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There is something that I have noticed several times when writing chords for orchestral strings (violins, cellos, etc), when I write standard triad (major, minor, etc) chords the strings make an intense annoying grinding sound, since the frequencies of each note are very close together, the solution would be perhaps to rewrite the chord by placing some notes in a different octave to make some space, which doesn't always give me the result I want.

My question is what should I do to avoid this annoying sound strings make when they play chords with notes very close together?

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You have already hit on part of the solution:

the solution would be perhaps to rewrite the chord by placing some notes in a different octave to make some space, which doesn't always give me the result I want.

When spreading out the triad, it might not give you the result you want at first, but there are many ways to voice a spread triad, so you might have to experiment with several different spread voicings to find the balance that you're looking for.

The following concepts apply to voicing chords for all instruments and ensembles:

  • The lower the notes, the further spread out they should be to avoid muddiness or unpleasant sounding intervals. This is why low and mid-low instruments (such as basses and celli) are often voiced in octaves. Close thirds generally will sound best around middle C (C4) and up, but can be made to work lower than that depending on the instrument. Fifths can sound good an octave or two below that, but low fifths do tend to create a harsher sound (heavy metal guitar players often play low fifths).
  • When more than three instruments are playing a triad, some notes must necessarily be doubled, either in unison or at the octave. Doubling the root of the triad produces the cleanest sound, followed by doubling the fifth, and finally the third. If the sound of a chord played by an ensemble is muddy or harsh, reduce the number of instruments playing the third down to one, and have that instrument play the third in a higher octave. Reduce the fifths being played to one or two, and try placing it in a middle octave. If I recall correctly, the opening chord of the Star Wars theme has the entire orchestra playing a triad, and all but three instruments are playing the root, and only one instrument plays the third.
  • Closer voicings can sound clearer when played on instruments with purer tone and/or when played more quietly. Fortissimo French horns playing a close third will sound pretty aggressive no matter what part of their range is being used. Flutes and oboes on the other hand can progress in thirds very pleasantly across a range of dynamics.

When it comes to strings, a section playing notes as double stops will sound harsher than that same section playing divisi.

I strongly suggest two resources for further study:

  • Principles of Orchestration by Nikolai Rimsky-Korsakov (link to free online Gutenberg edition). The canonical, invaluable resource for orchestration, including voicing chords across ensembles.
  • https://imslp.org/wiki/Main_Page - The Petrucci Music Library. Studying how the great composers arranged their strings and trying their methods out for yourself might be the best way to learn to arrange strings. Baroque, Classical, and most Romantic compositions are in the public domain, and if you search for pieces you have listened to repeatedly, you'll be able to connect what's written in the scores with what you've heard in your ears, and find how to make those sounds yourself. Pachelbel's Canon (in D) might be a good place to start for string arrangements.

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