Method and device for calculating inherent frequency of longitudinal vibration of rod piece, medium and equipment

Abstract

The invention discloses a method and a device for calculating inherent frequency of longitudinal vibration of a rod piece, a medium and equipment. The method comprises the following steps: judging whether the rod piece is of a uniform section type or a section step change type; if the type is the uniform section type, calculating the equivalent mass of the current micro-unit at the concentrated mass applying point according to a first equivalent mass calculation mode; if yes, the equivalent mass of the current micro-unit at the concentrated mass applying point is calculated according to a second equivalent mass calculation mode; calculating micro-unit inertia force according to the equivalent mass and integrating the micro-unit inertia force to obtain the equivalent mass; and calculating the inherent frequency of longitudinal vibration of the rod piece. According to the method, when the equivalent mass is calculated, integration is carried out on micro-unit inertia force applied to a concentrated mass point, and different from integration carried out on kinetic energy through a vibration kinetic energy method in the prior art, kinetic energy integration of all points is not equal to mass center kinetic energy and concentrated mass point kinetic energy; therefore, the equivalent mass obtained by integrating the inertia force of the micro-unit is more accurate.

Description

Technical Field

[0001] The present invention relates to the technical field of mechanical vibration, and in particular to a method, device, medium and equipment for calculating the natural frequency of longitudinal vibration of a rod. Background Art

[0002] The natural frequency refers to the specific frequency determined only by the nature of the system itself when the structural system is stimulated by external forces to produce motion. In forced vibration, when the excitation frequency is equal to or close to the natural frequency of the vibrating body, resonance may occur and the amplitude is greatly amplified. The purpose of calculating the natural frequency is to understand at what frequency the vibrating body will resonate, so as to avoid or promote the occurrence of resonance, reduce the harm of resonance or use resonance to benefit mankind.

[0003] However, the current vibration mechanics is a "science" full of errors. Although the forced vibration equation based on spring oscillators and concentrated masses and its solutions as well as the formula for calculating the natural frequency are correct, there are a lot of errors in its application to rigid bodies (or "elastic bodies") (i.e., calculating the natural frequency). Even the natural frequencies of the same object obtained by different branches of theory cannot remain equal.

[0004] Therefore, there is an urgent need for a method, device, medium and equipment for calculating the natural frequency of longitudinal vibration of a rod to solve the above technical problems. Summary of the invention

[0005] The present invention aims to solve the above technical problem, that is, to solve the problem that errors occur in the existing calculation of the natural frequency of the longitudinal vibration of the rod, and even the natural frequencies obtained by different branches of the theory for the same object cannot remain equal, which makes users confused and brings great confusion.

[0006] To this end, in a first aspect, the present invention provides a method for calculating the natural frequency of longitudinal vibration of a rod, comprising the following steps:

[0007] Determine whether the rod is of a uniform cross-section type or a cross-section step-change type, wherein the uniform cross-section type means that the cross-section area of ​​the entire section of the rod is equal, and the cross-section step-change type means that there are at least two sections with different cross-section area sizes and the cross-section area of ​​each section remains consistent;

[0008] If the rod type is a constant cross-section type, the equivalent mass of the current micro-unit at the concentrated mass application point is calculated according to the first equivalent mass calculation mode;

[0009] If the rod type is a cross-section step-change type, the equivalent mass of the current micro-unit at the concentrated mass application point is calculated according to the second equivalent mass calculation mode;

[0010] Calculate the micro-unit inertial force applied to the concentrated mass application point according to the calculated equivalent mass;

[0011] Integrating the inertial force of the micro-unit to obtain the equivalent mass of the entire rod;

[0012] The equivalent stiffness coefficient of the entire rod is calculated, and the natural frequency of the longitudinal vibration of the rod is calculated according to the equivalent mass and the equivalent stiffness coefficient, wherein the formula for calculating the natural frequency is as follows:

[0013]

[0014] Where f0 is the natural frequency; m eq is the equivalent mass; K eq is the equivalent stiffness coefficient.

[0015] In a specific implementation of the above method for calculating the natural frequency of longitudinal vibration of a rod, the rod type is a constant cross-section type, and the first equivalent mass calculation mode includes:

[0016] The equivalent mass of the current micro-element at the concentrated mass application point is calculated according to the following formula:

[0017] dM=dm=ρ·A·dξ

[0018] Among them, dM is the equivalent mass; dm is the actual mass of the current micro unit; dξ is the current micro unit; ρ is the density of the rod; A is the cross-sectional area of ​​the rod.

[0019] In a specific implementation of the above-mentioned method for calculating the natural frequency of longitudinal vibration of a rod, when the rod type is a constant cross-section type, the step of "calculating the micro-unit inertia force applied to the concentrated mass application point according to the equivalent mass obtained by calculation" specifically includes:

[0020] Calculate the vibration acceleration of the current point ξ according to the following formula:

[0021]

[0022] in, is the vibration acceleration of the current point ξ; l is the overall length of the rod; is the vibration acceleration at ξ=l;

[0023] The micro-unit inertial force is calculated according to the following formula:

[0024]

[0025] Where d is the micro-unit inertial force generated by the equivalent mass dM.

[0026] In a specific implementation of the method for calculating the natural frequency of longitudinal vibration of the rod, when the rod type is a constant cross-section type, the step of "integrating the inertial force of the micro-unit to obtain the equivalent mass of the entire rod" specifically includes:

[0027] The micro-unit inertial force is integrated to obtain the total inertial force applied to the concentrated mass application point, and the integral formula is:

[0028]

[0029] Among them, F0 is the total inertia force;

[0030] The total inertial force of the concentrated mass at the point where the concentrated mass is applied is calculated using the following formula:

[0031]

[0032] Where, M is the concentrated mass;

[0033] Will Substitute into the formula In, and according to m eq =Conversion, the final equivalent mass is:

[0034]

[0035] Among them, m eq is equivalent mass.

[0036] In a specific implementation of the above method for calculating the natural frequency of longitudinal vibration of a rod, the rod type is a cross-section step-change type, and the second equivalent mass calculation mode includes:

[0037] Determining the number of sections having different cross-sectional areas on the rod;

[0038] The equivalent mass of the concentrated mass application point of the current micro-element on the i-th segment of the rod is calculated according to the following calculation formula:

[0039] dM i =m i =·A i ·ξ i

[0040] Among them, dM i is the equivalent mass of the i-th segment; dm i is the actual mass of the current micro-unit in the i-th segment; dξ i is the current micro-unit of the i-th segment; ρ is the density; A i is the cross-sectional area of ​​the i-th section; i=1, 2, 3..., n is the total number of sections.

[0041] In a specific implementation of the method for calculating the natural frequency of longitudinal vibration of the rod, when the rod type is a cross-sectional step-change type, the step of "calculating the micro-unit inertia force applied to the concentrated mass application point according to the equivalent mass obtained by calculation" specifically includes:

[0042] The vibration acceleration of the current point ξ1 on the i=1th segment of the rod is calculated according to the following formula:

[0043]

[0044] in, is the vibration acceleration of the current point ξ1; l1 is the length of the first section of the rod; is the vibration acceleration of the end of the first section of the rod relative to the origin of the first section coordinates; the origin of the first section coordinates refers to the first section fixed point of the rod;

[0045] Calculate the current point ξ of the i-th section on the member according to the following formula i Vibration acceleration:

[0046]

[0047] Wherein, i = 2, 3..., n is the total number of segments; is the current point ξ of the i-th segment on the member i The vibration acceleration of the current point ξ i The coordinate origin is the starting point of the i-th segment; is the vibration acceleration of the end of the i-1th segment on the rod relative to the starting point of the i-1th segment; is the current point ξ of the i-th segment on the member i Vibration acceleration relative to the starting point of the i-th segment;

[0048] The micro-unit inertial force is calculated according to the following formula:

[0049]

[0050] Among them, dF i is the equivalent mass of the i-th section of the rod dM i The micro-unit inertial force generated.

[0051] In a specific implementation of the above-mentioned method for calculating the natural frequency of longitudinal vibration of a rod, when the type of the rod is a type of step-change in cross section, the step of "integrating the inertial force of the micro-unit to obtain the equivalent mass of the entire rod" specifically includes:

[0052] The micro-unit inertial force on each section of the rod is integrated to obtain the total inertial force applied at the concentrated mass application point, and the integral formula is as follows:

[0053]

[0054] Where F0 is the total inertia force; l2 is the length of the second section of the rod; l n is the length of the nth section of the rod;

[0055] The total inertial force of the concentrated mass at the point where the concentrated mass is applied is calculated as follows:

[0056]

[0057] Where, M is the concentrated mass; is the vibration acceleration of the rod at ξ = l; is the vibration acceleration of the end of the nth segment on the rod relative to the starting point of the nth segment;

[0058] Will Substitute into the formula In, and according to m eq =Conversion, the final equivalent mass is:

[0059]

[0060] Among them, m eq is equivalent mass.

[0061] In a second aspect, the present invention further provides a device for calculating the natural frequency of longitudinal vibration of a rod, comprising:

[0062] A first processing unit is used to determine whether the rod is of a uniform cross-section type or a cross-section step-variation type, wherein the uniform cross-section type means that the cross-section area of ​​the entire section of the rod is equal, and the cross-section step-variation type means that the rod has at least two sections with different cross-section area sizes;

[0063] A second processing unit is used to calculate the equivalent mass of the current micro-unit at the concentrated mass application point;

[0064] A third processing unit is used to calculate the micro-unit inertial force applied to the concentrated mass application point according to the equivalent mass obtained by calculation;

[0065] A fourth processing unit, used for integrating the inertial force of the micro-unit to obtain the equivalent mass of the entire rod;

[0066] The fifth processing unit is used to calculate the equivalent stiffness coefficient of the entire rod, and calculate the natural frequency of the longitudinal vibration of the rod according to the equivalent mass and the equivalent stiffness coefficient.

[0067] In a third aspect, the present invention further provides a computer storage medium having a computer program stored thereon, wherein when the computer program is executed by a processor, the method for calculating the natural frequency of longitudinal vibration of a rod member described in any one of the first aspects can be implemented.

[0068] In a fourth aspect, the present invention further provides a computer device comprising a memory, a processor, and a computer program stored in the memory and executable on the processor, wherein when the processor executes the computer program, the method for calculating the natural frequency of the longitudinal vibration of a rod member described in any one of the first aspects is implemented.

[0069] Compared with the prior art, the present invention has the following beneficial effects:

[0070] When calculating the equivalent mass, the present invention integrates the micro-unit inertial force applied to the concentrated mass point, which is different from the vibration dynamics energy method in the prior art that integrates the kinetic energy. Since the integral of the kinetic energy of each point is not equal to the kinetic energy of the center of mass, let alone the kinetic energy of the concentrated mass point, the equivalent mass obtained by integrating the micro-unit inertial force in the present invention is more accurate, that is, the calculated natural frequency value is more accurate. In addition, the present invention is divided into a constant cross-section type and a cross-section step change type according to whether the cross-sectional area of ​​the rod is equal, and the equivalent mass is calculated according to different types according to different equivalent mass calculation modes, thereby improving the calculation accuracy of the equivalent mass, and further improving the calculation accuracy of the natural frequency. BRIEF DESCRIPTION OF THE DRAWINGS

[0071] The preferred embodiments of the present invention are described below in conjunction with the accompanying drawings, in which:

[0072] Figure 1 It is a flow chart of the steps of the method for calculating the natural frequency of the longitudinal vibration of the rod provided by the present invention. DETAILED DESCRIPTION

[0073] In order to make the purpose, technical solution and advantages of the present invention clearer, the technical solution of the present invention will be clearly and completely described below in conjunction with the accompanying drawings. Obviously, the described embodiments are part of the embodiments of the present invention, not all of the embodiments. Based on the embodiments of the present invention, all other embodiments obtained by ordinary technicians in this field without making creative work are within the scope of protection of the present invention.

[0074] In the description of the present invention, it should be noted that the terms "upper", "lower", "inner", "outer", etc., indicating the orientation or positional relationship, are based on the orientation or positional relationship shown in the drawings, and are only for the convenience of describing the present invention and simplifying the description, rather than indicating or implying that the system or element referred to must have a specific orientation, be constructed and operated in a specific orientation, and therefore cannot be understood as limiting the present invention. In addition, the terms "first", "second", etc., are used to define components, only for the convenience of distinguishing the above components, and unless otherwise stated, the above terms have no special meanings and cannot be understood as indicating or implying relative importance.

[0075] In the description of the present invention, it should be noted that, unless otherwise clearly specified and limited, the terms "installation", "setting", and "connection" should be understood in a broad sense, for example, it can be a fixed connection, a detachable connection, or an integral connection; it can be a mechanical connection or an electrical connection; it can be a direct connection, or it can be an indirect connection through an intermediate medium, or it can be the internal communication of two components. For ordinary technicians in this field, the specific meanings of the above terms in the present invention can be understood according to specific circumstances.

[0076] The present invention relates to the field of mechanical vibration technology, and in particular to a method, device, medium and equipment for calculating the natural frequency of longitudinal vibration of a rod. The purpose is to solve the problem that errors occur when calculating the natural frequency of longitudinal vibration of a rod, and even the natural frequencies obtained by different branches of the theory of the same object cannot be kept equal, which makes the user confused and brings great confusion. To this end, the method for calculating the natural frequency of longitudinal vibration of a rod provided by the present invention is characterized in that it includes the following steps: judging whether the rod is a uniform cross-section type or a step-change cross-section type, wherein the uniform cross-section type means that the cross-sectional area of ​​the entire section of the rod is equal, and the step-change cross-section type means that the cross-sectional area of ​​the rod has at least two sections with different cross-sectional area sizes; if the rod type is a uniform cross-section type, the equivalent mass of the current micro-unit at the concentrated mass application point is calculated according to the first equivalent mass calculation mode; if the rod type is a step-change cross-section type, the equivalent mass of the current micro-unit at the concentrated mass application point is calculated according to the second equivalent mass calculation mode; according to the calculated equivalent mass, the inertia force applied to the concentrated mass application point is calculated; the inertia force of the micro-unit is integrated to obtain the equivalent mass; the rod is calculated. The present invention integrates the micro-unit inertial force applied to the concentrated mass point when calculating the equivalent mass, which is different from the vibration dynamics energy method in the prior art that integrates the kinetic energy. Since the integral kinetic energy of each point is not equal to the kinetic energy of the center of mass, let alone the kinetic energy of the concentrated mass point, the equivalent mass obtained by integrating the micro-unit inertial force is more accurate, that is, the calculated natural frequency value is more accurate. In addition, the present invention divides the rod into an equal-section type and a step-change section type according to whether the cross-sectional area of ​​the rod is equal, and performs equivalent mass calculation according to different equivalent mass calculation modes according to different types, thereby improving the calculation accuracy of the equivalent mass, and further improving the calculation accuracy of the natural frequency.

[0077] The following is a detailed description of the method, device, medium and equipment for calculating the natural frequency of longitudinal vibration of a rod provided by an embodiment of the present invention in conjunction with the accompanying drawings.

[0078] See also Figure 1 The present invention provides a method for calculating the natural frequency of longitudinal vibration of a rod, comprising the following steps:

[0079] S1, determining whether the rod is of a uniform cross-section type or a cross-section step-change type, wherein the uniform cross-section type means that the cross-section area of ​​the entire section of the rod is equal, and the cross-section step-change type means that there are at least two sections with different cross-section area sizes and the cross-section area of ​​each section of the rod remains consistent;

[0080] S2, if the rod type is a uniform cross-section type, the equivalent mass of the current micro-element at the concentrated mass application point is calculated according to the first equivalent mass calculation mode;

[0081] S3, if the rod type is a cross-section step change type, the equivalent mass of the current micro-unit at the concentrated mass application point is calculated according to the second equivalent mass calculation mode;

[0082] S4, calculating the micro-unit inertial force applied to the concentrated mass application point according to the calculated equivalent mass;

[0083] S5, integrate the inertial force of the micro-element to obtain the equivalent mass of the entire rod;

[0084] S6, calculate the equivalent stiffness coefficient of the entire rod, and calculate the natural frequency of the longitudinal vibration of the rod according to the equivalent mass and the equivalent stiffness coefficient according to the following formula:

[0085]

[0086] Where f0 is the natural frequency; m eq is the equivalent mass; K eq It is the equivalent stiffness coefficient, such as series or parallel components, or the equivalent stiffness coefficient of the whole after multiple components are synthesized.

[0087] It should be noted that the rods in this application are all homogeneous rods, that is, the density and elastic modulus of the rods as a whole are equal. In addition, regarding the order of calculating the equivalent stiffness coefficient, although the equivalent stiffness coefficient of the rod is calculated in step S6, this is only an example, and the equivalent stiffness coefficient can also be calculated before calculating the equivalent mass. Of course, the equivalent stiffness coefficient and the equivalent mass can also be calculated at the same time, which are all within the scope of protection of this application. In addition, the longitudinal vibration of the rod refers to the vibration of the rod in the length direction, that is, the vibration in the x-axis direction.

[0088] Specifically, when the member type is a uniform cross-section type, the step of "calculating the equivalent stiffness coefficient of the entire member" specifically includes:

[0089] The equivalent stiffness coefficient of the entire member is calculated according to the following formula:

[0090]

[0091] Where E is the elastic modulus.

[0092] When the member type is a step-change type, the steps of "calculating the equivalent stiffness coefficient of the entire member" include:

[0093] If a rod is composed of n sections connected in series, the total stiffness coefficient K after series connection is equal to the stiffness coefficient K of each section of the rod. i The relationship between (i=1, 2, ....., n) is a reciprocal superposition relationship, that is:

[0094]

[0095] The total stiffness coefficient K after synthesis is:

[0096]

[0097] Since the n-segment rod is a series structure, the total stiffness coefficient K after synthesis is the equivalent stiffness coefficient K eq , that is, the formula is as follows:

[0098]

[0099] In addition, in this application, since this application calculates the natural frequency of the longitudinal vibration of the rod, the point of application of the inertial force is independent of the deformation, so the mass of the current point is the same as the mass effect of the concentrated mass application point, that is, the equivalent mass is equal to the actual mass.

[0100] The calculation of equivalent mass and natural frequency of the rod with uniform cross-section is described in detail below.

[0101] In one embodiment, in step S2, the first equivalent mass calculation mode includes:

[0102] The equivalent mass of the current micro-element at the concentrated mass application point is calculated according to the following formula:

[0103] dM=dm=ρ·A·dξ

[0104] Among them, dM is the equivalent mass; dm is the actual mass of the current micro unit; dξ is the current micro unit; ρ is the density of the rod; A is the cross-sectional area of ​​the rod.

[0105] In one embodiment, when the rod type is a constant cross-section type, step S4 of "calculating the micro-unit inertial force applied to the concentrated mass application point according to the calculated equivalent mass" specifically includes:

[0106] Calculate the vibration acceleration of the current point ξ according to the following formula:

[0107]

[0108] in, is the vibration acceleration of the current point ξ; l is the overall length of the rod; is the vibration acceleration at ξ=l;

[0109] The micro-unit inertial force is calculated according to the following formula:

[0110]

[0111] Where d is the micro-unit inertial force generated by the equivalent mass dM.

[0112] The specific origin of the vibration acceleration of the current point ξ is: the deformation of the rod at ξ is represented by x, and its linear strain is equal to a constant under the condition of constant external force, that is, x = C·ξ, where C is a constant; if the deformation at ξ = l is assumed to be x0, then x = ξ·x0 / . Correspondingly, if the vibration acceleration at ξ = l is set to The vibration acceleration at point ξ is

[0113]

[0114] In one embodiment, when the rod type is a constant cross-section type, step S5 of "integrating the micro-unit inertial force to obtain the equivalent mass of the entire rod" specifically includes:

[0115] The inertial force of the micro-unit is integrated to obtain the total inertial force applied at the concentrated mass application point. The integral formula is:

[0116]

[0117] Among them, F0 is the total inertia force;

[0118] The total inertial force of the concentrated mass at the point where the concentrated mass is applied is calculated using the following formula:

[0119]

[0120] Where, M is the concentrated mass;

[0121] Will Substitute into the formula In, and according to m eq =Conversion, the final equivalent mass is:

[0122]

[0123] Among them, m eq is equivalent mass.

[0124] From the equivalent mass calculated above, it can be seen that when the member type is a constant cross-section type, the equivalent mass is half of the actual mass.

[0125] When the member type is a uniform cross-section type, the equivalent mass calculated above and the stiffness coefficient of the entire member are substituted into the calculation formula of the natural frequency, and the natural frequency is obtained as follows:

[0126]

[0127] The following is a detailed explanation of the calculation of equivalent mass and natural frequency for rods with step-change cross-sections.

[0128] In one embodiment, in step S3, the second equivalent mass calculation mode includes:

[0129] Determine the number of sections with different cross-sectional areas on the rod; the cross-sectional area of ​​each section of the rod is equal, and the sections are numbered according to the cross-sectional area starting from the fixed point of the rod;

[0130] The equivalent mass of the concentrated mass application point of the current micro-element on the i-th segment of the rod is calculated according to the following calculation formula:

[0131] dM i =m i =·A i ·ξ i

[0132] Among them, dM i is the equivalent mass of the i-th segment; dm i is the actual mass of the current micro-unit in the i-th segment; dξ i is the current micro-unit of the i-th segment; ρ is the density; A i is the cross-sectional area of ​​the i-th section; i=1, 2, 3..., n is the total number of sections.

[0133] In one embodiment, when the rod type is a cross-section step-change type, step S4 of "calculating the micro-unit inertial force applied to the concentrated mass application point according to the calculated equivalent mass" specifically includes:

[0134] The vibration acceleration of the current point ξ1 on the i=1th segment of the rod is calculated according to the following formula:

[0135]

[0136] in, is the vibration acceleration of the current point ξ1; l1 is the length of the first section of the rod; is the vibration acceleration of the end of the first section of the rod relative to the origin of the first section coordinates; the origin of the first section coordinates refers to the first section fixed point of the rod;

[0137] The current point ξ of the i-th section on the member is calculated according to the following formula i Vibration acceleration:

[0138]

[0139] Wherein, i = 2, 3..., n is the total number of segments; is the current point ξ of the i-th segment on the member i The vibration acceleration of the current point ξ i The coordinate origin is the starting point of the i-th segment; is the vibration acceleration of the end of the i-1th segment on the rod relative to the starting point of the i-1th segment; is the current point ξ of the i-th segment on the member i Vibration acceleration relative to the starting point of the i-th segment;

[0140] The micro-unit inertial force is calculated according to the following formula:

[0141]

[0142] Among them, dF i is the equivalent mass of the i-th section of the rod dM i The micro-unit inertial force generated.

[0143] Specifically, if it is assumed that the number of sections with cross-sectional area changes is n, the length of the first section is l1 and the area is A1; the length of the second section is l2 and the area is A2; the length of the nth section is l n , area A n ;Total length l=l1+2+....+l n The n-segment rod is respectively represented by n coordinates ξ1, ξ2, ... n Indicates that, the origin of the coordinates of ξ1 is at the fixed point of the first section of the rod, the origin of the coordinates of ξ2 is at the starting point of the second section of the rod (i.e., the end of the first section), and ξ n The coordinate origin is at the starting point of the nth section of the rod.

[0144] Let the deformation of the first section ξ1 of the rod be x1, the deformation of the second section ξ2 be x2, and the deformation of the nth section ξ n Point deformation is x n When a force F is applied to the end of the rod (F can be tension or compression, usually an alternating force, tension and compression alternating), the deformation of the first segment ξ1 point is x1 = ·ξ1 / (E·A1), and the deformation of the end is x 10 =·l1 / (E·A1), x1= 10 ·1 / 1. The deformation x of the second segment ξ2 point relative to the ξ2 coordinate origin 2相对 =·ξ2 / (E·A2), its end deformation x 20 =·l2 / (E·A2),x 2相对 = 20 ·2 / 2, then it corresponds to the absolute deformation x2 of the fixed position of the rod = 10+ 2相对 . Section n ξ n Point relative to ξ n Deformation of the origin x n相对 =·ξ n / (E·A n ), whose end is deformed by x n0 = l n / (E·A n ),

[0145] x n相对 = n0 · n / n , then it corresponds to the absolute deformation of the fixed position of the rod

[0146] x n = 10 + 20 +....+x n相对 , for a rod divided into n segments, the absolute deformation at the end of the rod is

[0147] x0= 10 + 20 +.....+x n0 .

[0148] For x1, x2 and x n Taking the second-order derivative, we can get the corresponding vibration acceleration and If the vibration acceleration at the end of the first section of the rod is The vibration acceleration at the end of the second section is The vibration acceleration of the second section ξ2 point of the rod relative to the ξ2 coordinate origin is: Vibration acceleration and They are:

[0149]

[0150] From this, the current point ξ of the i-th section on the rod can be calculated i Vibration acceleration, i=1, 2, 3...n.

[0151] In the case where the rod type is a cross-section step-change type, step S5 of "integrating the micro-element inertial force to obtain the equivalent mass" specifically includes:

[0152] The inertial force of the micro-element on each segment of the rod is integrated to obtain the total inertial force applied at the concentrated mass application point. The integral formula is as follows:

[0153]

[0154] Where F0 is the total inertia force; l2 is the length of the second section of the rod; l n is the length of the nth section of the rod;

[0155] The total inertial force of the concentrated mass at the point where the concentrated mass is applied is calculated as follows:

[0156]

[0157] Where, M is the concentrated mass; is the total vibration acceleration at the end of the entire rod at ξ = l; is the vibration acceleration of the end of the nth segment on the rod relative to the starting point of the nth segment;

[0158] Will Substitute into the formula In, and according to m eq =Conversion, the final equivalent mass is:

[0159]

[0160] Among them, m eq is equivalent mass.

[0161] When calculating the equivalent mass, the present invention integrates the micro-unit inertial force applied to the concentrated mass point, which is different from the vibration dynamics energy method in the prior art that integrates the kinetic energy. Since the integral of the kinetic energy of each point is not equal to the kinetic energy of the center of mass, let alone the kinetic energy of the concentrated mass point, the equivalent mass obtained by integrating the micro-unit inertial force in the present invention is more accurate, that is, the calculated natural frequency value is more accurate.

[0162] The calculation of equivalent mass and natural frequency is described in detail below by taking the cross-section step change number n=2 as an example.

[0163] The length of the first section is l1, and the area is A1; the length of the second section is l2, and the area is A2, and the total length l = l1 + 2. The two sections of the rod are represented by two coordinates ξ1 and ξ2 in the same direction and on the same axis, where the origin of the coordinate of ξ1 is at the fixed point of the first section of the rod, and the origin of the coordinate of ξ2 is at the end of the first section of the rod (i.e. the starting point of the second section).

[0164] about The calculation formula is as follows:

[0165]

[0166] Therefore, the inertial force of the micro-unit on each section of the rod is integrated to obtain the total inertial force applied to the concentrated mass application point:

[0167]

[0168] And because, It can be concluded from this Substituting this formula into the above total inertia force calculation formula yields:

[0169]

[0170] However, the inertial force F0 can be expressed as:

[0171]

[0172] By comparing the two total inertial forces, the equivalent mass can be obtained as:

[0173]

[0174] The stiffness coefficients of the two rods are K1 = ·A1 / 1 and K2 = ·A2 / 2 respectively; the stiffness of the two rods belongs to a series structure, and the equivalent stiffness coefficient after series connection is

[0175] K eq =1·2 / (K1+2)=·A1·2 / (A1·2+2·1)

[0176] Substituting the equivalent mass and equivalent stiffness coefficient of the rod into the natural frequency calculation formula, the natural frequency can be obtained as follows:

[0177]

[0178] The present invention is divided into two types: equal cross-section type and cross-section step change type according to whether the cross-sectional areas of the rods are equal. The equivalent mass is calculated according to different equivalent mass calculation modes according to different types, thereby improving the calculation accuracy of the equivalent mass and further improving the calculation accuracy of the natural frequency.

[0179] In another embodiment, the present application also provides a device for calculating the natural frequency of the longitudinal vibration of a rod member that implements the method for calculating the natural frequency of the longitudinal vibration of a rod member provided in the various embodiments described above. The natural frequency calculation device can be implemented by software, hardware, or a combination of software and hardware. For example, the natural frequency calculation device can include integrated or separate functional modules or functional units to execute the corresponding steps in the methods of the various embodiments described above. Since the device for calculating the natural frequency of the longitudinal vibration of a rod member provided in the present application is basically similar to the method embodiment, the process described in this embodiment is relatively simple. For relevant matters, please refer to the partial description of the above method embodiment. The device for calculating the natural frequency of the longitudinal vibration of a rod member in this embodiment is merely schematic.

[0180] This embodiment also provides a device for calculating the natural frequency of longitudinal vibration of a rod, comprising:

[0181] A first processing unit is used to determine whether the rod is of a uniform cross-section type or a cross-section step-variation type, wherein the uniform cross-section type means that the cross-section area of ​​the entire section of the rod is equal, and the cross-section step-variation type means that the rod has at least two sections with different cross-section area sizes;

[0182] A second processing unit is used to calculate the equivalent mass of the current micro-unit at the concentrated mass application point;

[0183] A third processing unit is used to calculate the micro-unit inertial force applied to the concentrated mass application point according to the equivalent mass obtained by calculation;

[0184] A fourth processing unit, used for integrating the inertial force of the micro-unit to obtain the equivalent mass of the entire rod;

[0185] The fifth processing unit is used to calculate the equivalent stiffness coefficient of the entire rod, and calculate the natural frequency of the longitudinal vibration of the rod according to the equivalent mass and the equivalent stiffness coefficient.

[0186] In another embodiment, the present application also provides a processing device for implementing the method for calculating the natural frequency of the longitudinal vibration of the rod provided in the above-mentioned various embodiments. The processing device can be a processing device for a client, such as a mobile phone, a laptop computer, a tablet computer, a desktop computer, etc., to execute the method of the above-mentioned embodiment.

[0187] The processing device includes a processor, a memory, a communication interface and a bus, and the processor, the memory and the communication interface are connected through the bus to complete mutual communication. The memory stores a computer program that can be run on the processor, and the processor executes the calculation method of the adhesion force between hydrate particles provided by the above various embodiments when running the computer program.

[0188] Preferably, the memory may be a high-speed random access memory (RAM), and may also include a non-volatile memory, such as at least one disk memory.

[0189] Preferably, the processor may be a central processing unit (CPU), a digital signal processor (DSP) or other general-purpose processors of various types, which are not limited here.

[0190] In another embodiment, the present invention also provides that the method for calculating the natural frequency of the longitudinal vibration of the rod described in the above various embodiments can be specifically implemented as a computer program product, and the computer program product may include a computer-readable storage medium carrying computer-readable program instructions for executing the methods described in the above various embodiments.

[0191] Computer readable storage media can be tangible devices that hold and store instructions used by instruction execution devices. Computer readable storage media can be, for example, but not limited to, electronic storage devices, magnetic storage devices, optical storage devices, electromagnetic storage devices, semiconductor storage devices, or any combination thereof.

[0192] Finally, it should be noted that the above embodiments are only used to illustrate the technical solutions of the present invention, rather than to limit it. Although the present invention has been described in detail with reference to the aforementioned embodiments, those skilled in the art should understand that they can still modify the technical solutions described in the aforementioned embodiments, or make equivalent replacements for some of the technical features therein. However, these modifications or replacements do not cause the essence of the corresponding technical solutions to deviate from the protection scope of the technical solutions of the embodiments of the present invention.

Claims

1. A method for calculating the natural frequency of longitudinal vibration of a rod, characterized in that: The following steps are involved: Determine whether the rod is of a uniform cross-section type or a cross-section step-change type, wherein the uniform cross-section type means that the cross-section area of ​​the entire section of the rod is equal, and the cross-section step-change type means that the rod has at least two sections with different cross-section area sizes; If the rod type is a constant cross-section type, the equivalent mass of the current micro-unit at the concentrated mass application point is calculated according to the first equivalent mass calculation mode; If the rod type is a cross-section step-change type, the equivalent mass of the current micro-unit at the concentrated mass application point is calculated according to the second equivalent mass calculation mode; Calculate the micro-unit inertial force applied to the concentrated mass application point according to the calculated equivalent mass; Integrating the inertial force of the micro-unit to obtain the equivalent mass of the entire rod; The equivalent stiffness coefficient of the entire rod is calculated, and the natural frequency of the longitudinal vibration of the rod is calculated according to the equivalent mass and the equivalent stiffness coefficient.

2. The method for calculating the natural frequency of longitudinal vibration of a rod according to claim 1, characterized in that: The rod type is a constant cross-section type, and the first equivalent mass calculation mode includes: The equivalent mass of the current micro-element at the concentrated mass application point is calculated according to the following formula: dM=dm=ρ·A·dξ Among them, dM is the equivalent mass; dm is the actual mass of the current micro unit; dξ is the current micro unit; ρ is the density of the rod; A is the cross-sectional area of ​​the rod.

3. The method for calculating the natural frequency of longitudinal vibration of a rod according to claim 2, characterized in that: In the case where the rod type is a constant cross-section type, the step of "calculating the micro-unit inertia force applied to the concentrated mass application point according to the equivalent mass obtained by calculation" specifically includes: Calculate the vibration acceleration of the current point ξ according to the following formula: in, is the vibration acceleration of the current point ξ; l is the overall length of the rod; is the vibration acceleration at ξ=l; The micro-unit inertial force is calculated according to the following formula: Wherein, dF is the micro-unit inertial force generated by the equivalent mass dM.

4. The method for calculating the natural frequency of longitudinal vibration of a rod according to claim 3, characterized in that: In the case where the rod type is a constant cross-section type, the step of "integrating the micro-unit inertial force to obtain the equivalent mass of the entire rod" specifically includes: The micro-unit inertial force is integrated to obtain the total inertial force applied to the concentrated mass application point, and the integral formula is: Among them, F0 is the total inertia force; The total inertial force of the concentrated mass at the point where the concentrated mass is applied is calculated using the following formula: Where, M is the concentrated mass; Will Substitute into the formula In, and according to m eq =M conversion, the final equivalent mass is: Among them, m eq is equivalent mass.

5. The method for calculating the natural frequency of longitudinal vibration of a rod according to claim 1, characterized in that: The rod type is a cross-section step-change type, and the second equivalent mass calculation mode includes: Determining the number of sections having different cross-sectional areas on the rod; The equivalent mass of the concentrated mass application point of the current micro-element on the i-th segment of the rod is calculated according to the following calculation formula: dM i =dm i =ρ·A i ·dξ i Among them, dM i is the equivalent mass of the i-th segment; dm i is the actual mass of the current micro-unit in the i-th segment; dξ i is the current micro-unit of the i-th segment; ρ is the density; A i is the cross-sectional area of ​​the i-th section; i=1, 2, 3.....n, n is the total number of sections.

6. The method for calculating the natural frequency of longitudinal vibration of a rod according to claim 5, characterized in that: In the case where the rod type is a cross-section step-variation type, the step of "calculating the micro-unit inertia force applied to the concentrated mass application point according to the equivalent mass obtained by calculation" specifically includes: The vibration acceleration of the current point ξ1 on the i=1th segment of the rod is calculated according to the following formula: in, is the vibration acceleration of the current point ξ1; l1 is the length of the first section of the rod; is the vibration acceleration of the end of the first section of the rod relative to the origin of the first section coordinates; the origin of the first section coordinates refers to the first section fixed point of the rod; The current point ξ of the i-th section on the member is calculated according to the following formula i Vibration acceleration: Wherein, i = 2, 3.....n, n is the total number of segments; is the current point ξ of the i-th segment on the member i The vibration acceleration of the current point ξ i The coordinate origin is the starting point of the i-th segment; is the vibration acceleration of the end of the i-1th segment on the rod relative to the starting point of the i-1th segment; is the current point ξ of the i-th segment on the member i Vibration acceleration relative to the starting point of the i-th segment; The micro-unit inertial force is calculated according to the following formula: Among them, dF i is the equivalent mass of the i-th section of the rod dM i The micro-unit inertial force generated.

7. The method for calculating the natural frequency of longitudinal vibration of a rod according to claim 6, characterized in that: In the case where the rod type is a cross-section step-variation type, the step of "integrating the micro-unit inertial force to obtain the equivalent mass of the entire rod" specifically includes: The micro-unit inertial force on each section of the rod is integrated to obtain the total inertial force applied at the concentrated mass application point, and the integral formula is as follows: Where F0 is the total inertia force; l2 is the length of the second section of the rod; l n is the length of the nth section of the rod; The total inertial force of the concentrated mass at the point where the concentrated mass is applied is calculated as follows: Where, M is the concentrated mass; is the vibration acceleration of the rod at ξ = l; is the vibration acceleration of the end of the nth segment on the rod relative to the starting point of the nth segment; Will Substitute into the formula In, and according to m eq =M conversion, the final equivalent mass is: Among them, m eq is equivalent mass.

8. A device for calculating the natural frequency of longitudinal vibration of a rod, characterized in that: include: A first processing unit is used to determine whether the rod is of a uniform cross-section type or a cross-section step-variation type, wherein the uniform cross-section type means that the cross-section area of ​​the entire section of the rod is equal, and the cross-section step-variation type means that the rod has at least two sections with different cross-section area sizes; A second processing unit is used to calculate the equivalent mass of the current micro-unit at the concentrated mass application point; A third processing unit is used to calculate the micro-unit inertial force applied to the concentrated mass application point according to the equivalent mass obtained by calculation; A fourth processing unit, used for integrating the inertial force of the micro-unit to obtain the equivalent mass of the entire rod; The fifth processing unit is used to calculate the equivalent stiffness coefficient of the entire rod, and calculate the natural frequency of the longitudinal vibration of the rod according to the equivalent mass and the equivalent stiffness coefficient.

9. A computer storage medium having a computer program stored thereon, characterized in that: When the computer program is executed by a processor, it is possible to implement the method for calculating the natural frequency of longitudinal vibration of a rod member according to any one of claims 1 to 7.

10. A computer device comprising a memory, a processor and a computer program stored in the memory and executable on the processor, characterized in that: When the processor executes the computer program, the method for calculating the natural frequency of longitudinal vibration of a rod member according to any one of claims 1 to 7 is implemented.

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