity and acceleration according to the parameter values k , N k , p and N p . If the frequency domain response analysis mode is selected, the type of the sensor is selected (including the displacement meter and Accelerometer], the type of free vibration response obtained by theoretical response analysis or the sensor used in the experiment determines the type of sensor. If the displacement timing is selected, the second-order central difference method is used to obtain the time domain of velocity and acceleration. Free vibration response, if the accelerometer is selected, the Simpson's law can be used to obtain the time domain free vibration response of displacement and velocity, and then the time domain free vibration response of displacement, velocity and acceleration is converted into the frequency domain free vibration response, and then according to the parameter value. k , N k , p and N p obtain the frequency domain free vibration response matrix of displacement, velocity and acceleration; select proportional damping free vibration response modal analysis method or general damping free vibration response modal analysis method to estimate system modal parameters, Contains natural frequencies Modal mode vector } and damping ratio .
前述較佳實施例僅舉例說明本發明及其技術特徵，該實施例之技術仍可適當進行各種實質等效修飾及/或替換方式予以實施；因此，本發明之權利範圍須視後附申請專利範圍所界定之範圍為準。The foregoing preferred embodiments are merely illustrative of the invention and the technical features thereof, and the techniques of the embodiments can be carried out with various substantial equivalent modifications and/or alternatives; therefore, the scope of the invention is subject to the appended claims. The scope defined by the scope shall prevail.
1‧‧‧理論自由振動響應分析流程單元1‧‧‧ Theoretical Free Vibration Response Analysis Process Unit
2‧‧‧實驗模態分析流程單元2‧‧‧Experimental modal analysis process unit
3‧‧‧自由振動響應模態分析實驗流程單元3‧‧‧ Free vibration response modal analysis experimental process unit
4‧‧‧自由振動響應模態分析流程單元4‧‧‧ Free vibration response modal analysis process unit
A‧‧‧區域A‧‧‧ area
B‧‧‧區域B‧‧‧Area
第1A圖：本發明較佳實施例之僅自由振動響應之模態分析系統執行時間域自由振動響應模態分析方法之示意圖。FIG. 1A is a schematic diagram of a time domain free vibration response modal analysis method performed by a modal analysis system of a free vibration response according to a preferred embodiment of the present invention.
第1B圖：本發明較佳實施例之僅自由振動響應之模態分析系統執行頻率域自由振動響應模態分析方法之示意圖。FIG. 1B is a schematic diagram showing a frequency domain free vibration response modal analysis method performed by a modal analysis system of a free vibration response according to a preferred embodiment of the present invention.
第2圖：本發明較佳實施例之僅自由振動響應之模態分析系統之流程方塊圖。Figure 2 is a flow block diagram of a modal analysis system for free vibration response in accordance with a preferred embodiment of the present invention.
第3圖：本發明較佳實施例之僅自由振動響應之模態分析系統執行理論自由振動響應分析之流程圖。Figure 3 is a flow chart showing the theoretical free vibration response analysis of the modal analysis system of the free vibration response of the preferred embodiment of the present invention.
第4圖：本發明較佳實施例之僅自由振動響應之模態分析系統執行實驗模態分析之流程圖。Figure 4 is a flow chart showing the experimental modal analysis performed by the modal analysis system of the free vibration response of the preferred embodiment of the present invention.
第5圖：本發明較佳實施例之僅自由振動響應之模態分析系統執行自由振動響應模態分析實驗之流程圖。Fig. 5 is a flow chart showing a free vibration response modal analysis experiment performed by a modal analysis system of a free vibration response according to a preferred embodiment of the present invention.
第6圖：本發明較佳實施例之僅自由振動響應之模態分析系統執行自由振動響應模態分析方法之流程圖。Fig. 6 is a flow chart showing a method of performing a free vibration response modal analysis of a modal analysis system of a free vibration response according to a preferred embodiment of the present invention.
1‧‧‧理論自由振動響應分析流程單元1‧‧‧ Theoretical Free Vibration Response Analysis Process Unit
2‧‧‧實驗模態分析流程單元2‧‧‧Experimental modal analysis process unit
3‧‧‧自由振動響應模態分析實驗流程單元3‧‧‧ Free vibration response modal analysis experimental process unit
4‧‧‧自由振動響應模態分析流程單元4‧‧‧ Free vibration response modal analysis process unit
A‧‧‧區域A‧‧‧ area
B‧‧‧區域B‧‧‧Area
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| TW200831893A (en) * | 2007-01-25 | 2008-08-01 | Pei-Ling Liu | The combined spectrum impact echo method |
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| CN100409233C (en) * | 2006-04-10 | 2008-08-06 | 西安交通大学 | Mode parameter recognition method based on experience mode decomposition and Laplace wavelet |
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