How to calculate displacement with variable force
Publish: 2021-05-13 12:11:34
1. Karnofsky's theorem (generally refers to the second Karnofsky's theorem)
the problem of beam deformation or displacement is very simple to understand with karnoky's theorem. However, when I studied mechanics of materials, I turned over several books and didn't introce them in detail. Maybe it's not right. I won't introce them in detail here. I found a tutorial website for you, You can also find related tutorials on the Internet by yourself, in which you need to use some knowledge of advanced mathematics.
http://wlxt.whut.e.cn/cllx/cllx_ web/pages.asp?c=11&s=4
the problem of beam deformation or displacement is very simple to understand with karnoky's theorem. However, when I studied mechanics of materials, I turned over several books and didn't introce them in detail. Maybe it's not right. I won't introce them in detail here. I found a tutorial website for you, You can also find related tutorials on the Internet by yourself, in which you need to use some knowledge of advanced mathematics.
http://wlxt.whut.e.cn/cllx/cllx_ web/pages.asp?c=11&s=4
2. 1. Junior high school physics only needs to master the balance force
2, senior high school needs to master the movement under the action of constant force
3, including the calculation of uniform variable speed linear motion and uniform circular motion
4, the calculation of variable force needs to give the change law of variable force, which can be learned by University
2, senior high school needs to master the movement under the action of constant force
3, including the calculation of uniform variable speed linear motion and uniform circular motion
4, the calculation of variable force needs to give the change law of variable force, which can be learned by University
3. Well, let's take a simple example
suppose that there is a relationship between velocity and time: v = T ^ 2 + 1, here we get the acceleration as a = 2T, which is obviously a variable acceleration motion
if we want to find the displacement here, we can use the integral s = ∫ T ^ 2 + 1 DT to get the expression of displacement
in this way, the velocity and acceleration can be obtained by constant derivation when the displacement is given
the velocity and displacement can be obtained by constant integration when the acceleration is given
suppose that there is a relationship between velocity and time: v = T ^ 2 + 1, here we get the acceleration as a = 2T, which is obviously a variable acceleration motion
if we want to find the displacement here, we can use the integral s = ∫ T ^ 2 + 1 DT to get the expression of displacement
in this way, the velocity and acceleration can be obtained by constant derivation when the displacement is given
the velocity and displacement can be obtained by constant integration when the acceleration is given
4. This is no good, because the average value of the variable force is the average of the time, not the average of the displacement,
you can draw the F-S image and analyze it to get the conclusion that the area under s and F in the image is work< br />O(∩_ ∩)O~
you can draw the F-S image and analyze it to get the conclusion that the area under s and F in the image is work< br />O(∩_ ∩)O~
5. This is no good, because the average value of the variable force is the average of the time, not the average of the displacement,
you can draw the F-S image and analyze it to get the conclusion that the area under s and F in the image is work.
O (∩)_ ∩)O~
you can draw the F-S image and analyze it to get the conclusion that the area under s and F in the image is work.
O (∩)_ ∩)O~
6. Converting variable force into constant force is equivalent method: the work done by the variable force can be converted into the work done by the constant force which is the same as the work done by the variable force by the equivalent method. At this time, the definition of work w = the work done by the variable force can be used to calculate the work of the constant force, so that the work of the variable force can be known. The key of equivalent conversion is to analyze which constant force does the same work as the variable force< In addition, there are six methods:
one: the average method
when the direction of a force is constant, but its size changes with the displacement evenly, the average value of the initial value F1 and the final state value F2 of the force can be used to calculate the work done by the variable force< Second, infinitesimal method can be used to calculate variable force and work. The whole process can be divided into many very short segments by infinitesimal accumulation method. In each very short segment, the force can be regarded as a constant force, then the work of each segment can be calculated by the formula of work, and then the generation sum of the work of each segment can be calculated. From this, we can calculate the work of friction and resistance by multiplying the force by the distance. The key of using the method of micro element accumulation is how to choose the appropriate micro element and how to deal with the micro element in physics and mathematics. The method of micro element accumulation has higher requirements for mathematical knowledge< If the images of variable force F and displacement s can be drawn, the area between F-S image and s axis represents the work done by variable force F in the process. The key of using the area of F-S image to calculate the work of variable force is to first express the functional relationship between variable force F and displacement s, and then draw the F-S image< In some physical problems, if we can skillfully transform the reference system, we can also transform the work done by variable force into work done by constant force, thus greatly simplifying the problem-solving process< The content of the functional principle is: the algebraic sum of the work done by the external force and internal force (excluding gravity and elastic force) of the system is equal to the increment of the mechanical energy of the system, if only one of these forces does work, and the work done by other forces and the variation of the mechanical energy of the system are relatively easy to solve, The work done by variable force can be solved by functional principle< The content of kinetic energy theorem is: the work done by external force to the object is equal to the increment of the kinetic energy of the object. Its expression is: W outside= Δ EK, w can be understood as the algebraic sum of work done by all external forces. If only one of the forces we study is a variable force, and the rest are constant forces, and the work done by these constant forces is relatively easy to calculate, and the increment of kinetic energy of the research object itself is relatively easy to calculate, the work done by this variable force can be obtained by using the kinetic energy theorem.
one: the average method
when the direction of a force is constant, but its size changes with the displacement evenly, the average value of the initial value F1 and the final state value F2 of the force can be used to calculate the work done by the variable force< Second, infinitesimal method can be used to calculate variable force and work. The whole process can be divided into many very short segments by infinitesimal accumulation method. In each very short segment, the force can be regarded as a constant force, then the work of each segment can be calculated by the formula of work, and then the generation sum of the work of each segment can be calculated. From this, we can calculate the work of friction and resistance by multiplying the force by the distance. The key of using the method of micro element accumulation is how to choose the appropriate micro element and how to deal with the micro element in physics and mathematics. The method of micro element accumulation has higher requirements for mathematical knowledge< If the images of variable force F and displacement s can be drawn, the area between F-S image and s axis represents the work done by variable force F in the process. The key of using the area of F-S image to calculate the work of variable force is to first express the functional relationship between variable force F and displacement s, and then draw the F-S image< In some physical problems, if we can skillfully transform the reference system, we can also transform the work done by variable force into work done by constant force, thus greatly simplifying the problem-solving process< The content of the functional principle is: the algebraic sum of the work done by the external force and internal force (excluding gravity and elastic force) of the system is equal to the increment of the mechanical energy of the system, if only one of these forces does work, and the work done by other forces and the variation of the mechanical energy of the system are relatively easy to solve, The work done by variable force can be solved by functional principle< The content of kinetic energy theorem is: the work done by external force to the object is equal to the increment of the kinetic energy of the object. Its expression is: W outside= Δ EK, w can be understood as the algebraic sum of work done by all external forces. If only one of the forces we study is a variable force, and the rest are constant forces, and the work done by these constant forces is relatively easy to calculate, and the increment of kinetic energy of the research object itself is relatively easy to calculate, the work done by this variable force can be obtained by using the kinetic energy theorem.
7.
The simplest method is the application of the principle of virtual work in structural mechanics, that is, the principle of virtual force. A unit force is fictitious at the required displacement, and the displacement is obtained by the formula that the external virtual work equals the internal virtual work. There is also a method of displacement in mechanics of materials
Small deformation, elastic body assumption, so the variables meet the superposition principle, that is linear equation. The displacement is taken as the independent variable and the constitutive relation (elastic range) is added. Finally, the linear equations are unified and solved by Gauss elimination method 
extended data:
the research methods of structural mechanics mainly include the use analysis, experimental research, theoretical analysis and calculation of engineering structures. In structural design and research, these three aspects are often alternating and complementary
usage analysis in the process of using the structure, it is an easy and reliable research method to analyze, compare and summarize the situation in the structure. Usage analysis plays an important role in the evaluation and improvement of structures. The newly designed structure also needs to be used to test its performance
experimental research can provide an important basis for the identification of structure, which is also the main means to test and develop the theory and calculation method of structural mechanics
8. Centripetal force F = MV & sup2/ R
from three, positive pressure n = f
friction F= μ N = μ F
F does not do work, only friction does work, the direction of friction is always opposite to the direction of motion, and the length of friction action path is s= π R
V = DS / DT, DW = - f DS
the rest is calculated by yourself.
from three, positive pressure n = f
friction F= μ N = μ F
F does not do work, only friction does work, the direction of friction is always opposite to the direction of motion, and the length of friction action path is s= π R
V = DS / DT, DW = - f DS
the rest is calculated by yourself.
9. In the calculation of displacement in structural mechanics, you should first understand the principle of virtual work of rigid body in theoretical mechanics, and that the external virtual work of deformed body structure is equal to the internal virtual work. In order to find the displacement of a certain point, it is practical. First, assume that the work done by unit force 1 on the actual displacement is called virtual work. Therefore, there is external virtual work = internal virtual work, from which the structural displacement can be calculated. The equation is 1 * D + F reaction force * D displacement = internal virtual work. When moving in the past, there is: 1 * d = internal virtual work - f reaction force * D displacement, so the front of D displacement is negative sign.
10. No, the variable force may be a function of displacement or time
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