(Solved): 1.1 A device in the shape of a rough cube measuring 0.750.750.75 is bolted t ...

$$1.1$$ A device in the shape of a rough cube measuring $$0.75^{??}\times 0.75^{??}\times 0.75^{??}$$ is bolted to a mounting plate as shown below. Its weight is $$0.5\mathrm{lbs}$$, and its natural frequency has been determined to be $$500\mathrm{Hz}$$. It is connected to a steel adaptor block measuring $$1.5^{??}\times 1.5^{??}\times 0.5^{??}$$ thick. Four bolts connect the adaptor block to the mounting plate: \#6-32 UNC $$\times 1.0$$ " long, Grade 8 . The mounting plate measures $$1.5^{??}$$ wide $$\times 4.0^{??}$$ long $$\times 0.250^{??}$$ thick and is made from 6061-T651 aluminum plate. Estimate (within 10\%) the natural frequencies of the assembly listed below, using the following assumptions: (i) the device is mounted rigidly to the adaptor block, (ii) the holes in the adaptor block and mounting plate may be neglected for mass calculations, and (iii) the effective mass of the simply-supported mounting plate is $$49\%$$ of its total mass. (a) Compute the natural frequency of the adaptor block-bolt SDoF system (b) Compute the natural frequency of the loaded mounting plate system (c) Compute the total lowest natural frequency of the entire system Problem 1.1. Front view of the device/adaptor/plate system Problem $$1.1$$ Top down view of the device/adaptor/plate system system