Consider the three degree-of-freedom system shown in Fig.4; it consists of three equal masses m and a foundation connected in series by three equal springs k. The absolute displacements of the masses are x1, x2, and x3. The stiffness coefficients are thus K11 = %3D 4k, K22 = 6k, K33 = 3k, K12 = K21 = -k, K23 = K32 = -k, and K13 = K31 = 0. Determine the frequencies of the system. min Ihing Tming Fig.4

Consider the three degree-of-freedom system shown in Fig.4; it consists of three equal masses m and a foundation connected in series by three equal springs k. The absolute displacements of the masses are x1, x2, and x3. The stiffness coefficients are thus K11 = %3D 4k, K22 = 6k, K33 = 3k, K12 = K21 = -k, K23 = K32 = -k, and K13 = K31 = 0. Determine the frequencies of the system. min Ihing Tming Fig.4

International Edition---engineering Mechanics: Statics, 4th Edition

4th Edition

ISBN:9781305501607

Author:Andrew Pytel And Jaan Kiusalaas

Publisher:Andrew Pytel And Jaan Kiusalaas

Chapter10: Virtual Work And Potential Energy

Section: Chapter Questions

Problem 10.62P: The bar ABC is supported by three identical, ideal springs. Note that the springs are always...

See similar textbooks

Similar questions

A helical spring is provided with a rigid plate at each end. A bolt passes through the spring and the end plates. By turning the nut, the spring is compressed until the coils touch. The height of the unloaded spring is 600 mm, its mean coil diameter is 100 mm and the diameter of the spring wire is 28 mm. The spring has 18 coils. The diameter of the bolt is 25 mm and the plates are each 25 mm thick. Calculate the elongation of the bolt when the spring is fully compressed as well as the stress in the spring wire (take E = 200 GPa and G = 80 GPa).
The inner spring of a compound helical spring is arranged within and concentric with the outer one and is shorter by 9 mm. The outer spring has 10 coils with a mean diameter of 24 mm and a wire diameter of 3 mm. (a) Determine the stiffness of the inner spring when an axial load of 162 N causes the outer spring to compress by 16 mm. If the radial clearance between the springs is 1.5 mm and the inner spring has 8 coils, find its wire diameter. (c) Disregarding the effect of curvature, find the maximum shear stress in each of the spring. Given G = 78 GPa.
Calculate the maximum force P that can be applied in a phosphor bronze spring having mean diameter of 150 mm and consisting of 24 turns of 10-mm diameter wire when the spring is stretched 180mm. Use G = 42 GPa.
The outside diameter of the coils of a safety valve spring is 120 mm while its wire diameter is 15 mm. This spring, having 10 active coils has the ends in plain ground, and has a free length of 200 mm. 1. Determine the length (in mm) at which this spring must be initially compressed to hold a pressure of 1400 kPa applied on a 32-mm diameter valve seat. Use a modulus of rigidity of 80 GPa. 2. calculate the spring’s maximum stress induced if it is compressed to its solid length
9. A compressive force of 15-N is applied to a flexible poly(vinyl chloride) (CAS# 9002-86-2) wire that is 5-m long and has a diameter of 3.6-mm. If the wire contracts by 0.5-mm, calculate the compressive modulus
A cable whose length is 16m and sag of 2m supports a weight of 1500 N/m. What is the minimum tension in the cable?
The bar ABC is supported by three identical, ideal springs. Note that the springs are always vertical because the collars to which they are attached are free to slide on the horizontal rail. Find the angle at equilibrium if W = kL. Neglect the weight of the bar.
For the system of springs shown below derive the formula for the overallstiffness cΣ and calculate the overall displacement s if F=200 N, c1=2300 N/m, andc2=2100 N/m.
A closely coiled helical spring is to carry a load of 500N. Its mean coil diameter is to be 10 times that of the wire diameter. Calculate these diameters if the maximum shear stress in the material of the string is to be 8OMN/mA2.
A vehicle of mass 21 tonnes runs into a buffer stop having two buffer springs connected in series each of 1300 kN/cm and 2100 kN/cm stiffness respectively. Find the maximum compression of the springs, if the vehicle is travelling at 115 km/hr. Also calculate the load acting on the spring. The maximum compression of the spring in mm is The load acting on the spring in kN is
The outside diameter of the coils of a safety valve spring is 120 mm while its wire diameter is 15 mm. This spring, having 10 active coils has the ends in plain ground, and has a free length of 200 mm. A.Determine the length (in mm) at which this spring must be initially compressed to hold a pressure of 1400 kPa applied on a 32-mm diameter valve seat. Use a modulus of rigidity of 80 GPa. B. Calculate the spring’s maximum stress induced if it is compressed to its solid length.
Four axially loaded members are shown below. All members have the same value for E (Young’s modulus) and for ν (Poisson’s ratio).